Looking to understand time dilation

[Mentz114]

But there are no frame dependent measurements in the Twin Paradox, just like in the real world. In fact, there can be no frame dependent measurements in any scenario, or else we would have a preferred frame and relativity would not be a viable theory about reality.

The meaning of "frame dependent" is the same as "dependent on relative velocity". The observations of the twins depend on their relative velocity at the time of the observation.

 

[ghwellsjr]

It doesn't matter which frame you use, you will determine that each twin makes the same measurements.

 

[Mentz114]

It doesn't matter which frame you use, you will determine that each twin makes the same measurements.

The time-dilation between the two frames is the result of the LT of coordinates between frames. But each twin realizes that the others clock is actually working properly in its rest frame, so how can the time-dilation be given any credence ? What is indisputable is the fact that they will have different ages.

I don't see the paradox.

 

[ghwellsjr]

What you need to do is pick ONE frame. Use time dilation and length contraction as appropriate for each twin as they measure the other one's clock, then you'll see the paradox.

 

[Mentz114]

What you need to do is pick ONE frame. Use time dilation and length contraction as appropriate for each twin as they measure the other one's clock, then you'll see the paradox.

No, I won't see a paradox because there isn't one. It sounds as if you're mixing measurements between frames.

I think it's time to bring on the muon. As you know, this particle decays after a short time and it's life-span can be estimated. When the life-span of a muon is measured in the lab, it is found to be much larger than calculated. This is a space-time diagram of a muon being created from a collision, then decaying a short time later into two other particles. Read the diagram from the bottom up which is how time is flowing. All the spatial movement is on the horizontal line, i.e. left-to-right or right-to-left.

In the lab frame the time measured is 8.9 units, but along the muons worldline the interval is 2.9 units. So what is the life-span of the muon ? I go for the time along the muons line for a very good reason, which I will now give, if you're still following me.

The case I've illustrated shows the muon traveling at 0.8c. Suppose in another lab a similar experiment is done where the muon travels at a different speed. The lab clocks now will give something different from the 8.9 I got but they will get the same value along the muons line. So, do we argue about the lab clock reading, or agree on the muons own time, which will be the same ?

 

[ghwellsjr]

You are the one who is mixing measurements between frames. If you won't do what I'm asking you to do, your eyes will never be open.

 

[matheinste]

What you need to do is pick ONE frame. Use time dilation and length contraction as appropriate for each twin as they measure the other one's clock, then you'll see the paradox.

I don't think this is the twin (non) paradox that we all love so much and never get tired of.

Matheinste.

 

[Mentz114]

GHWells, I think we've said all that can be said and we're not getting through to each other so it's probably best to leave it there.

 

[phyti]

But why do you say that a and b are moving? It is just as true to say that A,B & C are moving at 0.8c relative to a or b.

That's the way you set it up, with A,B, & C in the reference (zero) frame, and a & b moving at .8c relative to it!
We're not dealing with frames in general, but this specific one which you proposed.

 

[granpa]

a and b are stationary and located at the same point and their clocks are synchronized.
b accelerates away at gamma=2
each sees the others clock as time dilated up to the point (call it 'x') that b starts to decelerate.
b reaches 'x' and decelerates to a complete stop
after b stops a perceives that b's clock has ticked half as many times as a's clock.
b agrees.

 

[Mike_Fontenot]

Mentz, you don't think that each twin observing and measuring the other one's clock as running slower than his own during both legs of the trip but yet only the traveler's clock ends up with a lower time is a paradox?

It's not a paradox, because the traveler (he) concludes the home twin (she) suddenly ages during his turnaround. When he adds her ageing during his inertial outbound leg, to her ageing during his turnaround, and then to her ageing during his inbound inertial leg, he gets her correct total ageing at the end of his trip (which of course must agree with HER conclusions about her own ageing during his entire trip).

Take the gamma = 2 case, and suppose he ages 20 years on each of his inertial legs, for a total of 40 years. Then she (according to her) ages 40 years during each of his inertial legs, with no ageing during his turnaround, for a total of 80 years.

According to him, she ages 10 years during each of his inertial legs, for a total on the inertial legs of 20 years, plus 60 years during his turnaround, for a total of 80 years during his entire trip (which agrees with her conclusion, as it of course must). No paradox, no inconsistency.

Anyone who insists that there can be no sudden ageing of the home twin, according to the traveler, during his turnaround, must then conclude that the traveler in NOT actually inertial during his constant-velocity legs. I.e., they must conclude that he isn't allowed to use the time-dilation result during his constant-velocity legs.

Mike Fontenot

 

[phyti]

a and b are stationary and located at the same point and their clocks are synchronized.
b accelerates away at gamma=2
each sees the others clock as time dilated up to the point (call it 'x') that b starts to decelerate.
b reaches 'x' and decelerates to a complete stop
after b stops a perceives that b's clock has ticked half as many times as a's clock.
b agrees.

Not if b uses the SR clock synch method, which results in reciprocal measurements, i.e., b will conclude the a clock is running at half rate. SR is symmetrical/reciprocal by design.

 

[ghwellsjr]

Anyone who insists that there can be no sudden ageing of the home twin, according to the traveler, during his turnaround, must then conclude that the traveler in NOT actually inertial during his constant-velocity legs. I.e., they must conclude that he isn't allowed to use the time-dilation result during his constant-velocity legs.

