[TyroJack (OP)]

This  has caused me some puzzlement:
If a clock takes longer to 'tick' - if it takes more time for each 'tick' -  then we say it runs slow.
Yet if we measure a clock to be running slow, it is measuring less time than a clock keeping the correct time.
So how can a clock measuring more time be running slow?

If the clock takes longer to tick then it will measure fewer ticks; yet the same clock, stationary relative to observer A and moving relative to observer B is but one clock and both observers are observing and counting the same number of 'ticks'.

So observer B will measure more time for each 'tick' but the same number of 'ticks' and, therefore, a greater quantity of time passing than observer A will measure.  So could we say that the clock must have run faster measured by observer B as it measured a greater time? Or slower because each 'tick' took longer?

I am not doubting anything about relativity, only pointing out how difficult it is to apply use the language of classic mechanics when we speak of relativity.

It seems to me that using a term like slowing adds connotations due to the way we use everyday language to describe something counter intuitive.

[Halc]

This  has caused me some puzzlement:
If a clock takes longer to 'tick' - if it takes more time for each 'tick' -  then we say it runs slow.

Well put.   "Ticks slow" is an absolutist term, which means that it takes more absolute time between ticks than does a different clock.  In relativistic (non-absolute) interpretation, a clock that ticks slow is inaccurate, and thus not really a clock.  There is simply more or less time between a pair of events in one frame as compared to another frame which orders those same events differently.  Nothing physical really changes for anything.

Yet if we measure a clock to be running slow, it is measuring less time than a clock keeping the correct time.

Only under an absolutist interpretation is there a concept of 'correct time', and since they cannot produce a standard of it, it seems like a pretty poor interpretation.  For instance, how long does it really take for Earth to make one sidereal revolution?  Relativity has no 'correct time', so the question is meaningless.  An absolute interpretation does have that, so the question is simply unanswered.

So how can a clock measuring more time be running slow?

If a clock ran slow, it would measure less time, not more.  It wouldn't really be a clock if it didn't accurately measure what it is supposed to.

If the clock takes longer to tick then it will measure fewer ticks; yet the same clock, stationary relative to observer A and moving relative to observer B is but one clock and both observers are observing and counting the same number of 'ticks'.

I cannot really parse that.  A clock that is stationary and local relative to an observer will appear to run at normal full rate, per principle of relativity.  Ones that move relative to some frame will measure less time in that frame, but not necessarily appear to run slower to a stationary observer.  An approaching clock appears to run faster for instance, but that's mostly due to blue shift.

So could we say that the clock must have run faster measured by observer B as it measured a greater time? Or slower because each 'tick' took longer?

You need to state the situation in terms of frames, not in terms of observers, since a clock not present at the observation has a frame dependent time that it reads but not a frame dependent time that is observed at that observation event.

So under absolute interpretation, the observers have nothing to do with anything.  A clock that moves takes longer to do a tick.  Under relativity, all clocks measure time accurately: the temporal distance between two events along the worldline of the clock.  These are frame independent measurements, and thus nothing 'ticks slow'.

I am not doubting anything about relativity, only pointing out how difficult it is to apply use the language of classic mechanics when we speak of relativity.

Use the relativistic language then.  Speak of frames and events, and not objective (lacking a relation) speeds or of appearances.

[Janus]

This  has caused me some puzzlement:
If a clock takes longer to 'tick' - if it takes more time for each 'tick' -  then we say it runs slow.
Yet if we measure a clock to be running slow, it is measuring less time than a clock keeping the correct time.
So how can a clock measuring more time be running slow?

If the clock takes longer to tick then it will measure fewer ticks; yet the same clock, stationary relative to observer A and moving relative to observer B is but one clock and both observers are observing and counting the same number of 'ticks'.

So observer B will measure more time for each 'tick' but the same number of 'ticks' and, therefore, a greater quantity of time passing than observer A will measure.  So could we say that the clock must have run faster measured by observer B as it measured a greater time? Or slower because each 'tick' took longer?

I am not doubting anything about relativity, only pointing out how difficult it is to apply use the language of classic mechanics when we speak of relativity.

