The Twins Paradox: A Controversial Truth or a Perplexing Paradox?

[russ_watters]

...Contraction is not a real thing - it is calculated consequent to time dilation...

This simply isn't true. It is the calculated consequence of time dilation, and that's what explains why it is real. By saying that its not real, you're implying a Universal Reference frame centered around the stationary (Stationary) observer. In actuality, this observer's distance measurement is no more valid than the "moving" observer's distance measurement. In fact, if we use the time in the "moving" frame and the distance in the "stationary" frame, as you suggest, we'll get nonsensical results from our calculations: things like greater than C speed.

 

[JesseM]

I am attempting to pin down things using only proper measurements. We will take the case of the traveler - jesse - you start off immediately by making an improper measurement - you first calculate the contracted distance based upon how the traveler views the 5ly in the Earth frame and from there you figure the time lapse in the traveling twins frame - in actuality - the traveling twin can only make one proper measurement - he has only one clock and he can only read that in his own frame

If he only has one clock, how should he assign time-coordinates to distant events? Einstein based the notion of a relativistic reference frame on the idea that each observer uses a large network of clocks which are all at rest relative to himself, and which have been synchronized using the assumption that light travels at the same speed in all directions relative to himself. Of course, he can also assign time-coordinates by noting the distance something was according to his own rulers and calculating (time he observed light from distant event, according to his own clock) - (distance of event from him, according to his own ruler)/(speed of light)...this will give exactly the same result as if he assigned coordinates using a network of synchronized clocks. For example, as I mentioned before, at t=6.75 years according to the traveling twin's clock he will see the earth-clock as reading t=2.25 years, and he will see the Earth next to the 3-light-year mark on a ruler at rest relative to himself, so if he calculates (6.75) - (3)/(1) he finds that this event should be assigned a time-coordinate of 3.75 years in his own system, just like if he had used a synchronized clock 3 light years away from him.

If you don't agree with either of these methods, please tell me, what physical procedure should the traveling twin use to assign a time-coordinate to the event of the earth-clock reading 2.25 years? Likewise, what physical procedure should the earth-twin use to assign a time-coordinate to the event of the traveling twin's clock reading 3.75 years?

based upon his reading at the start and arrival (the time accumulated from when the two twins were together and the time when the traveler reaches the distant planet that is 5ly distant in the Earth frame).

Again, what physical procedure should the earth-twin use to assign a time-coordinate to the even of the traveling twin reaching the planet? Obviously he can't just use the time he sees the traveling twin reach the planet, since light doesn't travel instantaneously. So it seems he has two options--either look at the local reading on a clock sitting on the planet which was synchronized with the Earth's clock using light signals, or do the calculation (time he observed light from distant event, according to his own clock) - (distance of event from him, according to his own ruler)/(speed of light). Either way, the point is that if the traveling twin uses precisely the same procedure to assign a time-coordinate to the event of the earth-clock reading 2.25 years, he will find that it happened when his own clock read 3.75 years, i.e. the moment he was passing the planet. Are you suggesting that the traveling twin should not use the same physical procedure as the earth-twin to assign time-coordinates to distant events? If not, why not? Even if you believe there is an absolute truth about simultaneity, if you have no physical procedure to determine whose definition of simultaneity is the correct one, then you have no reason to prefer the earth-twin's definition over the traveling twin's definition (after all, even if you believe in ether, it is possible that the Earth has a velocity of 0.8c relative to the ether, and that the traveling twin is the one who is at rest relative to the ether).

You like all relativist want to slide back and forth between the two frames to save reciprocity...but Contraction is not a real thing - it is calculated consequent to time dilation - the proper reading on the travelers clock gives a permanent number that will be there after the motion stops - you can use that to calculate what the traveler would mistakently believe to be the distance to the planet

Uh, why in the hell do you think the earth-twin's distance reading is correct while the traveling twin's distance reading is mistaken? Even if there is an ether frame and only measurements made in the ether frame are "really" correct, if there is no experiment you can do to determine which frame this is, then you have absolutely no reason to believe the Earth is any more likely than the traveling twin to be at rest in the ether frame.

but that is a non proper measurement - one calculated from the travelers own clock that he reads at the end of the trip time - take a look at ResnicK - "Introduction of SR"

What page? I am quite sure that Resnick does not say one frame's measurements are objectively true while the others are mistaken.

Keep it simple - the traveler reads his clock when the two twins are together - they can be flying past each other or in the same reference system. Whatever - there will be some start time on his watch - and upon arrival the traveler will read a different time on this same watch. This is his proper time lapse in the only frame he can make a proper reading - in the Earth frame there can be two clocks - one at the Earth and one on the planet

Uh, why can the Earth frame have two clocks but the traveling twin can have only one? That's just silly and arbitrary. Especially since I was secretly told by Zeus that it is actually the traveling twin who is at rest relative to the ether, while the Earth is moving at 0.8c relative to the ether, so if people in the earth-frame try to synchronize their clocks by assuming light travels at the same speed in all directions relative to them, their clocks will be objectively out-of-sync.

or if you don't like that, the traveler can send a radio signal back to Earth informing the stay at home twin what his clock reads as he passes the planet - in which case there is only one clock in the Earth frame and one watch in the travelers frame.

