The discussion centers on the synchronization of clocks in the context of Special Relativity (SR), specifically between two coordinate systems, K and k. Participants argue that while clocks in each system can be synchronized according to their respective frames, they cannot be considered synchronized when viewed from the other frame due to the relativity of simultaneity. The equation T=t/gamma illustrates time dilation, emphasizing that although T and t share units, they do not equate, and thus the clocks do not tick at the same rate across different inertial frames.
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DaleSpam said:I don't know what you mean by that. Also, what is your amended version of your third point.
Yes, if t is measuring in seconds and T is measuring in hours then you cannot use equation 3 directly, you must include a conversion factor. Is this what you mean?JM said:The early replies to my first post seemed to interpret point 3 to say that T and t must be the same. So I amended ( explained ) that I meant only that the units of measure of t and T must be the same.
In their respective rest frames, yes.JM said:If the units are the same then the clocks measuring T,t must advance at the same rate.
DaleSpam said:Yes, if t is measuring in seconds and T is measuring in hours then you cannot use equation 3 directly, you must include a conversion factor. Is this what you mean?
In their respective rest frames, yes.
Think of it this way. When we say that we have two identical rulers we mean that if we measure the same distance with both rulers we get the same result. A clock is just a ruler which measures timelike intervals. So when we say that we have two identical clocks we mean that if we measure the same interval with both clocks we get the same result.
If we use one ruler to measure the base of a right isosceles triangle and the other identical ruler to measure the hypotenuse then we will find that the measurements differ by a factor of \sqrt{2}. We attribute this difference to a difference in the thing being measured instead of to the rulers, since they are identical. Similarly, if we have one clock measure a vertical line through spacetime (at rest) and another clock measure a diagonal line through spacetime (in motion) then we will find that the measurements differ by a factor of \gamma. We again attribute this difference to a difference in the thing being measured instead of to the clocks, since they are identical.
No. The clocks of K are in synch with each other. The clocks of k are in synch with each other. But the clocks of K are not in synch with the clocks of k. Therefore it is not true that "all of the clocks of both K and k are in synch".JM said:I would express the result as 'all the clocks of both K and k are in synch'.
DaleSpam said:No. The clocks of K are in synch with each other. The clocks of k are in synch with each other. ".
No, because the phrase "when the origins coincide" refers to two separate sets of events for k and K. Also although you can say that they "advance at the same rate" they also "advance in different directions (in spacetime)" so even if you de-synchronized all of the clocks in k such that the first statement is true in K that would not imply that they would remain in sync in K. There is no sense in which "all the clocks of both K and k are in sync".JM said:All the clocks of K and k start at 0 when the origins coincide ( point 2) and all advance at the same rate ( point 3). Isn't this 'in synch?'
DaleSpam said:. Similarly, if we have one clock measure a vertical line through spacetime (at rest) and another clock measure a diagonal line through spacetime (in motion) then we will find that the measurements differ by a factor of \gamma. We again attribute this difference to a difference in the thing being measured instead of to the clocks, since they are identical.
I thought that I was pretty clear in multiple posts that what I was objecting to is your statement that "all the clocks of both K and k are in sync". There is no sense in which that is true, and "identical" is not a synonym for "synch". Two identical clocks may not be synchronized and two synchronized clocks may not be identical.JM said:However, your last post 37 seems to be disagreeing with something, but I’m not sure what. Is it my use of the term ‘synch’ instead of ‘identical’.
No, it doesn't mean that at all. Same units doesn't mean same rate any more than the fact that the same units are used for velocity means that the velocity of a specific clock is the same in K as in k. Relative velocity is a frame dependent quantity, so it has a different value in K than in k for each clock. Relative tick rate is also frame dependent.JM said:I gather that you agree that T and t must be expressed in the same units. What that means is that the clocks used to measure T and t must tick at the same rate...
Of course clocks don't change their behavior due to motion. That's a common misconception of SR.JM said:Thus the common expression that ‘moving clocks run slow’ is not literally correct, and clocks don’t change their behavior due to motion.
DaleSpam said:I thought that I was pretty clear in multiple posts that what I was objecting to is your statement that "all the clocks of both K and k are in sync". There is no sense in which that is true, and "identical" is not a synonym for "synch". Two identical clocks may not be synchronized and two synchronized clocks may not be identical.
"Identical" means that they are physically constructed the same and operate the same, as described above. "Synchronized" means that they have some agreed upon procedure for comparing their displayed time and that when they do so they get the same result. In relativity the standard procedure for comparing clock times is called the Einstein synchronization convention. Under that convention the clocks of K are synchronized with each other and the clocks of k are synchronized with each other, but the clocks of K are not synchronized with the clocks of k.
