Looking to understand time dilation


by hprog
Tags: dilation, time
Mike_Fontenot
Mike_Fontenot is offline
#37
Nov4-10, 12:35 PM
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Quote Quote by ghwellsjr View Post
[...]
If no inertial reference frame can be considered "preferred" according to SR, [...]
[...]
If the traveler is perpetually inertial, then he certainly DOES have a "preference" for one particular inertial frame. There is only one inertial frame that agrees with the elementary measurements and elementary calculations that he makes, using clocks and rulers with which he is stationary. That preferred inertial frame is the one in which he is stationary.

Of course, other inertial observers (who are moving at some constant velocity with respect to the above inertial observer) will prefer a different inertial frame (the one in which THEY are stationary).

What special relativity says is that there is no single inertial frame that ALL inertial observers prefer. There is no single inertial reference frame that is UNIVERSALLY special.

Mike Fontenot
DaleSpam
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Nov4-10, 02:10 PM
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Quote Quote by Mike_Fontenot View Post
If the traveler is perpetually inertial, then he certainly DOES have a "preference" for one particular inertial frame.
Only as a matter of personal and computational convenience, not as a matter of physical necessity. And there may be some situations where a different frame is more convenient, e.g. the center of momentum frame for a collision.

Quote Quote by Mike_Fontenot View Post
There is only one inertial frame that agrees with the elementary measurements and elementary calculations that he makes, using clocks and rulers with which he is stationary.
You have never provided any substantiation for this, and it is only even possibly true if you define "elementary calculations" such that it is a tautology. Otherwise the principle of relativity ensures that all inertial reference frames will give the same predictions for the result of any given measurement and your statement is wrong.
ghwellsjr
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Nov4-10, 03:33 PM
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Quote Quote by Mike_Fontenot View Post
If the traveler is perpetually inertial, then he certainly DOES have a "preference" for one particular inertial frame. There is only one inertial frame that agrees with the elementary measurements and elementary calculations that he makes, using clocks and rulers with which he is stationary. That preferred inertial frame is the one in which he is stationary.

Of course, other inertial observers (who are moving at some constant velocity with respect to the above inertial observer) will prefer a different inertial frame (the one in which THEY are stationary).

What special relativity says is that there is no single inertial frame that ALL inertial observers prefer. There is no single inertial reference frame that is UNIVERSALLY special.

Mike Fontenot

The term "preferrred frame" has a specific meaning. You are making the same mistake that I am dealing with someone else on in this thread:

http://www.physicsforums.com/showthr...=442132&page=2

It doesn't mean a personal preference like "I prefer blondes". Even if everyone in the world preferred blondes, it wouldn't mean they are "UNIVERSALLY special". I hope you don't think the word "special" in Special Relativity has anything to do with the concept of "preferred". This has nothing to do with anyone's preferences. It has to do with whether we base our physics on the concept of an Šther.
Mike_Fontenot
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Nov4-10, 03:41 PM
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Quote Quote by DaleSpam View Post
Quote Quote by Mike_Fontenot View Post
[...]
If the traveler is perpetually inertial, then he certainly DOES have a "preference" for one particular inertial frame.
[...]
Only as a matter of personal and computational convenience, not as a matter of physical necessity.
[...]
It's not a matter of physical necessity that you refrain from constantly hitting yourself in the head with a hammer, either.

The well-known results of time-dilation and length-contraction are directly available for your use (when you are an inertial observer), provided that you choose to use the usual Lorentz coordinates, in an inertial frame in which you are stationary. And the time coordinate, with that choice, corresponds to the time shown on your OWN watch. The spatial coordinate, with that choice, correponds to the lengths as reported by your OWN rulers and measuring tapes. There is a REASON why Einstein chose those coordinates, when developing his special theory.

In the spirit of general relativity, you are of course free to choose some other set of coordinates, by transforming those Lorentz coordinates in an almost unlimited number of ways, provided that the eigenvalues of the resulting metric are either {1, -1, -1, -1} or {-1, 1, 1, 1}, assuming that spacetime is everywhere flat.

In those alternative coordinate systems, your "clocks" would behave in very odd ways, compared to ordinary clocks. And likewise for your "rulers". Real work-a-day experimental physicists would seldom, if ever, choose those types of "measuring devices" to do their experiments in their laboratories. There is a REASON that the phrase "in the laboratory frame" is used so often.

