Looking to understand time dilation

[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.

 

[ghwellsjr]

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.

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

Length contraction is just as physically real as time dilation is or else a light clock would keep a different time as it was rotated. (Remember MMX?)

A clock can be used to accumulate distance as well as time. If you know your speed relative to some other object, and there are many ways to know this, you can use your clock to determine how far you have traveled from that object. This is how the traveling twin knows how far he has traveled. Note that in the Twin Paradox, each twin has a different measurement of the distance traveled.

 

[Grimble]

- 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.

No, I'm sorry but how can the 'speed of a body be relative to the speed of light which is 'c' for any and every FoR?

-Yes, but an outside observer can only detect what's there,

Yes, of course but if you were to observe two people and one was half the height of the other, or appeared to be because he was further away would you say he was actually shorter than the nearer one. (simple perspective) SO does the clock slow or is it the measuring at speed that makes it appear to slow?

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.

But if he is reading the clock it will still say the same time has passed wherever it is read from, the difference must surely be that the magnitude of the units of time have changed.

Let me put this another way and try to shew you just what is bothering me. Maybe you can explain it to me...

A is a clock and it keeps 'regular' time - (however you want to define regular)- and it will accumulate time at the same rate for ever unless something happens to change it.

If we now introduce an observer B, and we don't meed to say where B is, he could be adjacent to A or he might be hundreds of Light Years away.

Let us say that B is traveling at velocity v relative to A, and therefore A is no longer stationary but traveling at v according to the observer B.

Now you say that B will observe A to be running slow, therefore it is running slow:

but an outside observer can only detect what's there, thus the moving clock must read differently than his.'

So we have clock A running along quite happily on its own at a steady rate but introduce an observer B at ANY distance from A and because they are moving with repect to one another A starts to run slow.

Can anyone explain cause and effect here??

 

[matheinste]

So we have clock A running along quite happily on its own at a steady rate but introduce an observer B at ANY distance from A and because they are moving with repect to one another A starts to run slow.

Can anyone explain cause and effect here??

There is no need to look for a cause as there is no effect on the clock even when constantly observed from the frame in which it is at rest. An observer moving relative to the clock has a different worldview and to that observer the cause of the different preceived rate of the clock is his speed relative to the clock. However to him this rate is part of his "reality", although, of course to this relative observer his own clock is the correct one. There are difficulties here with the terminology when using such words as "perceived, reality" and such like. But this dilation of the time unit, or slowing of the clock is more than a mere optical effect.

This is absolutely fundamental to SR and if reading Einstein's text does not make it clear then try one of the many others out there.

Matheinste.

 

[ghwellsjr]

Grimble--

Some people here think I'm being a little too harsh on you because they think you picked up your false notions from some introductory textbook or other reference that states that there really is no age difference between the traveling twin and the home twin after they re-unite. I have asked you where you picked up that idea but you have not responded. Please tell us where you got that idea.

 

[Grimble]

There is no need to look for a cause as there is no effect on the clock even when constantly observed from the frame in which it is at rest. An observer moving relative to the clock has a different worldview and to that observer the cause of the different preceived rate of the clock is his speed relative to the clock.

So, if I am to understand that this has no physical effect upon the clock, then I am fine with that.

However to him this rate is part of his "reality", although, of course to this relative observer his own clock is the correct one.

Then the clock runs slow, only in the 'reality' of the observer, not in the clock's reality? - I am fine with that, too.

So we have the clock measured(read) at rest showing one time and measured(read) at speed showing a different time? That seems to me to be a difference in the measurement due to the conditions under which the measurement is taken.

If we go a step further we have the conclusion that for every observer traveling at a different relative velocity to the clock, the clock will show a different time.

So to go from here to saying that it is the clock that has a different 'reality' to every observer seems a large leap compared to saying the speed affects/distorts the reading.