I don't know how I can possibly be more clear than this.
Al68 said:Of course clocks don't change their behavior due to motion. That's a common misconception of SR.
It depends whether you define "rate of ticking" as a "behavior", doesn't it? I think Al68's point was that rate of ticking is one of a number of quantities which are inherently frame-dependent, just like momentum or velocity. "Moving clocks run slow" is literally correct in the same sense that "faster-moving 1-kilogram masses have a greater momentum" is literally correct, but the latter doesn't imply the 1-kilogram masses "change their behavior due to motion", if "behavior" is defined solely in frame-invariant terms.JM said:Hello, Al68. So, do you agree with the statement that ' the common expression that 'moving clocks run slow' is not literally correct'?
Yes, I already said so in post 33.JM said:I accept your comments as subjects for further discussion.
In the meantime, let me ask:
Isn't it a fundamental principle of physics equations that all terms in an equation must be expressed in the same units?
If so, isn't it required that T and t in the equation t = T/gamma must be expressed in the same units?
Doesn't that require that t and T not only have the same name, e.g. seconds, but also that the seconds must be the same size for both?
A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.JM said:Hello, Al68. So, do you agree with the statement that ' the common expression that 'moving clocks run slow' is not literally correct'?
Are you arguing that "tick rate" can be defined in a frame-invariant way? It seems to me that "tick rate" always means "rate of ticking relative to coordinate time in some frame", I don't see how you could meaningfully define it relative to proper time (since the number of ticks along a worldline defines the proper time along that worldline) or any other frame-invariant quantity. If "tick rate" is an inherently frame-dependent notion then clocks do change their tick rates just like they change their velocities or momenta or x-coordinate.Al68 said:A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.
Sure, all you have to do is operationally define "tick rate". For example, you may define "tick rate" by comparison to some co-moving reference standards (in which case the tick rates would be the same). Or you may define "tick rate" by comparison to some single reference standard using a given simultaneity convention (in which case the tick rates would be different).matheinste said:Given two identical clocks in relatively moving inertial frames, one clock at rest in each, and given that the laws of physics are the same in all inertial frames, can we not in any meaningfully way ask if the two clocks tick at the same rate although we are unable to directly compare them side by side.
DaleSpam said:Sure, all you have to do is operationally define "tick rate". For example, you may define "tick rate" by comparison to some co-moving reference standards (in which case the tick rates would be the same). Or you may define "tick rate" by comparison to some single reference standard using a given simultaneity convention (in which case the tick rates would be different).
The statement "clocks do change their tick rates" misleadingly attributes the difference in its tick rate in different frames to an action performed by or to the clock.JesseM said:Are you arguing that "tick rate" can be defined in a frame-invariant way? It seems to me that "tick rate" always means "rate of ticking relative to coordinate time in some frame", I don't see how you could meaningfully define it relative to proper time (since the number of ticks along a worldline defines the proper time along that worldline) or any other frame-invariant quantity. If "tick rate" is an inherently frame-dependent notion then clocks do change their tick rates just like they change their velocities or momenta or x-coordinate.Al68 said:A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.
lugita15 said:I'm not so sure about that. Suppose you have a train of length L traveling speed v to the right. If two beams of light are emitted from either end of the train, at the same time according to the train's reference frame, then they will arrive at the center of the train at the same time according to the train's reference frame. But if I'm not mistaken, according to an observer on the ground they will have arrived at the center of the train at different times. Correct me if I'm wrong, though, since I haven't really studied special relativity in great detail. What I know comes mainly from popular books, which can be misleading.
But when people say "cars can change their velocities" they're not talking about measuring the speed of a single inertial car from the perspective of two different frames, they're talking about measuring the velocity of a car before and after it accelerates, as seen in a single inertial frame. Similarly if someone says "clocks do change their tick rates" the normal context would be talking about a clock that accelerates (or multiple identically-constructed clocks moving at different velocities) as seen in a single inertial frame; from the perspective of this single frame, the frame-dependent quantity "rate of ticking" does change.Al68 said:The statement "clocks do change their tick rates" misleadingly attributes the difference in its tick rate in different frames to an action performed by or to the clock.
If one measures the speed of a car relative to the ground, then measures the speed of the same car relative to another car, we wouldn't say the car "slowed down". Saying that the car slowed down would be inaccurate and misleading. It would prompt questions like: "what caused the car to slow down?"
Sorry, I misunderstood your post. I was referring to the statement that a "moving clock runs slow", which I took to mean a clock in inertial motion running slower in a different reference frame than the one in which it is at rest.JesseM said:But when people say "cars can change their velocities" they're not talking about measuring the speed of a single inertial car from the perspective of two different frames, they're talking about measuring the velocity of a car before and after it accelerates, as seen in a single inertial frame. Similarly if someone says "clocks do change their tick rates" the normal context would be talking about a clock that accelerates (or multiple identically-constructed clocks moving at different velocities) as seen in a single inertial frame; from the perspective of this single frame, the frame-dependent quantity "rate of ticking" does change.