It seems to me that using a term like slowing adds connotations due to the way we use everyday language to describe something counter intuitive.

I think your confusion arises from trying to treat "time" as being absolute. 
 
If I measure a clock moving relative to me to be ticking slower than my own clock, It may only tick once for every tow ticks of my own clock,  If one tick is one second fro me than the other clock takes two sec between ticks  But this only according to me. There is no absolute measure of time against which to judge the other clock.   For that clock own perspective, it is ticking once per sec. It is just that the same time period the other clock measures as being one sec, I will measure as being two sec.
 In addition, someone at rest with respect to that clock would measure my clock as only ticking once for every two ticks of that clock. His clock measures one sec per tick and mine takes two sec per tick.

As Einstein but it " Time is what clocks measure".    In that vein, there is no absolute measure of time only what each clock measures as time.( keeping in mind that we are considering "ideal" clocks; clocks that essentially keep perfect time.)

People many times get the idea that Relativity says that a "moving" clock will run slow, as in  the motion physically alters the manner in which the clock works.    This isn't what is happening.  An observer will measure a clock that has a relative motion with respect to the observer to tick slower than the observer's own clock.    It isn't that motion physically effects the clocks, it is that observers in relative motion with respect to each other also measure time differently than each other.  And neither observer's measurement of time is any more valid than the other's.
   

[evan_au]

If a clock takes longer to 'tick' - if it takes more time for each 'tick' -  then we say it runs slow.

We are used to a clock indicating a time of day; the ticks come in discrete intervals. But that's not the only type of clock.

Another kind of clock is the frequency of a spectral line in a star's radiation or a radio transmitter; the radiation is "continuous".
- We can compare this by saying that the frequency emitted by one source is higher or lower than the frequency emitted by another source, one of which could be a reference in our laboratory (in our frame of reference).

Note that in either clock, you must disentangle the different rates due to relativity from the (usually much larger) effect of Doppler shift.

One relativistic time variation that is easier to disentangled from Doppler shift is gravitational redshift.

See: https://en.wikipedia.org/wiki/Gravitational_redshift

[TyroJack (OP)]

Clock A's worldline passes through events P and Q.
Event P is the start of a tick and Q is the end of the tick. The tick takes one second.
From Frame B each tick of clock A is measured to be 2 seconds.
Clock A ticks between P and Q
Measured by A this takes 1 second.
Measured by B moving clock A takes 2 seconds to tick, but that is two seconds in frame A. Clock B is an ideal clock in an inertial frame, measured by a resting observer, so will measure the same time (postulate 1) as clock A, 1 second.
So, one might say that from B, A did not tick slower, but measured more time for each tick - so time passed quicker for frame A, measured by frame B, 2 seconds instead of one second, during each tick.

[Halc]

Clock A's worldline passes through events P and Q.
Event P is the start of a tick and Q is the end of the tick. The tick takes one second.
From Frame B each tick of clock A is measured to be 2 seconds.
Clock A ticks between P and Q
Measured by A this takes 1 second.
Measured by B moving clock A takes 2 seconds to tick, but that is two seconds in frame A.

It is one second in frame A, as you stated above.  "Measured by A this takes 1 second".  It is two seconds in frame B, and frame B is not a proper measurement between events P and Q since the B clock is not present at both events P and Q.  The A clock is present at both of them, as you stated on the first line.

You don't specify, so let's say clock B's worldline passes through events P (0), R (0.5) and S(2) in a straight line.  In frame A, events Q and R are simultaneous.  In frame B, events S and Q are simultaneous.  That difference in event ordering is what relativity is about.

Clock B is an ideal clock in an inertial frame, measured by a resting observer, so will measure the same time (postulate 1) as clock A, 1 second.

Both clocks are ideal clocks (how is an ideal clock distinct from a clock anyway?), both in inertial frames, with separate observers next to each if you find that useful, but they're stationary in different frames, so neither clock measures the same length-of-worldline as the other.
Clock A measures the proper time between events P and Q because it is present at both events and its worldline between those events is straight.  Clock B is not measuring proper time between those two events because it is not present at both of them, but is instead measuring proper time between events P R and S.