So in an effort to resolve this I made the thought experiment I gave earlier:


A----------------------------------------C----------------------------------------B

a->0.8c................0.8c<-b

Where a and b pass A and B respectively at time t0.
AC = CB = 4 light years.
A, B and C have synchronised clocks.
a and b will pass each other at C 5 at t1 = t0 + 5years as measured on C's clock.
a and b each consider themselves to be stationary.
a observes A pass him at 0.8c and at t1 will see see C and b pass him.
b observes B pass her at 0.8c and at time t1 will see C and a pass her.
a and b will each see the other traveling at 0.975c.

But as long as all these calculations are made using the observer's own clocks and the distance AB is measured as 8 light years using A, B and C's rulers. What other conclusions can we make?

A, B, C observe a and b each pass C 5 years after they started at A & B. Therefore they know that they have each traveled 4 light years at 0.8c and that a's and b's clocks will therefore read 5 years as does c's clock.
a and b each know that C passes them at 0.8 c, 5 years after A and B respectively so they can calculate that after traveling for 5 years at 0.8c that AC and CB each = 4 light years.

There can be no time dilation or length contraction in this thought experiment as ALL the measurements have been made using the observers' own clocks.

If A had read a's clock directly he would have seen time dilation as it would be a moving clock; but he doesn't, he times it using his own observers' clocks.

There are difficulties here with the terminology when using such words as "perceived, reality" and such like. But this dilation of the time unit, or slowing of the clock is more than a mere optical effect.

Yet the only part of the whole scenario that is affected by the speed is the observer, or rather, what he observes. The traveling clock is not itself affected as it continues undisturbed in its own FoR and if it were a distance away, say a light year, then, as any effect on it would be instant, it is negating relativity, or at least, the second postulate...


This is absolutely fundamental to SR and if reading Einstein's text does not make it clear then try one of the many others out there.

Matheinste.[/QUOTE]

All I want to see is the logic of how this can be... Science should never be a matter of faith surely.

 

[Grimble]

Grimble--

Some people here think I'm being a little too harsh on you because they think you picked up your false notions from some introductory textbook or other reference that states that there really is no age difference between the traveling twin and the home twin after they re-unite. I have asked you where you picked up that idea but you have not responded. Please tell us where you got that idea.

I am not trying to get you into trouble with anyone Mr. Wells(?) and your response to me is not a problem. As I have said the only 'introductory textbook' I have referenced is http://www.bartleby.com/173/" .

It is a very simple, straightforward and erudite text.

I have tried to shew what difficulties I have with SR as it is today by stating what I have understood and been shown in Einstein's writing.

I am, humbly, looking for explanation of the logic that obviously eludes me. If it is logical and complete then surely someone will be able to show it to me?

Again, many apologies for upsetting the applecart...

Sorry, in case I still haven't answered your question; That is the understanding I have had for many years. I left University in 1969 so you will excuse me, I hope if I cannot give you the titles and authors of the publications.

 

[ghwellsjr]

Einstein says that the traveling twin comes back younger. Why do you deny what he says?

 

[nismaratwork]

I am not trying to get you into trouble with anyone Mr. Wells(?) and your response to me is not a problem. As I have said the only 'introductory textbook' I have referenced is http://www.bartleby.com/173/" .

It is a very simple, straightforward and erudite text.

I have tried to shew what difficulties I have with SR as it is today by stating what I have understood and been shown in Einstein's writing.

I am, humbly, looking for explanation of the logic that obviously eludes me. If it is logical and complete then surely someone will be able to show it to me?

Again, many apologies for upsetting the applecart...

Sorry, in case I still haven't answered your question; That is the understanding I have had for many years. I left University in 1969 so you will excuse me, I hope if I cannot give you the titles and authors of the publications.

From what I can see you've failed to understand the most basic concepts in his paper. My advice would be to approach this in a manner that's more conducive to actually learning the material. Far from upsetting the applecart, you're just being a little difficult, but far from shocking for someone new to the material. You're asking for the logic behind the papers?... they PRESENT their logic, which is new and then explains itself. Subsequent decades have only supported the conclusions presented there, so you might want to take in some more material designed to introduce someone to the basic concept of what "RELATIVE" means.