I insist that there can be no sudden aging of anyone and I do not come to either of your other two conclusions. If you will pay attention to what I am going to explain to you here, then you will also be able to understand what is now evading you. OK? Please pay close attention.

First off, you have to understand how an observer in relative motion to another observer measures the time-dilation of the other observer. It has to do with relativistic doppler. It simply means that each twin has an identical clock that the other one can observe. An easy way to make this happen is for each of them to have a clock that flashes at some interval, say, once per second or once per minute. Each observer will count their own flashes and will count their twin's flashes when they see them. They will also calculate the ratio of the clock rate of their twin's clock compared to their own. As long as they are stationary with respect to each other, their own outgoing flash will occur as often as their twin's incoming flash. When they see the flash rates being identical, they can conclude that there is no relative motion between them and there is no time dilation.

Now as soon as the traveling twin accelerates away and achieves a terminal speed, the ratio of the incoming flashes will be lower than the outgoing flashes. From this ratio, they can each calculate the relative speed between them and from that they can calculate the time-dilation factor. It will be symmetrical, they will both measure the same ratio and detemine the same speed and the same time dilation. While they are moving apart, this ratio will be less than one. At the turn around point, assuming the traveling twin achieves the same speed on the inbound leg as the outbound leg, the traveling twin will immediately see an increase in the doppler frequency, in fact, it will be the reciprocal of what it was before, but this new ratio will determine the same speed as before and the same time dilation as before.

However, the home twin will not see the shift in the doppler frequency (from a ratio of less than one to greater than one) until some time later because it takes time for the distant increased frequency of the flashes of light to reach him. But when it does, he will still determine that the speed of his twin is the same as it was before, just in the opposite direction (approaching instead of retreating) and the time-dilation factor is the same as it was before.

Now what accounts for the difference in the aging of the twins? It is simply that they are counting the low rate doppler versus the high rate doppler for different lengths of time. The traveling twin counts the low rate and high rate coming from the home twin for an equal amount of time (corresponding to the outgoing and incoming legs) but the home twin counts the low rate doppler for much longer than the high rate doppler of the traveling twin so his sum total will be much smaller. They both agree on the final age difference of themselves and their twins and they both agree that the traveling twin aged less.

Now if you want to say that each twin can observe the aging of the other twin, you would have to say that each twin always measures a constant aging of the other twin because the time-dilation factors never change except for the brief moments during acceleration.

Now I want to point out for the sake of others on this thread, that I have not declared any frame of reference in the analysis of the scenario. In fact, it doesn't matter which frame of reference you want to use, the analysis will be identical. All measurements and observations made by observers in a scenario will not change just because you analyze it from different reference frames.

 

[Grimble]

I think I should point out that the classical twin paradox where one remains inertial is just a special case of two worldlines starting at the same point and rejoining after they have done some travelling. In all cases, regardless of how the travellers moved, the elapsed time on their clock will be the Lorentzian length between the parting and meeting of the 4D curves that describe their journeys.

That's it. All observers agree on those elapsed times because they are the geometric invariant of Minkowski spacetime. What more can be said ? There is no paradox or confusion possible about this, surely ?

And the time measured along those those world lines, between two points/events on those world lines will be identical. That is how it seems to me. How can it be anything else?

The Lorentzian length, must be the same for each as calculated from the other, they are, after all, reciprocal journeys, one of the other.

 

[granpa]

Not if b uses the SR clock synch method, which results in reciprocal measurements, i.e., b will conclude the a clock is running at half rate. SR is symmetrical/reciprocal by design.

As I clearly stated, a and b are, at that point, stationary with respect to each other.

 

[Grimble]

Yes. This is called the relativity of simultaneity.

The clock can only show one time, that is what clocks do ...

Isn't it just that different observers read/observe/record different times on that same single clock?

And what has that to do with thehttp://www.bartleby.com/173.html" ?

 

[Grimble]

And which conclusion is that?

Before we can come to any resolution of the Twin Paradox, we have to understand what it is. The two twins start out at the same age in the same location. One of them accelerates away to some high speed. During this time, as they each observe the other's clock, they are each running slower than their own. This part is symmetrical. Eventually, the traveling twin decelerates and comes back at the same high speed. During this time, as they each observe the other's clock, they are each running slower than their own, just like before. The only time when this is not true is during the brief period of time when they observe the process of acceleration/deceleration. Eventually the traveling twin comes to a stop at the starting point and when they compare the actual times on their clocks, the traveling one has less time on it. Do you agree with this as a statement of the Twin Paradox?

Yes that is the twin paradox, but I don't see any reason at all why the acceleration should have that effect. The paradox to me is that they should each see that the other is younger than they are and that occurs in the outward leg of the journey.

 

[granpa]

acceleration changes the relativity of simultaneity which changes the accelerating twins calculated value of the present time on the stationary twins clock

 

[Grimble]

acceleration changes the relativity of simultaneity which changes the accelerating twins calculated value of the present time on the stationary twins clock

Yes, it changes the angle of rotation between the FoRs?

 

[Dale]

The clock can only show one time, that is what clocks do ...

Isn't it just that different observers read/observe/record different times on that same single clock?

And what has that to do with thehttp://www.bartleby.com/173.html" ?

One clock only reads a single number at any given event, and all observers in all reference frames agree on that value. But that is not the issue here. The issue here is how two different clock's times compare, and that is determined by the relativity of simultaneity.

 

[ghwellsjr]

And which conclusion is that?

