Understanding Time Dilation in Einstein's Special Theory of Relativity

[cos]

Will writes "...the rate of a moving clock must always be compared to a set of clocks that are in an inertial frame...a set of clocks that are at rest with respect to the center of the Earth." i.e. your 'notional lattice of stationary clocks'.

He continues "The ground clock is moving at a speed determined by the rotation rate of the Earth and thus ticks more slowly than the fictitious inertial clocks; the flying clock is moving even more quickly relative to the inertial clocks, so it is ticking even more slowly. Thus time dilation makes the flying clock run slowly relative to the ground clock."

In other words Will points out that there is 'a comparison of the rates of the clocks in the air relative to the rates of the clocks on the surface' and that the clocks aboard the aircraft tick over at a slower rate than the laboratory clocks.

Well, I should have said no "direct comparison" for clarity.

Will's comparison of the rate of the flying clock relative to the inertial clocks compared to the rate of the ground clock relative to the inertial clocks is a direct comparison!

One clock (the ground clock) is ticking over at a slower rate than the inertial clocks and another clock (the flying clock) is ticking over at a slower rate than the ground clock. If that data is not determined as a result of a direct comparison between the rate of operation of the flying clock compared with the rate of operation of the ground clocks I don't see how else this determination is arrived at other than by direct comparison between their respective rates of operation.

According to the Hafele-Keating experiment - if I am looking at a clock attached to an aircraft that is moving past me from West to East it will by direct comparison be ticking over at a slower rate than my own clock (allowing, of course - as did Will - for any Doppler and gravitational time variation effect).

If I am located in 'empty' space standing alongside a stationary clock (Einstein's section 4 clock B) and another clock (Einstein's clock A) is moving in a closed curve around me I will see it continuously ticking over at a slower rate than my own clock by direct comparison.

The point is that it's the lattice clocks against which the direct comparison is being made, with the indirect comparisons between the flying and surface clocks working out so that the eastward flying clocks go slow, while the westward flying clocks go fast. So the lattice clocks or "reference frame" is very important.

I read Will's book in about 1992 (and specifically it's reference to the HKX many times since then) and am fully aware of the relevance of his reference to "...a set of clocks that are in an inertial frame."

My argument is in relation to the irrelevance of the point of view of a person traveling past the planet whose 'opinion' or 'determination' or 'calculation' or 'prediction' has no bearing or affect whatsoever on what the clocks are actually doing.

From the point of view of all observers in the ground clocks' (quasi-inertial) reference frame the Eastward flying clock is ticking over at a slower rate than their own clock.

Unlike some people - if I am looking at an aircraft that is flying overhead I am of the opinion that that I am stationary and that it is moving i.e. that it is not the atmosphere that has been made to move relative to it's wings - an opinion that, as far as I am concerned, is asinine.

 

[cos]

]When people respond with (as far as I am concerned) totally irrelevant comments such as 'not according to other reference frames' I am forced to respond to such arguments pointing out that the determinations arrived at by numerous other reference frames have no bearing whatsoever - no affect - on those arrived at by the observer in the reference frame in which the event takes place.

When I explain this to those people and they respond with 'not according to other reference frames' and refuse to respond to my relevant points of view I tend to become a bit upset with their intolerance however I am of the opinion that they are deliberately maintaining this attitude for no other reason than to upset me which I see as being arrogant harassment.

The reason everyone keeps going on about other reference frames is because that's the only way you will ever understand how relativity works.

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

I am only interested in what Einstein wrote in section 4!

If you really only want to ever consider a single reference frame then there is no explanation for relativity. You will just have to accept that's the way it is without understanding why.

In all of my postings I fully accept that there are at least two reference frames - that of the observer and that of a moving clock.

 

[Mentz114]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

I am only interested in what Einstein wrote in section 4!

Why ? You're obsessed. Is this really an intellectual exercise ? Picking over the bones of an old paper and looking for literalisms is a waste of time. What do you hope to achieve ?

 

[JesseM]

Unlike some people - if I am looking at an aircraft that is flying overhead I am of the opinion that that I am stationary and that it is moving i.e. that it is not the atmosphere that has been made to move relative to it's wings - an opinion that, as far as I am concerned, is asinine.

The problem is that you apparently refuse to accept that it's meaningless to talk about whether something is "moving" (or the 'rate' a clock is ticking) except in the context of a particular reference frame (coordinate system), in physics there is no non frame-dependent way to talk about "rate of movement", it's an intrinsically frame-dependent concept. And as I said before, physical events don't occur "in" one frame or another, so there is no one frame that defines the "real truth" about a particular set of events.