So, one might say that from B, A did not tick slower, but measured more time for each tick - so time passed quicker for frame A, measured by frame B, 2 seconds instead of one second, during each tick.

Or one might stop using absolute language and not talk about tick rates at all.
From frame B, clock A is dilated.  From frame A, clock B is dilated.  Neither clock ticks slow or measures any different time than one second per second.  The time shown is the actual temporal length the worldline measured.

[Janus]

Clock A's worldline passes through events P and Q.
Event P is the start of a tick and Q is the end of the tick. The tick takes one second.
From Frame B each tick of clock A is measured to be 2 seconds.
Clock A ticks between P and Q
Measured by A this takes 1 second.
Measured by B moving clock A takes 2 seconds to tick, but that is two seconds in frame A. Clock B is an ideal clock in an inertial frame, measured by a resting observer, so will measure the same time (postulate 1) as clock A, 1 second.
So, one might say that from B, A did not tick slower, but measured more time for each tick - so time passed quicker for frame A, measured by frame B, 2 seconds instead of one second, during each tick.

For a little more clarity, I put events P and Q three ticks(sec) apart rather then one.  I also added event "R" which represents three sec according to clock B.  A and B both start event P. Relative speed is  0.8c This is relative speed. both diagrams below describe exactly the same scenario, just from different frames of reference.

World lines for A and B from the rest frame of A.


Image21.png (7.42 kB . 602x302 - viewed 980 times)

By the in the Time clock A goes from event P to Q( three sec as measured by clock A),  clock R has not yet ticked off three sec.   Event R has not happened yet according to A and event P happens before event R. Light signals ( yellow lines) leave both A and B after 1 tick has past on each clock.  Each signal reaches the other clock when it reads 3 ticks (sec)

World lines for A and B according to B's rest frame.

Image23.png (7.12 kB . 603x301 - viewed 1431 times)

In the time it takes for B to go from P to R( three sec as measured by clock B), A has not yet reached ticked off three sec. Event Q has not happened yet according to B, and event R occurs before event Q.

The light signals sent by each clock when it has ticked off one sec each reach the other clock when that clock reads 3 sec.

[jeffreyH]

I can select a reference frame such that A and B are traveling at identical velocities. From my point of view both frames have the same clock rate. Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more. Otherwise the twins thought experiment makes no sense.

Also GPS makes no sense and shouldn't work. Time dilation has physical effects. All the arguments about everything being totally relative dodges the issue.

[Halc]

I can select a reference frame such that A and B are traveling at identical velocities.

Identical speeds at least, yes.  Velocity is a vector quantity so in this frame, A and B are travelling at opposite velocities.

From my point of view both frames have the same clock rate. Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more. Otherwise the twins thought experiment makes no sense.

A and B are dilated identically in that frame.  You're the one who is dilated not at all.  One is never dilated in one's own frame.

The twins scenario cannot be illustrated in that example since A and B will never meet again at that velocity.  To meet again, somebody needs to change velocity.

Also GPS makes no sense and shouldn't work. Time dilation has physical effects. All the arguments about everything being totally relative dodges the issue.

The GPS satellites actually run faster than us on Earth, but that's mostly due to GR effects, not SR.  The average speed of a GPS satellite is larger than your average speed in any inertial frame, and it being totally relative doesn't change that.

[jeffreyH]

I can select a reference frame such that A and B are traveling at identical velocities.

Identical speeds at least, yes.  Velocity is a vector quantity so in this frame, A and B are travelling at opposite velocities.

Yes, speed. My apologies.

From my point of view both frames have the same clock rate. Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more. Otherwise the twins thought experiment makes no sense.

A and B are dilated identically in that frame.  You're the one who is dilated not at all.  One is never dilated in one's own frame.

The twins scenario cannot be illustrated in that example since A and B will never meet again at that velocity.  To meet again, somebody needs to change velocity.

And there is the problem. Stating that acceleration has to occur for a difference in dilation to be a physical thing. A change in velocity is only required for it to be observable. This guarantees the proximity of observer and observed. If the twin just travels in a straight line for t amount of time and never returns he will still be time dilated. It is just that you will never be able to detect it.