Before we can come to any resolution of the Twin Paradox, we have to understand what it is. The two twins start out at the same age in the same location. One of them accelerates away to some high speed. During this time, as they each observe the other's clock, they are each running slower than their own. This part is symmetrical. Eventually, the traveling twin decelerates and comes back at the same high speed. During this time, as they each observe the other's clock, they are each running slower than their own, just like before. The only time when this is not true is during the brief period of time when they observe the process of acceleration/deceleration. Eventually the traveling twin comes to a stop at the starting point and when they compare the actual times on their clocks, the traveling one has less time on it. Do you agree with this as a statement of the Twin Paradox?

Yes that is the twin paradox, but I don't see any reason at all why the acceleration should have that effect. The paradox to me is that they should each see that the other is younger than they are and that occurs in the outward leg of the journey.

If you agree that the traveling twin in the Twin Paradox ends up aging less than the home twin, we do you insist that the traveler, a, in your scenario ends up aging the same as the stationary observer, A?

Also, why do you think the time-dilation occurs only on the outward leg of the journey?--it occurs during the entire journey except for the brief intervals of acceleration/deceleration.

Please explain your concern about acceleration, it's just the way one twin gets to a new speed with respect to the other twin. The acceleration itself has no affect on the age, it just changes the aging rates. They have to spend time at the relative speed for the different aging rates to result in a different ages. If you don't understand that, please be more specific in your questions/comments.

 

[Grimble]

If you agree that the traveling twin in the Twin Paradox ends up aging less than the home twin, we do you insist that the traveler, a, in your scenario ends up aging the same as the stationary observer, A?

No he ages the same but that age appears to be less to the other twin.
Each sees the other as younger.

Also, why do you think the time-dilation occurs only on the outward leg of the journey?--it occurs during the entire journey except for the brief intervals of acceleration/deceleration.

Time dilation occurs for the whole time that they are moving one to the other.
The amount of time dilation is a function of the current velocity and exists only while the relative motion exists, and it changes every time their relative velocity changes. But once they come to rest with each other and there is no longer a relative velocity there is, no longer, any time dilation. As an effect of their motion it can only exist while there is motion.

Please explain your concern about acceleration, it's just the way one twin gets to a new speed with respect to the other twin. The acceleration itself has no affect on the age, it just changes the aging rates. They have to spend time at the relative speed for the different aging rates to result in a different ages. If you don't understand that, please be more specific in your questions/comments.

Yes acceleration merely changes the apparent ageing rate;
and No, the length of time spent in motion has no effect whatsoever, the ONLY thing that affects the amount of time dilation is the current velocity.

 

[Passionflower]

I include a spacetime diagram of 5 twins, the elapsed time on the twins clocks depends on the length of their spacetime paths, only when the lengths are identical they will record an identical elapsed time.
[PLAIN]http://img713.imageshack.us/img713/9677/event.gif

 

[Grimble]

Diagram 1. The Minkowski diagram of the twin paradox drawn to scale.
The diagram is the FoR of the resting twin. (the floater)
As it is from that FoR, the travellers times and distances are dilated and contracted respectively'

http://img707.imageshack.us/img707/3873/simultaneity.jpg

Uploaded with ImageShack.us

Diagram 2. The path of the traveller shown as rotations, the rotation changing as the traveller decelerates and returns.

http://img17.imageshack.us/img17/9214/figure5z.jpg

Uploaded with ImageShack.us

When the velocity is shown as rotation a change in the velocity will be shown as the rotation increasing or decreasing and the corresponding contracted length changing.

 

[Mike_Fontenot]

Anyone who insists that there can be no sudden ageing of the home twin, according to the traveler, during his turnaround, must then conclude that the traveler in NOT actually inertial during his constant-velocity legs. I.e., they must conclude that he isn't allowed to use the time-dilation result during his constant-velocity legs.

I insist that there can be no sudden aging of anyone and I do not come to either of your other two conclusions.
[...]

Using the gamma = 2 example I gave previously, it is indisputable that the TOTAL ageing by the home twin, during the entire trip, must be 80 years. The home twin AND the traveler can't possibly disagree about that fact.

IF you insist that, ACCORDING TO THE TRAVELER, the home twin doesn't age AT ALL during the turnaround, then he (the traveler) must conclude that ALL of her (the home twin's) ageing must occur during the two constant-velocity legs of the trip. So the sum of her ageing during his two constant-velocity legs MUST be 80 years (while he ages a total of only 40 years).

But if you consider him to be "inertial" on his OUTBOUND leg (and thus justified in using the time-dilation result), he would conclude that she ages only 10 years during his outbound leg.

Similarly, if you consider him to be "inertial" on his INBOUND leg (and thus justified in using the time-dilation result), he would conclude that she ages only 10 years during his inbound leg.

So, if you consider him to be inertial on BOTH of his constant-velocity legs, AND if you Insist that she doesn't age (according to him) during his turnaround, then he MUST conclude that her TOTAL ageing during his entire trip was only 20 years. But it is indisputable that her total ageing during his entire trip is 80 years. There is a missing 60 years. Where does it occur?

ANY proposed alternative frame for the traveler that gives zero ageing for the home twin during the traveler's turnaround, MUST get a total of 80 years for the home twin's ageing during the two constant-velocity legs. There is just no way of avoiding that (given the insistence that no ageing occurs during the turnaround).