By the way, suppose someone fires a bullet inside the plane, with the right speed and direction so that the bullet is at rest relative to you on the surface of the Earth--would you say it was more "asinine" to describe the air inside the plane moving relative to the bullet, or the bullet inside the plane moving relative to the air inside the plane?

 

[Al68]

Al68 wrote:- "Sorry if I haven't addressed every single statement in your posts. I only addressed the ones I considered most relevant due to time considerations."

This is not a continuation of that discussion but is a general note to the several people that have made similar comments.

I note that it is always the more salient points and questions in my postings that are ignored due to the fact that a response to same would mean a commitment by the respondent which is why I specifically raised those matters.

I can appreciate that. I didn't realize that the points I didn't respond to were particularly important.

My responses tend to be lengthy due to the fact that the messages to which they apply are themselves of extreme length or else I am forced to break things down into extended simple explanations and/or provide analogies.

When people respond with (as far as I am concerned) totally irrelevant comments such as 'not according to other reference frames' I am forced to respond to such arguments pointing out that the determinations arrived at by numerous other reference frames have no bearing whatsoever - no affect - on those arrived at by the observer in the reference frame in which the event takes place.

When I explain this to those people and they respond with 'not according to other reference frames' and refuse to respond to my relevant points of view I tend to become a bit upset with their intolerance however I am of the opinion that they are deliberately maintaining this attitude for no other reason than to upset me which I see as being arrogant harassment.

My habit of being specific about reference frames is an effort to be accurate, not intolerant. Especially when speaking of something (such as a clock's rate "slowing down") that is particularly dependent on reference frame, since a statement that is true in a particular reference frame is simply not true in general.

 

[atyy]

I read Will's book in about 1992 (and specifically it's reference to the HKX many times since then) and am fully aware of the relevance of his reference to "...a set of clocks that are in an inertial frame."

My argument is in relation to the irrelevance of the point of view of a person traveling past the planet whose 'opinion' or 'determination' or 'calculation' or 'prediction' has no bearing or affect whatsoever on what the clocks are actually doing.

From the point of view of all observers in the ground clocks' (quasi-inertial) reference frame the Eastward flying clock is ticking over at a slower rate than their own clock.

Unlike some people - if I am looking at an aircraft that is flying overhead I am of the opinion that that I am stationary and that it is moving i.e. that it is not the atmosphere that has been made to move relative to it's wings - an opinion that, as far as I am concerned, is asinine.

OK, I won't press the point on direct versus indirect comparisons, since the only point of that distinction was that the notional lattice of clocks or reference frame is necessary for the sorts of rate comparisons being discussed - a point on which we seem to agree. In a particular situation in which a specific physical clock and a specific lattice clock have identical worldlines, it is conventional and convenient jargon to say that the reference frame belongs to that specific physical clock (and observer). However, the lattice fills all of "space", and is present wherever any physical clocks are, so in another non-jargony sense, the lattice does not belong to only one physical clock, but belongs to any physical clock (and observer), whether or not its/her wordline coincides with any lattice clock. In the Hafele-Keating experiment as presented by Will, there is no lattice clock whose worldline coincides with the wordline of a physical clock (or observer), so by conventional jargon, the reference frame used does not belong to any physical clock (or observer). However, in the non-jargony sense, the lattice used belongs to all observers, and any observer can use any lattice. Since any observer can use any lattice, and there are an infinite number of lattices she can use, she should always state which lattice she is using (perhaps by using the conventional jargon for naming lattices), if she wishes others to understand what she is saying.

Edit: Will, for example, specifies the lattice he uses as "at rest with respect to the center of the earth".

 

[phyti]

The physical explanation is that time itself passes at different rates for different observers/clocks. a clock that is not broken will reflect this. The number of "ticks" shown on each clock will be proportional to the time elapsed for each clock. The details of how a particular clock keeps good time is a side issue, since we are assuming that all clocks used in SR have the same tick rate relative to the proper time elapsed.Why would I add that when the clock's rate was always frame dependent. If the tick rate is different for different observers, it's because the observers are at different relative velocities, not because the clock itself changes in any way.

In other words, a clock runs at the constant rate of T*sqr(1-v^2/c^2) where v is the relative velocity between the clock and an inertial reference frame, and T is time in that reference frame. Only the relative rate between a clock and observer changes, because the relative velocity of the observer changes, not because the clock changes.

I'll try again. The two clocks are synchonous initially.
After the trip, the two clocks are together in the same frame, with one clock showing fewer ticks than the other. There is no relative motion. Where did the missing ticks go, or what caused the difference in readings?