[...]
And there may be some situations where a different frame is more convenient, e.g. the center of momentum frame for a collision.
[...]
Not if you're one of the two people involved in the impending collision. I've spent a lot of hours flying airplanes and gliders, constantly needing to avoid mid-air collisions. In all that time, I've NEVER used the center of mass coordinate system to help me avoid mid-air collisions.

Mike Fontenot
Mike_Fontenot
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#41
Nov4-10, 03:56 PM
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Quote Quote by ghwellsjr View Post
[...]
I hope you don't think the word "special" in Special Relativity has anything to do with the concept of "preferred". This has nothing to do with anyone's preferences. It has to do with whether we base our physics on the concept of an Šther.
[...]
No, the term "special" in "special relativity" refers to the special case of limitless flat spacetime (no gravitational fields).

My other use of the term "special", as in "There is no single inertial reference frame that is UNIVERSALLY special", referred to the fact that in flat spacetime, there is no single inertial reference frame that is preferred by ALL inertial observers.

Mike Fontenot
ghwellsjr
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#42
Nov4-10, 05:17 PM
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You got the word "special" right, I just don't know why you can't get the word "preferred" right.
ghwellsjr
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Nov4-10, 05:44 PM
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Quote Quote by Mike_Fontenot View Post
Real work-a-day experimental physicists would seldom, if ever, choose those types of "measuring devices" to do their experiments in their laboratories. There is a REASON that the phrase "in the laboratory frame" is used so often.
I thought your CADO formula was for a traveler going at substantial speeds, traveling incredible distances for almost an entire liftetime to "know" at any instant of time how old his daughter was back at home.
JesseM
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Nov4-10, 06:11 PM
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Quote Quote by Mike_Fontenot View Post
And the time coordinate, with that choice, corresponds to the time shown on your OWN watch.
But your own watch can only be used to assign coordinates to events on your own worldline, an accelerating observer could come up with multiple non-inertial coordinate systems which all agree that the coordinate time between events on his worldline is equal to his own proper time between those events, but which disagree about the time between events far from him or about simultaneity of distant events. There is no physical reason to think any of these non-inertial coordinate systems more accurately represents his "own measurements" of time than any other.
Quote Quote by Mike_Fontenot
The spatial coordinate, with that choice, correponds to the lengths as reported by your OWN rulers and measuring tapes.
For an inertial observer "their own" ruler presumably means an inertial ruler at rest relative to themselves. But what does it mean for an accelerating observer? Does it mean that they are using an accelerating ruler, and if so how to decide how parts far from them are accelerating (is the ruler accelerating in a Born rigid way for example?) Or are you supposing that at each moment they define "their own" ruler to be a different inertial ruler which is instantaneously at rest relative to themselves at that moment?
Quote Quote by Mike_Fontenot
In those alternative coordinate systems, your "clocks" would behave in very odd ways, compared to ordinary clocks. And likewise for your "rulers".
Again this is meaningless if you haven't defined precisely what "your clocks" and "your rulers" means for an accelerating observer, and why you think the accelerating observer doesn't have a choice of how clocks far from his own worldline should move or be synchronized with one another, and likewise why he doesn't have a choice about how points on his own (accelerating?) ruler far from his own worldline should themselves be moving (remember that in SR there is no simple notion of how the back end of a 'rigid ruler' should accelerate if we know how the front end is accelerating, since there is no well-defined notion of 'rigidity' for objects undergoing arbitrary acceleration, physical rulers will behave like silly putty or slinkys when you accelerate one end)
DaleSpam
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Nov4-10, 10:10 PM
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Quote Quote by Mike_Fontenot View Post
It's not a matter of physical necessity that you refrain from constantly hitting yourself in the head with a hammer, either.
...
I've spent a lot of hours flying airplanes and gliders, constantly needing to avoid mid-air collisions. In all that time, I've NEVER used the center of mass coordinate system to help me avoid mid-air collisions.
Very cute. Completely irrelevant to the topic, but cute.