If you insist that there is no ageing of the home twin (according to the traveler) during the turnaround, then you have various alternatives for apportioning the required 80 years of home-twin ageing, among the two constant-velocity legs.

You can adopt PassionFlower's frame for the traveler, in which the traveler is inertial (and thus justified in using the time-dilation result) during the outbound leg, but NOT on the inbound leg. So, in that alternative, the total home-twin ageing during the traveler's outbound leg is 10 years, and so her total ageing during his inbound leg must be 70 years.

Or, you can use the Dolby & Gull frame for the traveler, in which the traveler isn't inertial (and thus isn't justified in using the time-dilation result) in EITHER of the constant-velocity legs.

I consider both of those alternatives to be fatally flawed. I have critiqued both of them in another thread, starting with this posting:

https://www.physicsforums.com/showpost.php?p=2983139&postcount=76 ,

and continuing in the following two posts.

Mike Fontenot

 

[phyti]

Diagram 1. The Minkowski diagram of the twin paradox drawn to scale.
The diagram is the FoR of the resting twin. (the floater)
As it is from that FoR, the travellers times and distances are dilated and contracted respectively'

Time dilation means the time units get stretched, not shortened. The clock slices time into longer intervals.
https://www.physicsforums.com/attachments/30116

 

[granpa]

 

[Dale]

Anyone who insists that there can be no sudden ageing of the home twin, according to the traveler, during his turnaround, must then conclude that the traveler in NOT actually inertial during his constant-velocity legs.

Nonsense. Whether or not a given worldline is inertial at some event is coordinate-independent. Specifically, a worldline is inertial iff the magnitude of the proper acceleration is zero.

 

[ghwellsjr]

The acceleration itself has no affect on the age, it just changes the aging rates. They have to spend time at the relative speed for the different aging rates to result in a different ages.

Yes acceleration merely changes the apparent ageing rate;
and No, the length of time spent in motion has no effect whatsoever, the ONLY thing that affects the amount of time dilation is the current velocity.

Grimble,

I have a digital alarm clock that I normally leave plugged into the wall when I'm at home and it keeps perfect time because it is getting its time base from the line frequency which is maintained to be accurate. However, when I take this clock on a trip, I have to unplug it from the wall and then it uses an internal battery and crystal oscillator to keep track of the time but this timebase is off and it runs 1% slow. Whenever I get where I'm going, I have to readjust the time.

For example, on my last trip, I traveled for 5 hours which is 300 minutes so it "lost" 3 minutes. If I momentarily uplug the clock and move it to another room and plug it in again, I cannot tell that it has lost any time even though I know that during that brief period of time, it was running 1% slow. We could say that while the clock is traveling, it is experiencing a time-dilation of 1%. I think you can see that the clock has to spend time traveling in order for there to be any time lost on the lock and the longer it travels, the more time is lost.

You are correct that the amount of time-dilation is a function of velocity only, but that just means the clock is running slower. If the moving clock doesn't spend much time at speed but quickly reverts back to its stationary state, then there won't be much slow-down of the clock. But if it spends a very long time at velocity, then the clock gets more and more behind and it doesn't somehow recover when it stops just like my alarm clock doesn't automatically switch back to the correct time after a long trip. It does switch back to the correct timebase but not the correct time.

Does this help you see the difference between aging rate and age? Or time-dilation and time "lost"?

 

[Grimble]

Grimble,

I have a digital alarm clock that I normally leave plugged into the wall when I'm at home and it keeps perfect time because it is getting its time base from the line frequency which is maintained to be accurate. However, when I take this clock on a trip, I have to unplug it from the wall and then it uses an internal battery and crystal oscillator to keep track of the time but this timebase is off and it runs 1% slow. Whenever I get where I'm going, I have to readjust the time.

For example, on my last trip, I traveled for 5 hours which is 300 minutes so it "lost" 3 minutes. If I momentarily uplug the clock and move it to another room and plug it in again, I cannot tell that it has lost any time even though I know that during that brief period of time, it was running 1% slow. We could say that while the clock is traveling, it is experiencing a time-dilation of 1%. I think you can see that the clock has to spend time traveling in order for there to be any time lost on the lock and the longer it travels, the more time is lost.

You are correct that the amount of time-dilation is a function of velocity only, but that just means the clock is running slower. If the moving clock doesn't spend much time at speed but quickly reverts back to its stationary state, then there won't be much slow-down of the clock. But if it spends a very long time at velocity, then the clock gets more and more behind and it doesn't somehow recover when it stops just like my alarm clock doesn't automatically switch back to the correct time after a long trip. It does switch back to the correct timebase but not the correct time.

Does this help you see the difference between aging rate and age? Or time-dilation and time "lost"?

No, because time dilation is only an effect seen by a remote observer moving with a relative velocity to the clock that is time dilated.

The whole idea that a clock can actually be time dilated because of it's speed is untenable!
Due to its speed relative to what?
Relative to an 'observer'? - then it would be something that only that observer would see.
The clock doesn't run any differently, it still follows its own world line and keeps proper time.
Any inertial clock in space can be considered to be stationary, it does not and cannot have any speed as a property of the clock only in respect to another body.

So time dilation is and can only be an effect observed by the moving observer caused by the way he takes his measurement. If the moving observer measures using his own clock he will find that time is not dilated.

 

[Grimble]

The relationship of times as experienced by two moving FoR

http://img440.imageshack.us/img440/5448/specialrelativitydiagra.jpg

Uploaded with ImageShack.us

 

[Dale]

Hi Grimble, there are a few problems with this chart.