 

[Al68]

If two synchronized clocks become out of synch when compared in the same frame, there is a physical explanation why, worn parts, weak battery, etc.
In the example with one clock moving away and returning, if the clocks literally ticked at the same rate for the duration of the trip, there would be no difference, The number of ticks would be invariant, yet we know the rate depends on the speed of the clock. The fact that one clock shows less ticks than the other (in the second case) when compared in a common frame is equivalent to the first case, and requires a physical explanation, not an abstract model representation.

If you're asking what physical mechanism "causes" the differential clock readings, I would say it's the same physical mechanism that causes a clock to keep proper time in its own frame.

In the case of a simple light clock (which measures how long it takes light to travel between two points in the clock's frame), it's easy to see that the physical mechanism that causes time dilation is the exact same mechanism that causes the velocity of light to be constant relative to every observer (instead of relative to its source).

And I mean "No clock changes its tick rate" in the same way I would say that a train whistle doesn't "change its pitch" when it passes me. The statement that "the whistle doesn't change its pitch" is entirely consistent with the statement "the relative pitch of the whistle changes" when the train passes, if we realize why the pitch changes.

Similarly, the statement "the clock didn't change its tick rate" is consistent with the statement "the clock's relative tick rate changed", the change just isn't caused by the clock.

 

[JesseM]

I'll try again. The two clocks are synchonous initially.
After the trip, the two clocks are together in the same frame, with one clock showing fewer ticks than the other. There is no relative motion. Where did the missing ticks go, or what caused the difference in readings?

Say two cars start at the same position A on flat 2D surface, and their odometers show the same reading. Then they drive along different paths along the surface to a different position B, where they meet and compare odometer readings. One car took a straight-line path between A and B, the other took a non-straight path, so since we know a straight line is the shortest distance between any two points, naturally the odometer reading of the car that took the straight path won't have increased as much as the odometer reading of the car that took a non-straight path. Where did the missing odometer increments go, or what caused the difference in readings?

 

[DrGreg]

I'll try again. The two clocks are synchonous initially.
After the trip, the two clocks are together in the same frame, with one clock showing fewer ticks than the other. There is no relative motion. Where did the missing ticks go, or what caused the difference in readings?

The ends of two tape measures are together. For the first 6 inches, the tapes are side-by-side and measure the same distance. Then one continues in a taut straight line, from its 6-inch mark to its 18-inch mark. The other is slack and takes a different route. Further along, both tape measures come together and run side-by-side one more. But where the taut tape measures 18 to 24 inches along this section, the slack tape measures 20 to 26 inches. Where did the missing two inches go, or what caused the difference in readings?

(If this sounds like JesseM's post, that's because we both posted at almost the same time as each other.)

 

[neopolitan]

I note that it is always the more salient points and questions in my postings that are ignored due to the fact that a response to same would mean a commitment by the respondent which is why I specifically raised those matters.

My responses tend to be lengthy due to the fact that the messages to which they apply are themselves of extreme length or else I am forced to break things down into extended simple explanations and/or provide analogies.

Salience is a relative thing. What is salient to one observer may not be salient to another observer. The question we should be asking is: are your salient points really salient, or are the points that everyone else seems to take as salient the true salient points?

As for trying to extract salient points from lengthy dissertations, you will run into problems with the relativity of salience. By that I mean that one comment (c) you make might have 0.6s (60% salience factor) relative to an argument (Э) relative to observer A and 0.8s (80% salience factor) relative to another argument (Б) relative to observer B but the salience of c to argument Э relative to observer B may be 0.2s or even 0s (the argument is at rest relative to observer B).

Then you have to take into account the paragraphical separation (p) of comments and arguments and the relativistic effect on salience. And don't get me started on the relative length of words (L_w) and sentences (L_s) and their use in phrasing both comments (^cП_ws) and arguments (^aП_ws).

But I stress, we should be investigating which points are really, truly, physically salient. We can't do that ourselves from first principles, of course, we should consult the Holy Book, "On the Salience of the Non-Moving Arguments", Section 4.

cheers,

neopolitan

 

[Mentz114]

neopolitan:

But I stress, we should be investigating which points are really, truly, physically salient. We can't do that ourselves from first principles, of course, we should consult the Holy Book, "On the Salience of the Non-Moving Arguments", Section 4.

Ha-ha. Well put. As I enquired earlier - what's this thread about ? Is Cos trying to show that Einstein was initially as confused as everyone else about the implications of SR ? So what if he was ?

 

[cos]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

I am only interested in what Einstein wrote in section 4!

Why ? You're obsessed. Is this really an intellectual exercise ? Picking over the bones of an old paper and looking for literalisms is a waste of time. What do you hope to achieve ?