Can the Earth also send a radio signal to the traveling twin when his clock reads 2.25 years, so if the twin assumes the signal traveled at velocity c relative to himself, he will conclude that this signal was sent at the same moment he was passing the planet?

Morover, we can substitute a high speed muon for the traveler and specify that it travels so fast it just reaches the planet as it decays - we know the decay time of the muon to be on average about 2 usec in its own frame. ..the proper time in the traveling frame is therefore 2usec - in the Earth frame the time is much greater (about 5 years).

How exactly does the Earth assign a time-coordinate to the distant event of the muon decaying? Can an observer traveling alongside the muon use the same method to figure out what the Earth clock read at the same time-coordinate (in his frame) that the muon decayed?

The invariance of the interval guarantees that the clock in the muon frame runs at a different rate than the clock in the Earth frame

Yes, from the point of view of an observer moving alongside the muon, the clock in the earth-frame runs slower.

We are therefore forced to conclude either - that the two twins age at different rates even though neither has turned around, or they have somehow both aged the same during the muons flight to a distant planet. Which?

Yes, the two twins age at different rates. In the muon's frame, the earth-twin ages slower, and in the Earth's frame, the muon-twin ages slower. But since Zeus let me in on the secret that it's actually the muon that's at rest relative to the ether, I know that it's really the earth-twin that aged less. But since there's no experiment you can do to actually determine the rest frame of the ether, and since you aren't tight with the Z-man like me, I'm afraid you'll just have to take my word for it.

 

[yogi]

Zeus hey - I knew he would mess things up.

I will answer your many misconceptions about what I have said by pointing out there is no need to do any simultanity procedures - there are two clocks in the same frame -one is owned by J on Earth and one is owned by Q his brother - there is no need in doing the experiment to add any more clocks - there is a spatial interval that is 5ly as measured in the Earth frame to a point P. We want to know what Q's clock reads if he travels to P at almost c velocity. At no time have I mentioned the ether in this discussion nor a preferred frame. So stop rambling on and on about things I never said. And I don't need a tutorial as to what relativity says - it is relativity that is being examined in the light of different thought experiments ... specifically to see why clocks behave the way they do.

Back to the subject and some further comments

Q's clock accompanies him - J's clock stays with him. Now there is an interesting issue raised by Russ - and it is very significant - is there a difference if Q and J are at rest and Q takes off as opposed to the situation where Q and J merely meet each other passing by? Let's take the case where Q and J are at rest and J takes off - so there is an acceleration at the beginning - this does not really tell us much about what is happening to Q's clock because all experiments have shown that acceleration per se does not add or subtract time to a clock or affect its rate - but this fact does tell us that it is Q that is moving relative to the proper spatial distance (5ly) that separates J and P. In other words the initial acceleration is significant for the purpose of telling all parties that Q is the one that has changed his velocity and that he is moving toward P rather than the earth-Planet system moving in the opposite direction. Now from the standpoint of Q, once he attains his crusing velocity, with no other physical object for reference, he would not be able to tell the difference as to who is moving. Correspondingly If Q remained initally at rest and the earth-Planet system were accelerated, from the standpoint of Q's at rest frame he can rightly conclude that P is doing all the moving, and it is all in relation to Q's reference frame. Q would conclude that P has taken off in his direction and he will measure the time it takes for P to arrive as 5ly (the distance between P and Q being initially 5LY years),

The two elements of the interval in the frame which did not undergo acceleration will be a time component (ct)^2 minus an length component (5ly)^2 and the interval in the frame which got accelerated will be a temporal component only (since the clock is carried along with traveler - there is no spatial component involved in the travelers interval). So - depending upon which frame gets initally accelerated, at the instant that P is adjacent to Q, one clock will read slightly more than 5 years and the other will real a few usec.

Now - take the case of both frames having equal inertial mass, and they are launched by a common spring which propels Q toward P and P toward Q. P and Q will meet - each can consider that they traveled have way with reference to the proper frame of the other - because only in this case is there true symmetry - and in this case only will the clocks of P and J read the same when P and Q meet as determined by a radio signal sent from either P or Q at the instant of their meeting.

How do we know this - not because of Zeus - but because of the difference in the clock rates of high speed particles compared to the time accumulated by a clock in the lab. The accelerated pion moves relative to the proper distance measured in the Earth frame and not vice versa - unless you can hitch a ride on a high speed particle and do the experiment in reverse - This does not mean the Earth is a preferred frame, but as between the particle and the earth, it is the particle that has been accelerated, and that accounts for the difference in the measured value of lifetimes

 

[JesseM]

I will answer your many misconceptions about what I have said by pointing out there is no need to do any simultanity procedures - there are two clocks in the same frame -one is owned by J on Earth and one is owned by Q his brother - there is no need in doing the experiment to add any more clocks - there is a spatial interval that is 5ly as measured in the Earth frame to a point P. We want to know what Q's clock reads if he travels to P at almost c velocity.

You do need to do a "simultaneity procedure" if you want to compare J's reading on Earth with Q's reading once he reaches point P. All frames will agree on what Q reads at the moment he reaches P (this is just Q's proper time), but since different frames define simultaneity differently, they will disagree about what J's clock reads "at the same moment".

At no time have I mentioned the ether in this discussion nor a preferred frame.