1) In spacetime diagrams the time axis is traditionally vertical and the space axis is horizontal. It is ok to switch it around, but then you should label it.

2) For AA (the clock going horizontally from A and staying on A) coordinate time will match proper time.

3) For BB coordinate time will match proper time.

4) For AB proper time will be slower than coordinate time by a factor of 0.8, meaning that on the line where coordinate time is 5 the proper time for AB is 4, not 5.

5) Similarly for BA.

6) You have not shown any lines of simultaneity for AB or BA, only for AA and BB.

 

[ghwellsjr]

No, because time dilation is only an effect seen by a remote observer moving with a relative velocity to the clock that is time dilated.

The whole idea that a clock can actually be time dilated because of it's speed is untenable!
Due to its speed relative to what?
Relative to an 'observer'? - then it would be something that only that observer would see.
The clock doesn't run any differently, it still follows its own world line and keeps proper time.
Any inertial clock in space can be considered to be stationary, it does not and cannot have any speed as a property of the clock only in respect to another body.

So time dilation is and can only be an effect observed by the moving observer caused by the way he takes his measurement. If the moving observer measures using his own clock he will find that time is not dilated.

Why didn't you start your posts by saying, "I don't believe in the Twin Pararox, I don't believe that when the traveling twin takes a trip and comes back to his home twin that there will be any difference in their ages. Einstein was wrong and so are all you people on this forum that are promoting Special Relativity."

Why are you wasting everyone's time here by posting spacetime drawings and posting thought experiments?

A lot of people here are taking you seriously, thinking you are just making a few technical blunders and that you could be helped by a little education.

From now on, if you want to post anything more, please start by saying, "I don't believe in Special Relativity" and then put down your inane comment or question and you won't waste all our time. If you don't state clearly that you are promoting an alternate theory which is prohibited on this forum, I will post it after you and I will report every one of your posts.

 

[Grimble]

Why didn't you start your posts by saying, "I don't believe in the Twin Pararox, I don't believe that when the traveling twin takes a trip and comes back to his home twin that there will be any difference in their ages. Einstein was wrong and so are all you people on this forum that are promoting Special Relativity.

I am sorry if it appears that way

I do not say that Einstein was wrong, what I am saying is that that these are the problems I have with other's explanations of his theory, where I do not follow their logic.

And that is not, Einstein's Logic which seems very clear and straightforward; but the logic of some of the extensions, explanations and conclusions that seem to have been drawn from Einstein's Theory.

A lot of people here are taking you seriously, thinking you are just making a few technical blunders and that you could be helped by a little education.

And I do appreciate all your efforts.

All I am saying is what I find is the logical outcome of what is explained.

I want to see how and where I am going wrong.

But just restating what I can read in many places doesn't help.

In the quoted post I was trying to help you see where I am seeing something that seems illogical.

I have been researching and trying to understand all about SR for a long time now but have found that there are some areas where the logic of some conclusions eludes me.

No doubt that is my fault but that is what I am trying to address; and I cannot address it without showing you where I have the problem and what that problem is.

From now on, if you want to post anything more, please start by saying, "I don't believe in Special Relativity" and then put down your inane comment or question and you won't waste all our time. If you don't state clearly that you are promoting an alternate theory which is prohibited on this forum, I will post it after you and I will report every one of your posts.

AS I have already said; I am not promoting anything, I am trying to further my understanding.

I do believe in what Einstein wrote. The core of my understanding is http://www.bartleby.com/173/"

Once again, let me say, I have no intention of promoting any other theory as I am a great fan of Einstein.

And I apologise for upsetting you after the kindness you all show by answering my questions.

 

[ghwellsjr]

Yes I agree that they are not what you were taught but in what way are they incorrect?

Why does modern thinking add such a load of baggage onto a simple clear principle?

I am so sorry that you still believe that I don't understand exactly what you are saying. I do and I have from the moment I first came across these concepts. It is simple and straightforward.

Differential ageing is something that occurs when an observer observes a moving clock.
The observer at rest observes the traveling clock to slow.
The traveling observer observes the resting clock to slow.
The only way this can be true is if neither clock actually slows and the slowing is merely an effect of measuring a moving object.

Simple logic leads to this conclusion however one thinks about it. Simple logic. Every explanation that says different has holes in it big enough to drive a bus through.

But those holes are obscured by assumptions that are seemingly accepted without any thought by everyone who understands differential ageing.

Saying go away and try again.

I have NO PRECONCEPTIONS. That is precisely the point. The accepted explanations are the ones with preconceptions that are unfounded.

Grimble

Any careful examination of LT shows that it is only an observed effect. Like the projection of an image depending on the distance it is projected and the angle of the screen upon which it is projected.
...
I can draw a set of simple diagrams that demonstrate EXACTLY how all this works. It is all VERY SIMPLE.

But it doesn't does it? It only appears to because of the distortion caused by taking measurements at speed.
...
Yet it doesn't does it? There is nothing in Einstein's SR that says that it would, only that the observer at rest would see it run slow.

BUT is those two observers were to compare the measurements taken only within their own FoRs they would agree about the results.

Well, again we have a difference between the accepted wisdom and teachings of the Minkowski diagram showing the dogleg portrayal of the traveling twin's journey.
...
Resolving these issues by drawing diagrams that reflect reality and answer all these points shows that indeed a anb will continue to have the same times on their clocks!