Al68 said:A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.These two statements seem contradictory to me. In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.
To resolve this I recognize a difference between the properties of clocks and the properties of light. The properties of clocks discussed in this thread suggest to me that the clocks of K and k 'tick' at the same rate. There seems to be various comments that support this idea. If the clocks all start at zero when the origins coincide then all the clocks read the same.
The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this. But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?
If you have some set of equations defining how particles/fields/etc. behave in one inertial coordinate system, like Maxwell's laws of electromagnetism, it is a purely mathematical question as to whether these equations are "Lorentz-symmetric", with Lorentz-symmetry meaning that if you describe the motions of the same particles/fields/etc. using a different inertial coordinate system obtained by doing a Lorentz transformation on the first coordinate system, the exact same set of equations will accurately describe their behavior in the second coordinate system. If all the underlying laws of physics governing the motions of the parts of a clock are Lorentz-symmetric, that is enough to guarantee that identically-constructed clocks at rest in different Lorentzian coordinate systems will each tick at the same rate relative to coordinate time in their own respective rest frames, which necessarily implies that each clock seems to be running slow in the other clock's rest frame.JM said:But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?
They are not contradictoryJM said:These two statements seem contradictory to me.
And what does "relative to a stationary clock in a specified reference frame" mean in ordinary language? It is an important part of the sentence which you have neglected.JM said:In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.
This is not correct. We have been over this before (e.g. post 37). You are going in circles.JM said:If the clocks all start at zero when the origins coincide then all the clocks read the same.
The experimental support for the Lorentz transforms is overwhelming, and includes the dilation of clocks whose mechanism is not based on light, such as the half-life of unstable particles. The important thing about the Lorentz transforms is that there is a speed which is invariant. The fact that light travels at the invariant speed is essentially a coincidence due to the photon being massless. If the photon were eventually discovered to have some very small non-zero mass then light would not travel at exactly c. However, all of the experimental results confirming time dilation etc. would still be valid as would the Lorentz transform and SR with very minor changes to the wording of the second postulate.JM said:The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this. But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?
A moving clock does not "run slow" in this "ordinary language" sense. It runs slow only in a relative sense, ie relative to a "stationary clock". Clocks in SR are assumed to be working properly and each keeping perfect proper time.JM said:These two statements seem contradictory to me. In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.Al68 said:A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.
In K, the clock of k runs slower than the clock of K. In k, the clock of K runs slower than the clock of k. In neither frame do the clocks run at the same rate, unless there is no relative motion between them.The properties of clocks discussed in this thread suggest to me that the clocks of K and k 'tick' at the same rate.
He didn't "blame the clocks" for anything. He assumed perfectly working clocks that each kept proper time. He attributed the difference to the fact that time itself passes at a different rate relative to different reference frames.The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this.
It's related to the speed of light being constant, yes. The clocks are each just keeping proper time.So I think that t<T is the fault of the light not the clocks.
JesseM;2732736...rest frames said:other[/i] clock's rest frame.
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Einstein's original 1905 paper can be found here: http://www.fourmilab.ch/etexts/einstein/specrel/www/JM said:I note that you say "seems to be running slow..' Does that refer to the relation t=T/gamma? If so, do you think that the apparent slowness is due to the properties of the clocks or due to the properties of the light?
Have you published on SR? If not, where have you gotten your knowledge? I have read everything I could find, and found no real explanations.
JM said:Al68 said:A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.No, not OK. The fact that t<T is neither the fault of light nor the fault of the clocks. It is the fault of time. Time is not an absolute concept that is the same for all observers. If you take two clocks that were made identically, then they will disagree about the duration of events if they happen to be moving at different speeds. The clocks are not malfunctioning, and light is not involved. Einstein mentions his procedure of using light beams, but this is a red herring. There he talks about using light beams only because the speed of light is the same for all observers. The time dilation phenomenon would be observed even if the observers used any other kind of particle to make their observations. The fact that people are using light to make observations makes their lives easier, but by no means is it necessary.These two statements seem contradictory to me. In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.
To resolve this I recognize a difference between the properties of clocks and the properties of light. The properties of clocks discussed in this thread suggest to me that the clocks of K and k 'tick' at the same rate. There seems to be various comments that support this idea. If the clocks all start at zero when the origins coincide then all the clocks read the same.
The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this. But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?
I thought this was already explained to you, but you keep reiterating your old points.