Yes, but you acted as if one frame's definition of simultaneity should be preferred over another's. Without choosing a definition of simultaneity, there is no answer to the question of what J's clock read "at the same time" that Q's clock read when he reached P, so there's no way to decide whose was running faster or slower.

Q's clock accompanies him - J's clock stays with him. Now there is an interesting issue raised by Russ - and it is very significant - is there a difference if Q and J are at rest and Q takes off as opposed to the situation where Q and J merely meet each other passing by. Let's take the case where Q and J are at rest and J takes off - so there is an acceleration at the beginning - this does not really tell us much about what is happening to Q's clock because all experiments have shown that acceleration per se does not time add to a clock or affect its rate - but this fact does tell us that it is Q that is moving relative to the proper spatial distance (5ly) that separates J and P. In other words the initial acceleration is significant for the purpose of telling all parties that Q is the one that has changed his velocity and that he is moving toward P rather than the earth-Planet system moving in the opposite direction.

No, again you seem to be assuming some notion of absolute velocity. But if you believe in absolute velocity, it is quite possible to believe that the absolute velocity of the Earth was initially 0.8c, and that when Q changed velocity, his absolute velocity dropped to zero, so it is the Earth that is moving while he is at rest. Of course, if you don't believe in absolute velocity, the phrase "he is moving toward P rather than the earth-Planet system moving in the opposite direction" is meaningless (unless you forgot to add the words "in the earth-Planet's frame", but in that case the issue of who accelerated and who didn't would be irrelevant to the question of who is moving and who isn't in this frame).

Now from the standpoint of Q, once he attains his crusing velocity, with no other reference, he would not be able to tell the difference. Correspondingly If Q remained initally at rest and the earth-Planet system were accelerated, from the standpoint of Q's at rest frame he can rightly conclude that P is doing all the moving, and it is all in relation to Q's reference frame.

From the standpoint of Q's rest frame, it is completely irrelevant who accelerated and who didn't, either way Q is at rest in this frame and P is moving.

Q would conclude that P has taken off in his direction and he will measure the time it takes for P to arrive as 5ly (the distance between P and Q being initially 5 years

No, in Q's rest frame the distance is 3 light years.

The two elements of the interval in the frame which did not undergo acceleration

Again, I don't see how acceleration is relevant.

Now - take the case of both frames having equal inertial mass, and they are launched by a common spring which propels Q toward P and P toward Q. P and Q will meet - each can consider that they traveled have way with reference to the proper frame of the other

"with reference to the proper frame of the other"? Are you implying that each one's "proper frame" is the frame in which he was initially at rest? That's a nonstandard definition, and it doesn't really make any sense, since both P and Q probably had to be accelerated earlier when they were put in place to be launched by the spring--do you have to consider an object's entire history back to its creation to determine its "proper frame"?

because only in this case is there true symmetry - and in this case only will the clocks of P and J read the same when P and Q meet as determined by a radio signal sent from either P or Q at the instant of their meeting.

What if, two hours before P and Q were launched, P was accelerated but Q wasn't? Would this break the symmetry somehow? Or if you're allowed to pick an arbitrary starting time for each object, with each one's "proper frame" being the object's rest frame at this starting time, then what if we pick a starting time after both were launched?

How do we know this - not because of Zeus - but because of the difference in the clock rates of high speed particles compared to the time accumulated by a clock in the lab. The accelerated pion moves relative to the proper distance measured in the Earth frame and not vice versa - unless you can hitch a ride on a high speed particle and do the experiment in reverse - This does not mean the Earth is a preferred frame, but as between the particle and the earth, it is the particle that has been accelerated, and that accounts for the difference in the measured value of lifetimes

You need to explain the details of your "the one who didn't accelerate is the one whose frame we must use" theory. For example, what about the fact that the Earth is constantly accelerating in its orbit, does that make a difference? What if two objects have been traveling at constant velocity for a million years, but the first one accelerated 1,000,001 years ago while the second acccelerated 1,000,002 years ago, does that somehow obligate us to look at things from the second object's frame?

 

[yogi]

The Earth may or may not be a preferred frame - it is certainly not unless there is something about the G field that renders it special (LR theory). But in any event, when the non rotating Earth is taken as a reference frame for measurements, we know from expereince that clocks in flight around the Earth will run slower than a stationary clock at the same height at the North Pole. There is no special sync required to check the results - we bring the clocks together at the start and set them both to zero - then fly one around the Earth - there are accelerations in the take off and there are accelerations due to the curved path the flying clock experiences - we can predict almost exactly what the difference in the clock rate will be based entirely upon the relative velocity using the LT. The clock which is moving in the space defined by its circumferential path will run slower and the two clocks can be compared on each passby. It is again a simple application of the interval - the proper space interval is the circumference of the Earth (a proper distance as measured by the clock at the north pole), the proper time interval for the fixed clock is the time logged for each passby and the proper time for the flying clock is the time logged by that clock between successive passbys. There is no proper space interval for the flying clock since the clock moves with the observer. If you speed up the aircraft until it has orbit velocity, the flying clock will no longer experience acceleration (at least not a G field).

The experiment I outlined previously is but a linear version of the same thing - instead of having the clock return by flying a circumference, the initially accelerated clock (the one that corresponds to the flying clock) simply sends a radio signal back to the stationary clock.