This is the big issue I have with opinions on SR.

Also GPS makes no sense and shouldn't work. Time dilation has physical effects. All the arguments about everything being totally relative dodges the issue.

The GPS satellites actually run faster than us on Earth, but that's mostly due to GR effects, not SR.  The average speed of a GPS satellite is larger than your average speed in any inertial frame, and it being totally relative doesn't change that.

[jeffreyH]

BTW This follows from time dilation in SR being a function of velocity and NOT acceleration.

[Halc]

The twins scenario cannot be illustrated in that example since A and B will never meet again at that velocity.  To meet again, somebody needs to change velocity.

And there is the problem. Stating that acceleration has to occur for a difference in dilation to be a physical thing.

I didn't say that.  I said that no objective comparison can be made between clocks not in each other's presence.  The acceleration itself does nothing.

BTW This follows from time dilation in SR being a function of velocity and NOT acceleration.

Exactly so, yes.  I can have two clocks here on Earth, both at identical speeds and depth in gravity well, but one with arbitrarily higher acceleration than the other.  SR says they will stay in sync.

[jeffreyH]

OK To reiterate: Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more.

[pzkpfw]

OK To reiterate: Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more.

You're mixing frames.

If we assume A is the "stay at home" twin and B moves away, then yes there could be a C for whom both A and B are the same speed relative to them. Note that C would also have to be moving, according to both A and B.

According to A, C is moving away at half the speed B is moving away.
According to B, C is moving away at half the speed A is moving away.
According to C, A and B are both moving away at the same speed (in opposite directions).
At this time, according to C, time dilation is the same for A and B.

Then there's the turn-around. B heads back to A. For your addition of C, C will also now need to head back ...

According to A, C is moving closer at half the speed B is moving closer.
According to B, C is moving closer at half the speed A is moving closer.
According to C, A and B are both moving closer at the same speed.
At this time, according to C, time dilation is the same for A and B.

During the two times of plain inertial movement, everyone can consider themselves as at rest, and their clocks will tick at one second per second - according to them. And also, according to them, the other peoples' clocks will tick slower. Your addition of C does not change this.

That B (and C) will be younger than A when they all get back together is not about some "real" physical dilation happening to one but not the other during the travel. That would imply some absolute rest, where A is "really" at rest and B is "really" moving.

It's an effect of one of them staying in a single inertial frame the whole time while the other (or others) do not.

(Although acceleration is needed to have B change direction, the effect is not specifically "caused" by the acceleration. Alternate methods of this experiment involve someone else coming back, and B passing them their clock reading as they cross paths. The clock that returns to A will still read less.)

While B moves away (according to A) the situation is symmetrical, i.e. B can consider A moving way.
While B moves closer (according to A) the situation is symmetrical, i.e. B can consider A moving closer.
(And this is where the "paradox" of "twins' paradox" comes from.)
But ... the overall scenario is not symmetrical, someone (A) just sat in their chair holding their clock and a cup of coffee. Someone else (B) had to change frames; they either spilled their coffee (by accelerating) or had to pass their clock to someone else to return to A.

[Halc]

OK To reiterate: Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more.

Dilation is relative.  Nobody is dilated more, absent that relation.  The principle of relativity demands this.

[jeffreyH]

OK To reiterate: Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more.

Dilation is relative.  Nobody is dilated more, absent that relation.  The principle of relativity demands this.

So we can pick a frame to make the problem with GPS go away then. If dilation is truly relative this has to be the case. This, however, doesn't solve the problem for the guy on the surface of the earth.

[jeffreyH]

OK To reiterate: Who is dilated more 1 A, 2 B, 3 Neither? Someone has to be physically dilated more.

You're mixing frames.

If we assume A is the "stay at home" twin and B moves away, then yes there could be a C for whom both A and B are the same speed relative to them. Note that C would also have to be moving, according to both A and B.

According to A, C is moving away at half the speed B is moving away.
According to B, C is moving away at half the speed A is moving away.
According to C, A and B are both moving away at the same speed (in opposite directions).
At this time, according to C, time dilation is the same for A and B.

Then there's the turn-around. B heads back to A. For your addition of C, C will also now need to head back ...

