Special Relativity Clocks

DaleSpam

It is the same theory as everyone else uses. The Lorentz transform for transforming coordinates between different reference frames, and the proper time formula for calculating the time measured by a clock.

ghwellsjr

OK, now I see what's going on. I did a search and found this reference to Taylor and Wheeler's Spacetime Physics where they mention a proper clock on page 160:

http://books.google.com/books?id=PDA...page&q&f=false

However, they define a proper clock on page 10 which is not available online [at least it wasn't yesterday, today it is???] so I checked the book out of the library and what they mean by a proper clock is one that travels between two events at a constant speed (without regard to any frame). In other words, it is measuring the frame invariant spacetime interval but this can only work for timelike intervals.
The restriction they are talking about is when the spacetime interval for the two events are spacelike, meaning that a clock would have to travel at faster than the speed of light to get from one event to the other. Instead, this interval is measured with a rigid ruler between the two events in a frame in which the events occur at the same time. They don't, however, call this a proper ruler.
Actually, although that single clock moving between two events at a constant speed is measuring the invariant spacetime interval, it can also be measured in a frame in which the clock is at rest and then it becomes identical to a co-ordinate clock. Look at page 160 of the link to the book above. There you will see "the frame clock is the proper clock". They use the term "frame clock" to mean "co-ordinate clock". So in this case, when the velocity is zero (clock is at rest, the events occur at the same place), gamma is one and so the "proper clock" never runs slow in the frame in which it is at rest. But in other frames it can have a speed other than zero and so can run slower than a co-ordinate clock in that other frame.

But this unique definition of a "proper clock" is not what we normally mean by proper time because we may want to have a clock that accelerates between the two events. If you look up the wikipedia article on "proper time", you will see that it makes the point:
Now since Taylor and Wheeler's "proper clock" can never accelerate, it will measure a greater time and therefore run faster than any other clock that accelerates between the two events.

I hope this clears up the confusion.

Mentz114

It does. Thanks for taking the trouble. It's a good idea but calling it a 'proper' clock is a bit non-standard since all clocks measure proper time.

ghwellsjr

By the way, JM, I just noticed that Taylor and Wheeler have a similar explanation to the one in wikipedia if you back up to page 156. There in Figure 5-12, they show two worldlines going between two events labeled O and B. The straight vertical worldline is the one for what they call a "proper clock" because it is constant velocity--no acceleration--and it has the "maximal lapse of proper time", 10, in this case. By contrast, they say a clock carried along the kinked worldline OQB has a proper time of 6, and then they say of the proper clock, "the direct worldline displays maximum proper time".

Then in the next paragraph, they contrast two different comparisons of time between two events. The first is what they call map time, frame time, latticework time, but what everyone else calls co-ordinate time and they make the point that different frames will generate different times but the least amount of time is the frame in which the two events are at the same location. This would be the case in which a "proper clock" is not moving. In other frames the "proper clock" is moving and runs slower than the co-ordinate time difference for the two events. So it is in this sense that "moving proper clocks run slow". They then proceed to the second contrast and repeat the statement that the "proper clock" with the straight worldline "registers maximal passage of proper time" meaning it runs the fastest not slower like a clock that accelerates, meaning that it is not a "proper clock".

JM

George- I see what you are doing in Post 80, you are following a clock as it moves wrt the stationary frame by specifying its two values of time t' for the same value of x', and working backwards to find the corresponding values of x and t. The only quibble I might make is that transforming from x',t' to x,t usually uses the + sign instead of the -sign. The transformed values are different but the 'deltas' are the same and the 'slow clock' formula is confirmed. Also, the two points in the stationary frame follow the relation Δx = 0.8 Δt, as Einstein assumed.
I'm fine with 'slow clocks' now.
JM

JM

If one takes the moving clocks to be moving in a straight line parallel to the stationary x axis, and the coordinates x,t to represent (perhaps isolated) events of interest (such as two lightning bolts hitting a train track), then there seems to be the possibility that no clock will be present at any two events. This is the picture that Einsteins 1905 paper suggests to me.
I gather from the discussion that there are additional ideas for clocks moving in arbitrary directions, accelerating , etc . Can you suggest a reference describing such theories?
JM

JM

George-
(I've shortened the quote only to save space)
Thanks for the ideas. 'Proper clocks' is evidently not a simple subject.
My efforts to date have been on understanding Einsteins 1905 paper. I feel comfortable with most of it ( there are a few questions about rod shortening, how the time t' is made to appear on the moving clocks, and the theory behind the linking of frames moving in different directions).
I'm looking for references for the theory that 'everyone else uses'. You have mentioned Wikipedia and Taylor/Wheeler. Are these the introductory authorities, or is there something better? I have looked at Taylor but find it difficult because of manner of presentation and the many 'off the wall ideas'.
JM

ghwellsjr

Yes, well since deltas never care about the sign of the difference, it can be done either way. I'm glad you scrutinized my post enough to notice the difference. And I'm glad you are fine with slow clocks now.

ghwellsjr

Moving clocks do not have to be moving just along the x-axis nor do they have to be moving at a constant velocity. That's merely the way Einstein developed the equation to show the tick rate of a moving clock compared to the tick rate of the stationary co-ordinate clocks. In his 1905 paper, after he derives the formula, he immediately moves on to a clock that is not moving in a straight line along the x-axis but rather is moving in a circular path so that it returns to a stationary clock and he determines that the moving clock will have accumulated less time on it than the stationary clock during the same time interval.