The important point is that time dilation (and Length contraction) only occurs when one is reading the others clocks.

I must apologise if I seem to be getting a bit excited but this is fascinating and I don't mean to be a pain but these things just don't fit as everyone thinks they do.
...
No, I'm sorry for I know that is what you have been taught, that is what everyone is taught, and so no-one bothers to work it out and see the errors.

If the diagram is drawn correctly all the errors disappear and it all starts to make sense.

I am not trying to rewrite Special Relativity but to understand something that doesn't seem to fit logically, when there is a much simpler way of seeing it - drawing the diagram - so everything fits.

It is not the science I have a problem with but the depiction of it.

These quotes show that you are not trying to learn but to teach.

And you have a serious problem with science if you do not accept the fact that the traveling twin is younger after his trip than the home twin.

 

[yuiop]

Why didn't you start your posts by saying, "I don't believe in the Twin Pararox, I don't believe that when the traveling twin takes a trip and comes back to his home twin that there will be any difference in their ages. Einstein was wrong and so are all you people on this forum that are promoting Special Relativity."

Why are you wasting everyone's time here by posting spacetime drawings and posting thought experiments?

A lot of people here are taking you seriously, thinking you are just making a few technical blunders and that you could be helped by a little education.

From now on, if you want to post anything more, please start by saying, "I don't believe in Special Relativity" and then put down your inane comment or question and you won't waste all our time. If you don't state clearly that you are promoting an alternate theory which is prohibited on this forum, I will post it after you and I will report every one of your posts.

I think you are being a little harsh on Grimble here and I believe he is genuinely trying to understand what is going on here. People who don't understand the twin's paradox usually do think believe in Special Relativity. When introduced to SR they are usually taught that when one observer is moving relative to another, that each observer sees the other observer's clock to be ticking slower than their own clock and both observers are equally right! This leads to the impression that time dilation in SR is not physically real and the twin paradox comes as a bit of a shock and seems to be a contradiction to what they have been taught. Rather than blame people like Grimble for being confused and assume they are being subversive, blame the over simplistic "educational texts" that they have been using. Let us take length contraction for example. Two observers moving relative to each other each measure the other's ruler to shorter than there own, but when they come to rest relative to each other they find the rulers are in fact the same length and so length contraction just appears to be a measurement abstraction with no real physical significance (a lot of people believe this). Is it not reasonable for someone new to relativity to assume time dilation is a similar measurement abstraction with no real physical significance given the treatment of the subject in some introductory texts? Would you agree that a lot of older texts claim that the twins experiment cannot be explained by SR because it involves acceleration (this is not true) and that GR is required to explain it. Would you not be shocked if you learned that the ruler of a traveling twin was shorter than the ruler of inertial twin when they came back together? Of course this does not really happen in the case length contraction, but it is not immediately obvious to a newcomer, why time dilation appears to be physically real and length contraction does not. I think rather than take an aggressive stance, you should ask why there is so much confusion about the twins paradox (witness the hundreds of twins paradox threads and confused posters asking about it) and how we can better explain it, or better still ask how SR can be better introduced/conceptualised/explained, so that the twins paradox does not seem so paradoxical. Basically I am saying, blame the "education system" rather than the pupils.

 

[matheinste]

Would you not be shocked if learned that the ruler of a traveling twin was shorter than the ruler of inertial twin when they came back together? Of course this does not really happen in the case length contraction, but it is not immediately obvious to a newcomer, why time dilation appears to be physically real and length contraction does not.

Yes I would be shocked because it it is not analgous to time dilation. This is how i interpret
that particular "diffrerence" between the behaviour of a ruler and a clock, however, I am open to correction.
A clock measures and records the accumulated measure along the timelike vectors of the spacetime path taken, and on reuniting with its equavalent stay at home clock ticks at the same rate as before, while also displaying the different accumulasted time. A ruler measures, but does not itself record this cumulative measure of the spacelike vectors along the path taken, but similarly, of course is of the same length of its stay at home couterpart on reuniting.

Matheinste

 

[yuiop]

Yes I would be shocked because it it is not analgous to time dilation. This is how i interpret
that particular "diffrerence" between the behaviour of a ruler and a clock, however, I am open to correction.
A clock measures and records the accumulated measure along the timelike vectors of the spacetime path taken, and on reuniting with its equavalent stay at home clock ticks at the same rate as before, while also displaying the different accumulasted time. A ruler measures, but does not itself record this cumulative measure of the spacelike vectors along the path taken, but similarly, of course is of the same length of its stay at home couterpart on reuniting.

Matheinste

That seems reasonable and is perhaps one of the aspects that should be made clearer in introductory texts ;)

 

[phyti]

No, because time dilation is only an effect seen by a remote observer moving with a relative velocity to the clock that is time dilated.

The whole idea that a clock can actually be time dilated because of it's speed is untenable!
Due to its speed relative to what?

- relative to the speed of light, or more precisely the point of its emission.
Someone at the back of a boat moving across the water, drops a stone into the water. The stone causes waves that move outward from the entry point and past the front of the boat. The time taken for the lead wave to travel from the back of the boat to the front depends on the speed of the boat. The wave speed depends on the properties of the water and is independent of the speed of the boat.
The water represents space (whatever it is), the waves represent light propagation, and the boat is the persons ref. frame.
The point is, the faster the boat moves, the more time required for the wave to travel the length of the boat. Substitute a photon for the wave and you have the essence of the light clock.