According to A, C is moving closer at half the speed B is moving closer.
According to B, C is moving closer at half the speed A is moving closer.
According to C, A and B are both moving closer at the same speed.
At this time, according to C, time dilation is the same for A and B.

During the two times of plain inertial movement, everyone can consider themselves as at rest, and their clocks will tick at one second per second - according to them. And also, according to them, the other peoples' clocks will tick slower. Your addition of C does not change this.

That B (and C) will be younger than A when they all get back together is not about some "real" physical dilation happening to one but not the other during the travel. That would imply some absolute rest, where A is "really" at rest and B is "really" moving.

It's an effect of one of them staying in a single inertial frame the whole time while the other (or others) do not.

(Although acceleration is needed to have B change direction, the effect is not specifically "caused" by the acceleration. Alternate methods of this experiment involve someone else coming back, and B passing them their clock reading as they cross paths. The clock that returns to A will still read less.)

While B moves away (according to A) the situation is symmetrical, i.e. B can consider A moving way.
While B moves closer (according to A) the situation is symmetrical, i.e. B can consider A moving closer.
(And this is where the "paradox" of "twins' paradox" comes from.)
But ... the overall scenario is not symmetrical, someone (A) just sat in their chair holding their clock and a cup of coffee. Someone else (B) had to change frames; they either spilled their coffee (by accelerating) or had to pass their clock to someone else to return to A.

This wasn't a twins experiment scenario. In my scenario there is no turn around point. You will never know if anyone's clock is running slower than the others. That is the whole point. I think we should admit when we actually don't know something. Rather than arguing in circles. That would be much more productive.

Knowing what the state of anyone's clock is requires close proximity. If we don't have close proximity then we don't know it's state. We are making an assumption.

[jeffreyH]

Space station A and space station B are a distance X apart. This is known in advance. Probe C is traveling between them at 0.8c. The speed itself is only significant because of the relativistic effects it will produce. As the probe moves along it records the number of seconds that have elapsed since it passed the first space station. When the probe reaches the destination it sends the count to the destination space station. The crew then check it against what they would expect in the absence of time dilation and at the speed the probe was traveling. What do they find?

[Halc]

So we can pick a frame to make the problem with GPS go away then. If dilation is truly relative this has to be the case. This, however, doesn't solve the problem for the guy on the surface of the earth.

Dilation due to motion is truly relative.  GPS dilation is due mostly to depth of gravity well, which is absolute, so the GPS clocks are less dilated than the Earth clocks in any frame.

This wasn't a twins experiment scenario. In my scenario there is no turn around point. You will never know if anyone's clock is running slower than the others.

Sure you can, but you need to pick a frame to do it. 

That is the whole point. I think we should admit when we actually don't know something.

The answer is frame dependent.  Being frame dependent doesn't mean that you can't know.

Knowing what the state of anyone's clock is requires close proximity.

Proximity is required for an objective comparison since the comparison is the same in any frame.  For separated events, the comparison is dependent on how the frame orders those events.  That ordering of events is not a physical difference, only an abstract one.  Thus neither clock runs physically slower or faster due to relative motion.

[TyroJack (OP)]

World lines for A and B according to B's rest frame.

Image23.png (7.12 kB . 603x301 - viewed 1431 times)

This diagram raises another thing that I wonder about.
This is what I believe to be a Minkowski diagram.
Why is the time scale for the moving one out of scale? Is it because the light paths are at 45 degrees?
This bothers me for it seems that is Newtonian mechanics with absolute space and time:

Imagine 2 identical light clocks, A and B, moving apart at speed v.
Seen from clock A the light from clock B moves up at ct while clock B moves away at vt, so the light as seen from the stationary clock can be moving vertically if v is vanishingly small
If B is moving away at approaching light speed, the time measured by clock B, will be almost zero.

If clock B travels at 0.866 c, for 1 second, measured by A, its light will have travelled 1 light second, measured by A, but only 0.5 light seconds, within clock B (this of course is the time clock B is shewing - its proper time).

So clock A, measures 1 time dilated second to have passed for clock B, when clock B reads 0.5 seconds.