As to your Q re whether one should consider a past history of how two objects that meet in space should decide which one had previously accelerated - I would say this. SR ignors all the rest of the universe - so two spaceships meeting far from any other reference can properly use Einsteins original derivation so that each can say, when I observe the other guys clock it appears to run slow. The operative word here is "observe" Obviously both clocks cannot be running slower than the other. SR would make no distinction between whether the Earth is moving in every direction at once so as to sweep up high speed muons - or alternatively that the muons are created by collisions with particles that are approaching the Earth in every direction.
Which is the more likely proposition. Einstein derived the LT for a situation which was observational - a subjective interpretation of lengths and times in another reference frame - then, undaunted by the fact that there was never even the slightest attempt to justify their applicability to real time differences (different rates between two clocks), he proceeded to due just that. I have read his 1905 manuscript over many times seaching for something I must have missed - but ...
Now Einstien must be given great credit for his bold rejection of a universal time. He was also very intuitive - he realized that actual time difference occurs when a clock is carried on a path that returns to the starting point - long before we knew of muon and pion decays - or had hi speed aircraft to test the hypothesis. Certainly, by the time he published his 1912 manuscript, he had fully rejected the notion that acceleration had anything to do with the clock paradox. But he still didn't explain it.

So in conclusion, while both observers are on an equal footing as far as making measurments in the other frame as to appearances, actual changes in clock rates can only be brought about by some physical cause. All the observations of the other guys clock and all of his observations about your clock can't change a thing. To my way of the thinking, H&K experiments, muon decay, and GPS provide compelling evidence that clocks in motion relative to one another will accumulate different times whether or not they are ever returned to the same point for comparison. You get answers that conform with the experiments if you consider the Earth as fixed and the high speed clock moving between two points that define a proper distance in the Earth frame. If you consider the muon frame as fixed, it will last 2 usec - so in the muon frame, the Earth could only move 600 meters between the beginning and end of the experiment. And if that is the case - how much time has passed on the Earth clock as calculated in the muon frame during the 2 usec? If you are content with these appearances and believe they should be given the designation of reality, so be it. I think the flaw in SR is the failure to take into account the inital conditions - who accelerated to bring about the relative velocity - not who turned around - because whatever time is lost going out will simply be doubled when added to the time lost on the inbound journey.

Unfortunately I must leave this interesting exchange as i will be away from my computer for a few days.

Regards

Yogi

 

[misogynisticfeminist]

I've got a question about the twin paradox myself.

What if I establish the frame S', anchored to the spaceship as the rest frame, then frame S, anchored to the Earth is moving away from me at a certain speed. According to my reference frame, the clocks in Frame S slow down, then why is it that I'm the younger one after the journey?

 

[Hurkyl]

I've got a question about the twin paradox myself.

What if I establish the frame S', anchored to the spaceship as the rest frame, then frame S, anchored to the Earth is moving away from me at a certain speed. According to my reference frame, the clocks in Frame S slow down, then why is it that I'm the younger one after the journey?

I assume the journey you mean takes you back to Earth? What you've stated is precisely the classic twin paradox. The mistake is that you assume S' is an inertial reference frame. In particular, clocks on Earth will be running very fast according to S' while you're turning around. (Notice I didn't say clocks in S: position is an important factor for this effect)

 

[misogynisticfeminist]

I assume the journey you mean takes you back to Earth? What you've stated is precisely the classic twin paradox. The mistake is that you assume S' is an inertial reference frame. In particular, clocks on Earth will be running very fast according to S' while you're turning around. (Notice I didn't say clocks in S: position is an important factor for this effect)

I'm actually new to SR, so I have to clarify lots of stuff. So what happens if S' is not an I.R.F, i thought that non I.R.Fs is only talked about in GR about the equivalence principle, what does it mean in SR? Also, why would the clocks in S be running very fast when I am turning around??

 

[Hurkyl]

i thought that non I.R.Fs is only talked about in GR about the equivalence principle, what does it mean in SR?

That's a common misconception. One of the basic principles of SR is that the laws of physics are the same in any inertial reference frame. Now, that doesn't mean that SR cannot handle noninertial reference frames, just that the laws of physics are different.

(One thing that makes GR special is that the laws of physics are the same in all reference frames)

A good example of the difference comes directly from classical mechanics: Coriolis and centrifugal forces.


Let's think about a spatial example for a moment. You get on a merry-go round and someone starts it spinning clockwise. Now, let's consider your noninertial rest frame. You observe things far in front of you moving rapidly to the left, and things far behind you moving rapidly to the right.

Accelerations are analogous to rotations. Clocks far in front of you (assuming you're facing the way you're accelerating) start ticking really fast, while clocks far behind you are running backwards, really fast.



If you aren't drawing space-time diagrams to get a geometrical picture, then another way of seeing this fact is through the Lorentz transforms. Accelerating a reference frame is equivalent to smoothly Lorentz transforming it. When you transform, clocks in the direction of the boost jump forward, and clocks in the other direction jump backwards.