My intention is in relation to Einstein's comment in Relativity - that special theory is invalidated by gravity - showing that the results of particle acceleration experiments that are said to ratify special theory's concept of a 'light barrier' are similarly invalidated.

I attribute your deprecatory attitude to ignorance.

 

[Mentz114]

My intention is in relation to Einstein's comment in Relativity - that special theory is invalidated by gravity - showing that the results of particle acceleration experiments that are said to ratify special theory's concept of a 'light barrier' are similarly invalidated.

I don't remember you saying this before. Why not start a thread with this topic instead of banging on about section 4.

I attribute your deprecatory attitude to ignorance.

Yes. Ignorance of what you're trying to say caused by your failure to communicate clearly.

 

[Dale]

Salience is a relative thing. ... we should consult the Holy Book, "On the Salience of the Non-Moving Arguments", Section 4

best post of the thread!

 

[JesseM]

My intention is in relation to Einstein's comment in Relativity - that special theory is invalidated by gravity

Of course Einstein also said that when it comes to the equations of the general theory, these equations hold good in all coordinate systems, not just the inertial systems used in special relativity--this would include the non-inertial coordinate systems that you have said before you don't like, such as a coordinate system where the Earth's clock suddenly starts ticking much faster relative to coordinate time or where objects can undergo huge coordinate accelerations without feeling any G-forces. Read chapter 28 of Relativity where Einstein writes the following (note that the translator here uses the word 'reference body' for what people on this thread have been calling a reference frame or coordinate system):

We can state this general principle of relativity in still another form, which renders it yet more clearly intelligible than it is when in the form of the natural extension of the special principle of relativity. According to the special theory of relativity, the equations which express the general laws of nature pass over into equations of the same form when, by making use of the Lorentz transformation, we replace the space-time variables x, y, z, t, of a (Galileian) reference-body K by the space-time variables x', y', z', t', of a new reference-body K'. According to the general theory of relativity, on the other hand, by application of arbitrary substitutions of the Gauss variables x1, x2, x3, x4, the equations must pass over into equations of the same form; for every transformation (not only the Lorentz transformation) corresponds to the transition of one Gauss co-ordinate system into another.

If we desire to adhere to our “old-time” three-dimensional view of things, then we can characterise the development which is being undergone by the fundamental idea of the general theory of relativity as follows: The special theory of relativity has reference to Galileian domains, i.e. to those in which no gravitational field exists. In this connection a Galileian reference-body serves as body of reference, i.e. a rigid body the state of motion of which is so chosen that the Galileian law of the uniform rectilinear motion of “isolated” material points holds relatively to it.

Certain considerations suggest that we should refer the same Galileian domains to non-Galileian reference-bodies also. A gravitational field of a special kind is then present with respect to these bodies (cf. Sections XX and XXIII).

In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity. The motion of clocks is also influenced by gravitational fields, and in such a way that a physical definition of time which is made directly with the aid of clocks has by no means the same degree of plausibility as in the special theory of relativity.

For this reason non-rigid reference-bodies are used which are as a whole not only moving in any way whatsoever, but which also suffer alterations in form ad lib. during their motion. Clocks, for which the law of motion is any kind, however irregular, serve for the definition of time. We have to imagine each of these clocks fixed at a point on the non-rigid reference-body. These clocks satisfy only the one condition, that the “readings” which are observed simultaneously on adjacent clocks (in space) differ from each other by an indefinitely small amount. This non-rigid reference-body, which might appropriately be termed a “reference-mollusk,” is in the main equivalent to a Gaussian four-dimensional co-ordinate system chosen arbitrarily. That which gives the “mollusk” a certain comprehensibleness as compared with the Gauss co-ordinate system is the (really unqualified) formal retention of the separate existence of the space co-ordinate. Every point on the mollusk is treated as a space-point, and every material point which is at rest relatively to it as at rest, so long as the mollusk is considered as reference-body. The general principle of relativity requires that all these mollusks can be used as reference-bodies with equal right and equal success in the formulation of the general laws of nature; the laws themselves must be quite independent of the choice of mollusk.

So, in the end you can see he refers to any arbitrary (Gaussian) non-inertial coordinate system as a "reference-mollusk", and goes on to say "all these mollusks can be used as reference-bodies with equal right and equal success in the formulation of the general laws of nature", meaning that every arbitrary non-inertial coordinate system is considered equally valid in general relativity, in much the same way that every inertial coordinate system is considered equally valid with respect to the laws of special relativity.

 

[Dale]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

This certainly explains a lot. Then your posts do not belong on this forum.

 

[jtbell]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

OK, that's it. It's clear that you are wasting our time, and we are wasting yours. This thread is done.