Relative to an 'observer'? - then it would be something that only that observer would see.
The clock doesn't run any differently, it still follows its own world line and keeps proper time.
Any inertial clock in space can be considered to be stationary, it does not and cannot have any speed as a property of the clock only in respect to another body.

-Yes, but an outside observer can only detect what's there, thus the moving clock must read differently than his. The owner of the moving clock is himself a composition of matter regulated by biological clocks, and is subject to the same slower rate of processes as the clock, along with his computer, and everything and anyone that travels with him. Since his sense of time agrees with his clock, his clock appears normal to him. Yes, it is HIS proper time, but it's also altered time.

 

[Mike_Fontenot]

[...]
Yes I would be shocked because it [length contraction] is not analgous to time dilation.
[...]

I suspect the essence of the difference, is that time and space actually AREN'T as "equivalent" as many modern treatments of special relativity try to make them.

Mike Fontenot

 

[Grimble]

These quotes show that you are not trying to learn but to teach.

And you have a serious problem with science if you do not accept the fact that the traveling twin is younger after his trip than the home twin.

I am sorry that you are still having a problem with what I have been saying. Some time ago I spent time asking about these aspects of SR and all I had in response was protestations of this is how it is ... but what I was needing to understand was WHY that as the way it worked or how it worked.

So I decided that if I said "surely it works like this ..." someone would EXPLAIN with reasons why I was wrong; I have been using Einstein's explanations and formulae and trying to apply them and get the results I am being advised of but failing. I am not saying I am right, I don't expect to be right but I would like to know WHY and HOW I am wrong.

AS I say repeatedly being told conclusions explains nothing.

If I could look these things up, I would have, but I cannot find anywhere where they are related back to what Einstein wrote.

AS I said above I have no intention of upsetting anyone but what should I do??

 

[Dale]

I would like to know WHY and HOW I am wrong.

AS I say repeatedly being told conclusions explains nothing.

Why don't we go over your figure. I pointed out several problems, let's start there.

 

[matheinste]

I suspect the essence of the difference, is that time and space actually AREN'T as "equivalent" as many modern treatments of special relativity try to make them.

Mike Fontenot

I was trying to point out that they are analogous, not entirely different, but that clocks record accumulated "time" but rulers do not record accumulated "distances"

If rulers kept a record of their travels then the accumulated distances of stay at home and traveller woulrd not be the same. An exact analogy with clocks. Stay at home ruler would read zero, traveling ruler would not. It would read greater than zero, that is, more than than stay at home and so Reciprocal to clocks.

Matheinste.

 

[ghwellsjr]

I think you are being a little harsh on Grimble here and I believe he is genuinely trying to understand what is going on here. People who don't understand the twin's paradox usually do think believe in Special Relativity. When introduced to SR they are usually taught that when one observer is moving relative to another, that each observer sees the other observer's clock to be ticking slower than their own clock and both observers are equally right! This leads to the impression that time dilation in SR is not physically real and the twin paradox comes as a bit of a shock and seems to be a contradiction to what they have been taught. Rather than blame people like Grimble for being confused and assume they are being subversive, blame the over simplistic "educational texts" that they have been using. Let us take length contraction for example. Two observers moving relative to each other each measure the other's ruler to shorter than there own, but when they come to rest relative to each other they find the rulers are in fact the same length and so length contraction just appears to be a measurement abstraction with no real physical significance (a lot of people believe this). Is it not reasonable for someone new to relativity to assume time dilation is a similar measurement abstraction with no real physical significance given the treatment of the subject in some introductory texts? Would you agree that a lot of older texts claim that the twins experiment cannot be explained by SR because it involves acceleration (this is not true) and that GR is required to explain it. Would you not be shocked if you learned that the ruler of a traveling twin was shorter than the ruler of inertial twin when they came back together? Of course this does not really happen in the case length contraction, but it is not immediately obvious to a newcomer, why time dilation appears to be physically real and length contraction does not. I think rather than take an aggressive stance, you should ask why there is so much confusion about the twins paradox (witness the hundreds of twins paradox threads and confused posters asking about it) and how we can better explain it, or better still ask how SR can be better introduced/conceptualised/explained, so that the twins paradox does not seem so paradoxical. Basically I am saying, blame the "education system" rather than the pupils.

There is no textbook, no teacher, no reference that says what Grimble believes. I already asked him where he got his ideas from:

So, you think that the Twin Paradox is that at the end, prior to the traveling twin stopping,
each one thinks that they have aged 10 years but their twin has aged only 6 years, and then when the traveling twin stops, they both agree that both of them have aged 10 years, correct?

If this is how you see it, then the two twins are always symmetrical, correct? And it doesn't matter which one takes the trip, correct?

Can you find a reference that describes the Twin Paradox like this? I'm interested in knowing where you learned this.

He did not give me a reference.

 

[ghwellsjr]

Someone at the back of a boat moving across the water, drops a stone into the water. The stone causes waves that move outward from the entry point and past the front of the boat. The time taken for the lead wave to travel from the back of the boat to the front depends on the speed of the boat. The wave speed depends on the properties of the water and is independent of the speed of the boat.
The water represents space (whatever it is), the waves represent light propagation, and the boat is the persons ref. frame.
The point is, the faster the boat moves, the more time required for the wave to travel the length of the boat. Substitute a photon for the wave and you have the essence of the light clock.