 

[JesseM]

The Earth may or may not be a preferred frame - it is certainly not unless there is something about the G field that renders it special (LR theory). But in any event, when the non rotating Earth is taken as a reference frame for measurements, we know from expereince that clocks in flight around the Earth will run slower than a stationary clock at the same height at the North Pole. There is no special sync required to check the results - we bring the clocks together at the start and set them both to zero - then fly one around the Earth - there are accelerations in the take off and there are accelerations due to the curved path the flying clock experiences - we can predict almost exactly what the difference in the clock rate will be based entirely upon the relative velocity using the LT. The clock which is moving in the space defined by its circumferential path will run slower and the two clocks can be compared on each passby.

Yes, and both an observer orbiting with the clock and the clock on the Earth would agree that the orbiting clock is running slower, if they use the method of checking the time they received a radio signal and subtracting (distance from origin of signal)/(speed of light) from that time.

If you speed up the aircraft until it has orbit velocity, the flying clock will no longer experience acceleration (at least not a G field).

"acceleration" means either changing speed or changing direction, so an orbiting clock is certainly accelerating even if its speed is constant. And it will experience some tiny g-force due to this acceleration (the 'centrifugal force').

The experiment I outlined previously is but a linear version of the same thing - instead of having the clock return by flying a circumference, the initially accelerated clock (the one that corresponds to the flying clock) simply sends a radio signal back to the stationary clock.

No, the difference is that in the experiment you outlined, if each observer uses the method of checking the time they received a radio signal and subtracting (distance from origin of signal)/(speed of light) from that time, they will both conclude the other is running slow. So there is really no way to break the symmetry here and decide whose clock is "really" running slower.

Also, what do you mean by "stationary clock"? I thought you were not arguing for a preferred reference frame--don't make me bring Zeus into this again!

As to your Q re whether one should consider a past history of how two objects that meet in space should decide which one had previously accelerated - I would say this. SR ignors all the rest of the universe - so two spaceships meeting far from any other reference can properly use Einsteins original derivation so that each can say, when I observe the other guys clock it appears to run slow. The operative word here is "observe" Obviously both clocks cannot be running slower than the other.

No, that isn't obvious at all. If you lived in the 19th century, would you also have disagreed with "Galilean relativity" because different reference frames might disagree about which of two objects has a greater velocity, and "obviously both objects cannot be moving faster than the other"? Would you also say that if we have two cartesian coordinate systems, and in one system point A has a greater x-coordinate than point B while in the other B has a greater x-coordinate than A, there must be an objective truth about the "correct" place to put the origin because "obviously both A and B cannot have a greater x-coordinate than the other"? I don't see any problem with saying that the question of which clock runs faster is analogous to the question of which of two objects has a greater velocity or the question of which of two points in space has a greater x-coordinate, in that none of these questions need have any "objective" answer and can instead depend on an arbitrary choice of which coordinate system you want to use.

SR would make no distinction between whether the Earth is moving in every direction at once so as to sweep up high speed muons

I don't understand what you mean by this--there is no inertial reference frame where the Earth is "moving in every direction at once", each frame will say the Earth is moving in a single direction at any given time.

Which is the more likely proposition. Einstein derived the LT for a situation which was observational - a subjective interpretation of lengths and times in another reference frame - then, undaunted by the fact that there was never even the slightest attempt to justify their applicability to real time differences (different rates between two clocks), he proceeded to due just that. I have read his 1905 manuscript over many times seaching for something I must have missed - but ...

I don't understand what you're talking about when you say "justify their applicability to real time differences". By "real" do you mean that you think there should be some objective answer to the question of which of two inertial clocks is running slower? If so, see my comment above.

Now Einstien must be given great credit for his bold rejection of a universal time. He was also very intuitive - he realized that actual time difference occurs when a clock is carried on a path that returns to the starting point - long before we knew of muon and pion decays - or had hi speed aircraft to test the hypothesis. Certainly, by the time he published his 1912 manuscript, he had fully rejected the notion that acceleration had anything to do with the clock paradox. But he still didn't explain it.

Didn't explain what?

So in conclusion, while both observers are on an equal footing as far as making measurments in the other frame as to appearances, actual changes in clock rates can only be brought about by some physical cause.

What do you mean by "actual changes in clock rates"? What's the difference between an actual and a non-actual change?

All the observations of the other guys clock and all of his observations about your clock can't change a thing. To my way of the thinking, H&K experiments, muon decay, and GPS provide compelling evidence that clocks in motion relative to one another will accumulate different times whether or not they are ever returned to the same point for comparison. You get answers that conform with the experiments if you consider the Earth as fixed and the high speed clock moving between two points that define a proper distance in the Earth frame. If you consider the muon frame as fixed, it will last 2 usec - so in the muon frame, the Earth could only move 600 meters between the beginning and end of the experiment. And if that is the case - how much time has passed on the Earth clock as calculated in the muon frame during the 2 usec?

It depends on the relative velocity of the muon and the earth, but it would be less than 2 usec. However, If you have different clocks which are at rest relative to the Earth and which are "synchronized" in the Earth's frame, the muon will see these clocks as wildly out-of-sync, so if it departs the Earth when the earth-clock reads t=0 usec, the clock at its point of arrival will read a time much greater than t=2 usec when it arrives there, because in the muon's frame it was ahead from the beginning.

If you are content with these appearances and believe they should be given the designation of reality, so be it. I think the flaw in SR is the failure to take into account the inital conditions - who accelerated to bring about the relative velocity - not who turned around - because whatever time is lost going out will simply be doubled when added to the time lost on the inbound journey.