This is an example of what Taylor and Wheeler discuss on page 156 where the two events in question are when Einstein's two clocks start out together and when they end up together. The stationary clock is following a straight line through spacetime and qualifies as what they call a "proper clock" since its velocity is constant (actually zero) and it is present at both events. The moving clock is constantly accelerating even though its speed is constant it's velocity is not. So it is not a "proper clock". It takes a curved line through spacetime and so its accumulated proper time is less than the accumulated proper time on the stationary "proper clock".

As Taylor and Wheeler point out on page 11, if two events have a spacelike spacetime interval, then it won't be possible for a single clock to traverse between the two events at a constant speed because that speed would have to be greater than the speed of light. But it has nothing to do with any axes.

ghwellsjr

"Proper clocks" is a very simple subject once you know what Taylor and Wheeler mean by them. This term was brought up by you and you brought up the Taylor and Wheeler reference. I don't like their approach nor their confusing, non-standard, "proper clocks" term. I would advise that you just forget about them as a bad experience. Einstein's 1905 paper develops everything you need to know about Special Relativity although some of his other writings are also helpful, such as his 1920 book.

Mentz114

I'm sorry, JM, I find that paragraph incomprehensible. Whether or not a clock is present at an event is irrelevant to the 1905 train scenario.
All clocks are the same whatever path they move on. They record the proper time along their worldlines. Every worldline may have its own proper time.
I don't know what you mean by 'theories'. Maybe start with finding out about worldlines and the proper time

dτ² = c²dt² - dx² - dy² - dz²

DaleSpam

Hi ghwellsjr, thanks for this information, I was unaware of this definition. So I must correct my previous statements, there is a such thing as a proper clock. A proper clock is not the same thing as proper time.

All clocks (proper or not) measure proper time according to the formula I gave above. However, for a proper clock the proper time formula simplifies even further. The proper time formula is more general than any proper clock formulas.

PAllen

Atypical mixing of units here. If you use c^2 dt^2, you usually call the invariant differential ds^2. If you use dt^2 on the rhh, the dτ^2.

Mentz114

Whoops. I should have said proper interval.

JM

George- Re the 1905 paper, what is the theory that supports the use of linked/accelerating frames? Doesn't 1905 restrict to inertial frames? I sense that many have divorced the time on the moving clock from its roots in the stationary frame and the 'events' that happen there, when 'viewing from the stationary frame'. The early posts in this thread explain my thoughts on this. I don't see this in 1905.
Re the 1920 book, whats the name and publisher?
JM

DaleSpam

Special relativity.

Yes, but accelerating frames are obtained simply by a coordinate transform from an inertial frame in SR. You don't need to change theories to GR until you want to add gravity.

Do you now understand that moving clocks always tick slow in an inertial frame?

ghwellsjr

I don't know what you mean by a linked frame and I see no advantage or need for an accelerating frame when any inertial frame will do everything that needs to be done and so much more simply. So I'm not the one to ask about other types of frames but I see DaleSpam has provided an answer. It's a good bet to trust what he says.
Yes, and so do I.
I'm sorry, I can't figure out what you mean here. What are the moving clock's roots in the stationary frame and what 'events' are you talking about?
What posts would those be? I thought we resolved that the confusion was over Taylor and Wheeler's restrictive definition of a 'proper clock' and you were fine (post #107) with the fact that any moving clock, inertial or not, will tick more slowly than the co-ordinate clocks in the frame in which it is moving
Using two frames, Eisntein showed the derivation for the equation to determine the tick rate of a moving clock as a function of its speed in an inertial frame and then he proceeds to show how two clocks, one stationary and one accelerating in a circle, both with respect to a single frame, will have accumulated different times on them every time they are colocated. In contrast, the 'proper clock' in this scenario is the stationary one because it is inertial between the two events of successive meetings of the two clocks. It's tick rate is not slowed down but is identical to the tick rate of the co-ordinate clocks in the single inertial frame. The other clock is the moving one and its tick rate is slowed down as it travels in a circle and each time it meets up with the stationary clock, it has accumulated less time on it. In other word, the proper time on the stationary 'proper clock' has advanced more than the proper time on the moving clock between each of the events when they meet.
The link to the book was provided by harrylin in post #18 and quoted by you in post #23 so I thought you had taken a look at it.