No, you have half a light clock. You also need the other half which is a mirror to reflect the light pulse back to its source where you also need a detector to recreate the next light pulse and provide an output to the observer.

 

[Mike_Fontenot]

[...]
I suspect the essence of the difference, is that time and space actually AREN'T as "equivalent" as many modern treatments of special relativity try to make them.
[...]

[...]
I was trying to point out that they are analogous, not entirely different, but that clocks record accumulated "time" but rulers do not record accumulated "distances"
[...]

It wasn't my intention to refute or rebut your comments. I actually thought they were very interesting and thought-provoking. But I also thought that there was more that could (and should) be said about the issue.

I think the spatial analogy with the clock is not a ruler, but rather a measuring tape whose end is always anchored at the home twin, and whose rolled-up end stays with the traveler ... so it always reads the current separation of the twins, according to the traveler. The analogous time is the current reading on the home twin's clock, according to the traveler.

When I first read your post, my immediate reaction was that the root of the difference was that (in the standard traveling twin scenario) that the traveler can (and does) return to his initial distance from the home twin (zero), but he CAN'T return to the initial TIME on her clock. So that IS a fundamental difference in the way time works, versus the way space works. Causality imposes an asymmetry.

And, even though the standard traveling twin scenario is just a specific example, I think it DOES suggest something quite general: space and time ARE different, even in special relativity. They are not completely independent as they are in Newtonian physics, but they aren't completely equivalent, either. The fact, that the time coordinate and the spatial coordinates show up in the mathematics of special relativity in ways that are almost symmetrical, has led (in my opinion) to an overreaching attempt to treat them as completely equivalent. But they are NOT completely equivalent. The fact the time and spatial coordinates have different signs in the metric is an immediate hint that they are not completely equivalent.

Mike Fontenot

 

[matheinste]

It wasn't my intention to refute or rebut your comments. I actually thought they were very interesting and thought-provoking. But I also thought that there was more that could (and should) be said about the issue.

I think the spatial analogy with the clock is not a ruler, but rather a measuring tape whose end is always anchored at the home twin, and whose rolled-up end stays with the traveler ... so it always reads the current separation of the twins, according to the traveler. The analogous time is the current reading on the home twin's clock, according to the traveler.

When I first read your post, my immediate reaction was that the root of the difference was that (in the standard traveling twin scenario) that the traveler can (and does) return to his initial distance from the home twin (zero), but he CAN'T return to the initial TIME on her clock. So that IS a fundamental difference in the way time works, versus the way space works. Causality imposes an asymmetry.

And, even though the standard traveling twin scenario is just a specific example, I think it DOES suggest something quite general: space and time ARE different, even in special relativity. They are not completely independent as they are in Newtonian physics, but they aren't completely equivalent, either. The fact, that the time coordinate and the spatial coordinates show up in the mathematics of special relativity in ways that are almost symmetrical, has led (in my opinion) to an overreaching attempt to treat them as completely equivalent. But they are NOT completely equivalent. The fact the time and spatial coordinates have different signs in the metric is an immediate hint that they are not completely equivalent.

Mike Fontenot

Thanks for your comments.

I understand your use of the unwinding tape, but it is flawed in regards to my analogy. Yes when the traveler returns he returns to the same distance away from the stay at home as when he started his journey, that is zero. But I am dealing with cumulative distance traveled not coordinate translated distance from another object. If I walk one meter in a straight line and return by the reversed path to my starting place, my final distnce from my starting point is zero meters, but I have accumulated two meters on my meter counter.

Matheinste.

 

[Mike_Fontenot]

[...]
I understand your use of the unwinding tape, but it is flawed in regards to my analogy.
[...]

But I think the two quantities that I gave are the ones that are DIRECTLY involved in the time-dilation result, and in the length-contraction result.

Mike Fontenot

 

[ghwellsjr]

I think the spatial analogy with the clock is not a ruler, but rather a measuring tape whose end is always anchored at the home twin, and whose rolled-up end stays with the traveler ... so it always reads the current separation of the twins, according to the traveler. The analogous time is the current reading on the home twin's clock, according to the traveler.

Tell me Mike, in your Twin Paradox scenario you proposed several posts back, how much tape gets played out?

And how does this relate to time dilation and length contraction?

 

[yuiop]

I think the spatial analogy with the clock is not a ruler, but rather a measuring tape whose end is always anchored at the home twin, and whose rolled-up end stays with the traveler ... so it always reads the current separation of the twins, according to the traveler. The analogous time is the current reading on the home twin's clock, according to the traveler.

I like the idea of the measuring tape as an instrument that measures accumulated distance similar to the way a clock measures accumulated elapsed time. I would add one small correction. The measuring tape reads the current separation according to the stay at home twin. For example let us say the traveling twin is traveling away from Earth at 0.8c for 2 years (Earth time) then he will be 1.6 lightyears away from Earth and this is what the tape measure will read and this is the distance the traveling twin has traveled according to the Earth twin. The traveling twin will consider themselves to have traveled 1.6*0.6 = 0.96 lightyears because the distance will appear to be length contracted to the traveller. A device that measures the number of rotations of the tape spool (or a rolling wheel) and calculates the accumulated distance based on the assumed rest circumference of the wheel (similar to a car odometer) will measure the length contracted distance (0.96 lightyears) that the traveling twin considers the distance to be.