You never really addressed my question about how far back we in an object's history we should go to see if it has ever accelerated, you just went off on a tangent about problems you have with relativity. Anyway, if you believe there is an objective truth about which of two clocks ticks faster, this is incompatible with the idea that we should define things in terms of who accelerated most recently. Suppose we have a space station moving inertially, and a ship accelerates to take off from it--you can't say that this means the ship's clock is "objectively" running slower than the station's clock, because what if the space station accelerated to get away from the Earth at some point further in the past, and the ship now has a lower velocity in the Earth's frame (and thus is less slowed down in this frame) than the station?

 

[yogi]

Back again - as to the issue of which clock accelerates - let's take the simple example of two clocks A and B separted by a distance d. The clocks are in the same reference frame and brought into sync (e.g. by Einstein's method). Then clock A takes off in the direction of B (A accelerates quickly up to a velocity v in a time interval that is short compared to the time it takes to travel the distance d at velocity v - then travels the rest of the distance at a constant velocity). When A arrives at B, the readings are compared. Question for Jesse - do the clocks read the same, and if not, which clock has accumulated the greater time.

 

[Hurkyl]

Clock B will read more when A arrives, no matter how A gets there.

 

[JesseM]

Back again - as to the issue of which clock accelerates - let's take the simple example of two clocks A and B separted by a distance d. The clocks are in the same reference frame and brought into sync (e.g. by Einstein's method). Then clock A takes off in the direction of B (A accelerates quickly up to a velocity v in a time interval that is short compared to the time it takes to travel the distance d at velocity v - then travels the rest of the distance at a constant velocity). When A arrives at B, the readings are compared. Question for Jesse - do the clocks read the same, and if not, which clock has accumulated the greater time.

What Hurkyl said. But acceleration isn't really relevant, all that matters is that they were initially synchronized in a frame where A was moving and B was at rest. If they had been initially synchronized in a frame where A was at rest after it accelerated while B was traveling at velocity v, then A would have accumulated a greater time when they met, even though it was A who accelerated.

 

[yogi]

So if A and B are in the stationary frame initially (yes Jesse - I said stationary - same term as used by Einstein) - and after the sync operation is completed A accelerates to v and travels at velocity v until he reaches B. We all agree that A's clock will have accumulated less time. And I assume we all agree that acceleration does not have anything significant to due with the answer - it just tells us which clock is in motion with respect to the frame in which the two clocks were brought into sync (the frame I refer to as the stationary frame).

Now if we introduce at the outset a third clock D which is initally adjacent to A, and bring it into sync with A and B, then if D remains in the stationary frame (does not change its position wrt to B), D will read the same as B thereafter (B and D will remain in sync). So when A arrives at B, the A clock will read less than the D clock (The event of arrival occurs in both frames, but not at the same time in both frames).

Now if D is the clock owned by the stay at home twin, and A is the clock carried by the traveling twin - then the one way trip results in a time differential which can be evaluated w/o having to reunite the twins (A simply flashes a light signal back to D upon arrival at B, and since D knows the distance d between himself and B) he calculates the actual time loss experienced by A.

 

[Hurkyl]

D will read the same as B thereafter

No. Such a statement is nonsensical unless you specify a coordinate chart against which this is measured.

D will read the same as B according to the reference frame in which they're stationary.

According to other reference frames, D and B will not read the same.

So when A arrives at B, the A clock will read less than the D clock

The same objection applies to this statement.

In particular, according to the reference frame in which A is stationary during its trip, the A clock will read more than the D clock.

 

[JesseM]

Now if we introduce at the outset a third clock D which is initally adjacent to A, and bring it into sync with A and B, then if D remains in the stationary frame (does not change its position wrt to B), D will read the same as B thereafter (B and D will remain in sync).

As Hurkyl said, D only is synchronized with B in the rest frame of B and D, not in other frames.

Now if D is the clock owned by the stay at home twin, and A is the clock carried by the traveling twin - then the one way trip results in a time differential which can be evaluated w/o having to reunite the twins (A simply flashes a light signal back to D upon arrival at B, and since D knows the distance d between himself and B) he calculates the actual time loss experienced by A.

That's not the "actual" time loss, just the time loss in his frame. After all, B used the assumption that light travels at c relative to himself to calculate the time loss, but in other frames light does not actually travel at c relative to B.

 

[yogi]

As always - you both want to obscure the simplicity. So I will say it again: D and B remain in sync in the stationary frame. There is nothing to be added by diversionary comments to the effect that B and D will be out of sync if viewed by any number of other frames in motion with respect to the stationary frame. "A" measures time according to the moving frame. B and D measure the passage of time in the stationary frame. The event (A's arrival at B) occurs at the same spatial point in both frames). Jesse - The proper distance between B and D is d and a light signal sent from either A or B (upon the event of A's arrival at B) will take d/c seconds to arrive at D. How can it possibly be anything else if the stationary frame is an isotroptic inertial frame?

 

[JesseM]

As always - you both want to obscure the simplicity. So I will say it again: D and B remain in sync in the stationary frame.

Einstein only used the term "stationary" for the purposes of developing his argument--in section 1 of his 1905 paper he says:

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the "stationary system.''