So Mike, are you going to continue to dodge the challenge and hide from the issue? After a dozen or so requests you have had plenty of opportunity but you still can't even define your terms let alone demonstrate your claim. I suspect that you know that your claim is wrong.
ghwellsjr
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#46
Nov5-10, 12:48 AM
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I think Mike has defined his terms "elementary measurements" and "elementary calculations". Look at this post:
Quote Quote by Mike_Fontenot View Post
If the traveler is perpetually inertial, then he certainly DOES have a "preference" for one particular inertial frame. There is only one inertial frame that agrees with the elementary measurements and elementary calculations that he makes, using clocks and rulers with which he is stationary. That preferred inertial frame is the one in which he is stationary.
And now this one:
Quote Quote by Mike_Fontenot View Post
The well-known results of time-dilation and length-contraction are directly available for your use (when you are an inertial observer), provided that you choose to use the usual Lorentz coordinates, in an inertial frame in which you are stationary. And the time coordinate, with that choice, corresponds to the time shown on your OWN watch. The spatial coordinate, with that choice, correponds to the lengths as reported by your OWN rulers and measuring tapes. There is a REASON why Einstein chose those coordinates, when developing his special theory.
It looks like Mike thinks that Einstein was claiming that you have to use the inertial frame in which you are stationary to make SR work.

Then, somehow, he slips from a perpetually inertial frame to a non-inertial frame when the traveler starts his voyage:
Quote Quote by Mike_Fontenot View Post
No, I use a SINGLE reference frame for the traveler during his entire voyage. I call that single reference frame the "CADO" or "{MSIRF(t)}" reference frame ... it is NOT an inertial frame.
And I'm sure he really believes this is what Einstein was promoting.
Grimble
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Nov5-10, 09:11 AM
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Quote Quote by matheinste View Post
This maybe where you are going wrong. When the traveller reaches the turnaround point he is momentarily, or for any desired length of time, at rest with respect to the stay at home and their clocks will be ticking at the same rate as each others as they are at rest with respect to each other.

The same is true when the traveller returns and halts next to the stay at home, they are at rest in the same inertial frame and so their clocks tick at the same rate as each other. And of course at that stage it is meaningful to compare clocks, and although they are now once again ticking at the same rate,
But yes I agree with what you are saying here! So where does this show that I am going wrong?

the traveller's clock shows less accumulated time.
Now this is where you lose me, What has SR and transforming measurements with LT possibly got to do with ACCUMULATED time?

LT is used to transform measurements: what a clock currently reads, not a calculation of the difference between two readings on a clock.

LT is a function of the CURRENT velocity. It has absolutely nothing to do with the history of how their relative speed might have varied over the course of their travel relative to one another.
DaleSpam
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Nov5-10, 09:15 AM
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Quote Quote by ghwellsjr View Post
It looks like Mike thinks that Einstein was claiming that you have to use the inertial frame in which you are stationary to make SR work.
Which is a complete misunderstanding of SR, particularly the first postulate. I think it is obvious to everyone besides Mike.
matheinste
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Nov5-10, 09:55 AM
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Quote Quote by Grimble View Post
i.e. When the traveller turns round he first comes to rest with respect to the home twin. At this moment their ages, as shown by LT, will once again be equal. Then the traveller returns and during that return journey their ages and apparent ages will differ once again but when the traveller has returned and come to rest once again they will have identical ages once again.

It is only if the traveller keeps on travelling past the home twin on his return that the age difference is apparent and it will be apparent to each of them.

Grimble
"when the traveller has returned and come to rest once again they will have identical ages once again."

"It is only if the traveller keeps on travelling past the home twin on his return that the age difference is apparent and it will be apparent to each of them."

These two statements are incorrect.

Perhaps I have missed something from your previous posts that puts these statements in context, if so forgive me and point them out.

Don't forget you cannot use one LT for the whole of the journey for the travellers non inertial frames.

Matheinste
ghwellsjr
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Nov5-10, 10:05 AM
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Quote Quote by Grimble View Post
Now this is where you lose me, What has SR and transforming measurements with LT possibly got to do with ACCUMULATED time?

LT is used to transform measurements: what a clock currently reads, not a calculation of the difference between two readings on a clock.

LT is a function of the CURRENT velocity. It has absolutely nothing to do with the history of how their relative speed might have varied over the course of their travel relative to one another.
The Lorentz Transform assumes that there has only ever been one velocity relative to the frame of reference. In this case, you can use LT to calculate both the difference in clock readings between the stationary one and the moving one, and/or you can calculate the relative tick rate between the two clocks. If you then accelerate the moving clock, you have to be very careful about how you describe what is happening to get a precise unique result. Usually, people just take a short cut and assume that the accelerating clock is gradually changing to its new tick rate as calculated by LT. Then to get an idea of the difference in the clock readings, you have to integrate, or multiply the time interval that a clock was ticking at a particular rate by its tick rate to find the accumulated time at the point of acceleration. And remember, this is all being done from the one frame of reference of the stationary observer (or any other single frame of reference).

In other words, if there were only one velocity involved, you could use LT directly to calculate the difference in clock readings OR you could use the tick rate multiplied by the time interval and you will get the same answer but when you introduce a new velocity, you cannot use the former method to calculate the difference in clock readings, you have to use the later twice, once for each time interval that the clock was moving at each speed and then add them together.
DaleSpam
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Nov5-10, 10:27 AM
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Quote Quote by ghwellsjr View Post
The Lorentz Transform assumes that there has only ever been one velocity relative to the frame of reference.
Careful here. The velocity referred to here is the velocity between two inertial reference frames, not the velocity of some object in a given inertial frame. I am sure that you understand, but some people may misread that and think that you meant that the Lorentz transform cannot be used if an object is accelerating.
hprog
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#52
Nov5-10, 12:01 PM
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Quote Quote by DaleSpam View Post
hprog, are you comfortable with the concept now or are you still confused?
Yes I am still confused.
Let me explain what I see here.
First let me say two principles I am taking out of the Special Relativity.
1) Any object in the same frame of reference - even if they are very far apart from each other - must agree on the fact that only one of them is younger, even if we have no clue who of them.
2) Any object next two each other must basically agree who is younger even if they are in different frames of reference.

Now let A and B move away in linear motion, A and B are far away and you claim that both can claim to be younger.
Now let's have C - which is using the same of frame of reference as A - next to B, and B and C will agree that they are the same age.
Yet since A and C must agree that only one of them is younger - even if they are far away -it follows that B and A must also agree that only one of them is younger, even if they are far away.

How is this fitting together with SR?
DaleSpam
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Nov5-10, 01:51 PM
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Quote Quote by hprog View Post
How is this fitting together with SR?
The presence of object C doesn't change the comparison of A and B. The relativity of simultaneity ensures that everything works out correctly.

The easiest way to visualize this is to draw a spacetime diagram and use the Lorentz transform to label the A- and B-frame coordinates.
Mike_Fontenot
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Nov5-10, 06:11 PM
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Some members of this forum have expressed the opinion that the coordinates used, in an inertial reference frame, can be chosen in many different ways, and that all such choices are equally good.

The first part of that opinion is true. The second part isn't.

To anyone who's opinion includes that second part, I've got these questions for you.

We have all seen how the Lorentz equations (which relate the coordinates in one inertial frame to the coordinates in another inertial frame) are derived ... any textbook on special relativity will give a derivation.

1) Have you ever seen a derivation, of the equations relating two inertial frames, that use any coordinates OTHER THAN the "standard Lorentz coordinates"? (By "standard Lorentz coordinates", I mean the case where one of the four coordinates is a TIME coordinate consisting of the readings on ordinary clocks that are stationary in the given inertial frame, and the other three coordinates are SPATIAL coordinates consisting of the readings on ordinary measuring tapes that are stationary in the given inertial frame).

2) Have you ever seen equations, relating two inertial frames, WRITTEN out, and/or USED in actual calculations, where the coordinates in the equation are OTHER THAN the standard Lorentz coordinates?

3) Have you ever seen the well-known time-dilation result (that everyone has heard about, and probably often used), expressed in terms of coordinates OTHER THAN the standard Lorentz coordinates?

4) Have you ever seen the similarly well-known length-contraction result expressed in terms of coordinates OTHER THAN the standard Lorentz coordinates?

If you took a poll of all work-a-day physicists, asking them the above questions, I think you'd get very few, if any, "Yes" answers. Wonder why not?

To any forum members who answer "yes" to any of those questions: Pick one of those equally-good sets of coordinates for the two inertial frames (different in non-trivial ways from the standard Lorentz coordinates), and, using those coordinates, write out the equations relating the two inertial frames, and then state the time-dilation and length-contraction results, in terms of those coordinates. State how the postulates of special relativity would be specified in those coordinates. And then, since those coordinates are equally good, maybe you should consider writing an entire textbook that exclusively uses those coordinates.

Mike Fontenot


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