The point here is that which frame we choose to call the "stationary system" is arbitrary, he never used the words "stationary system" to mean the frame where the physical objects you're analyzing are at rest. So, we have no obligation to define it as the frame where A and B are initially at rest in this problem.

There is nothing to be added by diversionary comments to the effect that B and D will be out of sync if viewed by any number of other frames in motion with respect to the stationary frame.

OK, I am defining the "stationary frame" as the one where A and B are initially moving at 0.99999c in the +x direction. Please, let's not have any diversionary comments about what things might look like in any other frames.

Jesse - The proper distance between B and D is d and a light signal sent from either A or B (upon the event of A's arrival at B) will take d/c seconds to arrive at D. How can it possibly be anything else if the stationary frame is an isotroptic inertial frame?

Well, if D emits a light signal, then since B is moving towards it at 0.99999c in the stationary frame as I have chosen to define it, and the distance between them is only d/\gamma in this frame, the time for the light signal to reach B will be far less than d/c.

 

[Chronos]

By whom's clock? That is just flat wrong.

 

[JesseM]

By whom's clock? That is just flat wrong.

By clocks at rest in the stationary frame, of course (which, remember, is the frame where B and D are traveling at 0.9999c in the +x direction). How else would one define the time between two events in a given frame?

 

[Chronos]

There is no stationary frame. B, D and my reference frame are SR time dilated and length contracted in the direction of motion.

 

[JesseM]

There is no stationary frame.

Read my previous post. I am just using "stationary" in the same way Einstein did in his paper (since yogi used this term earlier and justified it by saying Einstein had also used it):

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the "stationary system.''

So, the "stationary" frame is simply an arbitrary inertial reference frame which we have chosen to label as stationary, in order to distinguish this frame verbally from others.

B, D and my reference frame are SR time dilated and length contracted in the direction of motion.

Motion in whose frame? Obviously your reference frame is not moving with respect to itself.

 

[gonzo]

It seems to me like a lot of people are arguing in circles or just for the sake of arguing. Trying to find one sentence out of context in someone else's post and finding some way of looking at it that you can say is wrong.

To put it in Dr. Phil terms, are you all interested in being right or actually having some issue explained?

It's gotten to the point where I can even tell what the discussion is about anymore.

It seems to have started with something to do with the "Twins Paradox", but I can't really tell anymore.

Perhaps it would be more productive if someone tried to summarize the finer points of what the actual disagreement is here. Unless of course you all really like this type of arguing in circles, in which case I'll leave you to it with my appologies for interrupting.

 

[Hurkyl]

As always - you both want to obscure the simplicity.

Simplicity has no merit if its wrong.


As we've said over and over again, statements like:

D will read the same as B thereafter

have no meaning, except relative to a coordinate chart. Yet, for some mysterious reason, you keep saying them over and over and over...


Since you ardently reject such a correction, we are all justified in our conclusion that you are implicitly assuming an absolute notion of time. (And, thus, implicitly rejecting the relativistic notion of space-time)


We keep raising our objection in the futile hope that you'll eventually see the point of our objections.

 

[yogi]

Hurkyl - If B and D are initally brought in sync they will remain so in what I have called the stationary frame so long as they are not moved wrt to each other. If you believe something different - that is your privilege - if not, stop harping on it.

If you read what I have said - it has nothing to do with universal time - it does have to do with clocks in the same frame keeping the same time. How can you keep misconstruing this?

For those who feel this thread has wandered to far to be meaningful - I will attempt to restate the point of concern which is the root of my proposed thought experiment. Einstein in the first part of his 1905 paper derives the LT based upon how one observer views space and time in a frame that moves at velocity v wrt to his frame. And because neither can claim a preferred frame the situation is reciprocal. Then, in section 4 of that paper he draws conclusions about the physical meaning of the equations that were derived from apparent observations - specifically the exact situation posed by the clocks A and B which I have associated with twins... he states: "If at points A and B there are stationary clocks which viewed in the stationary system, are synchronous, and if clock A is moved with the velocity v along the line AB to B then on its arrival the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (1/2)t(v/c)^2 ..."
If this is correct, which we assume it is, then it should also be true that a third clock D that remained at the point where A was initially at rest in the stationary frame, can be brought into sync with B and should read the same as the B clock thereafter. Ergo, if B and D read the same in the stationary frame, D can access his brothers age upon receipt of a light signal sent by ether A or B (upon A's arrrival at B) w/o having A undergo turn around.

 

[JesseM]

Ergo, if B and D read the same in the stationary frame, D can access his brothers age upon receipt of a light signal sent by ether A or B (upon A's arrrival at B) w/o having A undergo turn around.

yogi, no one would disagree with you if you didn't use absolute terminology like "his brother's age" with no qualifiers. For example, if you said "D can access his brothers age in D's own frame upon receipt of a light signal sent by ether A or B (upon A's arrrival at B) w/o having A undergo turn around" then of course this is correct. But there is no absolute truth about what B's age is at the moment that D receives the light signal, because there is no preferred definition of simultaneity. Do you agree that any statement about their relative ages that doesn't explain which frame is being used does not provide the reader with enough information to evaluate whether it's true or false?

 

[gonzo]

Okay, Yogi, I understand what you are saying, but I don't understand what is controversial about that, aside from everyone feeling the need to nit-pick how they feel you worded things.

As far as I can tell you are just talking about the general idea of a latice work of synchronized clocks in an inertial frame, which is how SR is generally talked about.

So, what's the conflict?

 

[Hurkyl]

Hurkyl - If B and D are initally brought in sync they will remain so in what I have called the stationary frame so long as they are not moved wrt to each other. If you believe something different - that is your privilege - if not, stop harping on it.

This statement is fine, I think. You did intend "in what I have called the stationary frame" to apply to both "B and D are brought in sync" and "they will remain in sync", right?

If you read what I have said - it has nothing to do with universal time

You usually make statements like "B and D are in sync", and not statements like "B and D are in sync relative to the frame in which they're stationary".

The former only makes sense if you have an absolute notion of time. We infer that you are implicitly assuming universal time because you ardently reject our criticisms that you aren't specifying to which frame your statements are relativie.

 

[JesseM]

Okay, Yogi, I understand what you are saying, but I don't understand what is controversial about that, aside from everyone feeling the need to nit-pick how they feel you worded things.

It's not just about wording--although he said "the situation is reciprocal" in his last post, in earlier post he was never willing to admit that it is just as valid to say that in the traveling twin's frame, it is the other twin who has aged less at the moment he reaches his destination. If the situation is really symmetrical, there is no "paradox" here, because each can say the other ages less without conflict, it's only when the two twins can meet and compare ages that you might conclude there was a paradox because each should conclude the other will be younger when they meet, but only one can be right. But of course, for them to meet one has to turn around, so the situation is not actually symmetrical, unlike in yogi's example where it really is symmetrical but the two twins never meet. So, you can't really have a "twin paradox" in a situation like that where both are moving at constant velocity the whole time.

Yogi seems to understand the mathematical idea that the situation is symmetrical in each frame, but conceptually he seems to want to hold onto the idea that there is some sort of absolute truth about who has aged less. For example, in this post he says:

SR ignors all the rest of the universe - so two spaceships meeting far from any other reference can properly use Einsteins original derivation so that each can say, when I observe the other guys clock it appears to run slow. The operative word here is "observe" Obviously both clocks cannot be running slower than the other.

...Einstein derived the LT for a situation which was observational - a subjective interpretation of lengths and times in another reference frame - then, undaunted by the fact that there was never even the slightest attempt to justify their applicability to real time differences (different rates between two clocks), he proceeded to due just that. I have read his 1905 manuscript over many times seaching for something I must have missed...

...So in conclusion, while both observers are on an equal footing as far as making measurments in the other frame as to appearances, actual changes in clock rates can only be brought about by some physical cause. All the observations of the other guys clock and all of his observations about your clock can't change a thing.

gonzo, would you agree it's obvious that both clocks cannot be running slower than the other? Would you agree that the slowdown measured in different frames is just a matter of "appearances", to be contrasted with "actual changes in clock rates" which requires a "physical cause"? Do you agree that Einstein's paper is missing something because it didn't justify the applicability of "a subjective interpretation of lengths and times in another reference frame" to "real time differences" like the objective difference in ages seen between two twins who reunite after one has made an interstellar trip?

 

[gonzo]

As far as I understand it, the twins do not have to meet up again, and there is still no paradox. Is this is the debate? Here is how I understand it, and why I don't think it matters whether or not the twin turns around. I've lost all track of who is what letter, so I'll start from the beginning and see if I cover the issues correctly.

Okay, you have two Twins, Travel Twin (TT) and Home Twin (HT) for ease. They start together at START PLACE (SP) and TT then travels to END PLACE (EP).

Now, we assume the SP and EP are in the same inertial frame. We further imagine a latice of synchronized clocks throughout the whole of this inertial frame. This is a common practice when talking about SR.

As TT zooms out from SP to EP in his Rocket Ship Frame (RSF) he looks out his windows at all these clocks in the SP-EP frame and thinks they are all running slow (show less elapsed time). At each of these clocks we have a little green man in the SP-EP frame who looks in the window of the passing ship and thinks that TT's RSF clocks are running slow.

This is the first apparent problem, but this is easily resolved by issues of simultaneity.

Now, then the apparent problem arises when TT reaches EP. Right when he gets there, there seems to be a conflict. TT looks at the clock on EP and sees not much time has elapsed on that clock. While the little green man on EP looks in the window and sees that it is actually TT RSF clock that shows not much time passing.

So, then you ask what happens when TT stops, who's clock is right?

But this isn't a real symetry because TT is the one changing frames, whether he goes back, or just stops somewhere else in the SP-EP frame. He changes from his RSF frame to the SP-EP frame.

This has a weird effect. If you draw spacetime maps of the frames and draw lines of simultaneity you can see it more clearly.

When TT is still in RSF he sees the EP clock no showing much time. But we know at the end the EP clock is supposed to show a lot longer time. There are all these missing clock ticks you could say.

What happens, as I understand it, is that while TT is still in the RSF those missing clock ticks are in his future. When he changes frames back to the EP-SP frame, those clock ticks shift into his past. Easier to see on a spacetime diagram I think.

Almost like the clocks jumped ahead when he stopped, making up for lost time you could almost say.

Of course, I could be wrong in my understanding of the situation since I'm just a dabbling amateur.