Your arguments ignore something which has been experimentally verified with cesium clocks in airplanes, and many times since. The logic is this: Einstein is presenting you with a new kind of universe from your previous Newtonian view... beyond that, what do you want, a burning bush to reassure you of SR's current standing?!

 

[matheinste]

So, if I am to understand that this has no physical effect upon the clock, then I am fine with that.



Then the clock runs slow, only in the 'reality' of the observer, not in the clock's reality? - I am fine with that, too.

So we have the clock measured(read) at rest showing one time and measured(read) at speed showing a different time? That seems to me to be a difference in the measurement due to the conditions under which the measurement is taken.

If we go a step further we have the conclusion that for every observer traveling at a different relative velocity to the clock, the clock will show a different time.

So to go from here to saying that it is the clock that has a different 'reality' to every observer seems a large leap compared to saying the speed affects/distorts the reading.



Yet the only part of the whole scenario that is affected by the speed is the observer, or rather, what he observes. The traveling clock is not itself affected as it continues undisturbed in its own FoR and if it were a distance away, say a light year, then, as any effect on it would be instant, it is negating relativity, or at least, the second postulate...


This is absolutely fundamental to SR and if reading Einstein's text does not make it clear then try one of the many others out there.

Matheinste.

All I want to see is the logic of how this can be... Science should never be a matter of faith surely.[/QUOTE]

Excuse for not replying in full to your calculations the reason being that although I am an unknowledgeable lover of mathematics I only find the formulae and comncepts of any beauty, numerical callculations detract from this beauty. I am also very lazy.

Sort of summing up your statements, yes, all measurements or observervations are observer dependent. That is, dependent on the observers state of motion, not on relative position, which is allowed for by taking into account signal travel times.

In regards to measurements being taken, it is my belief that the only clocks and rulers that you can reliably use are those at rest with respect to you. Almost anything that you can say about lengths or times in a frame moving relative to you is arrived at from measurements in your reference frame with your rods and your clocks.

Certain things, such as proper time and the intrerval, are the same for all obsevers and so are not frame or speed dependent, and these things are at the heart of the matter being as it were entities in themselves.

As for being a matter of faith, once you agree to accept the hypotheses as a working basis, which you are of course not obliged to, then whole of SR follows from logic, and we must insist that everyone buys into fundamental logical priciples.

The concepts are fairly simple, but they are not intuitive, that ids usually the problem.

Matheinste.

 

[Mike_Fontenot]

[...]
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.
[...]

The tape measure that I was describing reads the current separation of the twins, at each instant in the traveler's life, ACCORDING TO THE TRAVELER.

But they can EACH have their OWN measuring tape.

The traveler holds the reel-end of HIS tape, with the tip of that tape permanently attached to the home twin. The traveler can read HIS tape to determine their separation, according to HIM, at each instant of HIS life.

The home twin holds the reel-end of HER tape, with the tip of that tape permanently attached to the traveler. The home twin can read HER tape to determine their separation, according to HER, at each instant of HER life.

Note that the above two descriptions of the two tapes are COMPLETELY SYMMETRICAL between the traveler and the home twin. But that symmetry DOESN'T occur in what I'm about to describe.

The point that is frequently missed, about the length contraction result, is this:

Suppose that d_T(t) is the separation of the twins at time t of the TRAVELER'S life, according to HIM.

Then the length contraction result says that d_H(t), which is their separation at time t of the TRAVELER'S life, according to HER, is given by

d_H(t) = gamma * d_T(t) ,

where gamma = 2 in my example. Note that for BOTH distances, the instant in question is time t of the TRAVELER'S life.

For example, take t = 20 years (the time in the traveler's life when he does his instantaneous turnaround).

The traveler says that, since his velocity has been 0.866c for 20 years, that his distance from his twin must be 0.866*20 = 17.32 lightyears.

The home twin says that she was 40 when he was 20 (at the turnaround). So she says he has been moving at 0.866c for 40 years, and therefore their separation must be 0.866*40 = 34.64 lightyears, which agrees with the above equation.

The frequently missed p
oint, is that the above result ISN'T symmetrical between the traveler and the home twin: each of the above distances are the distances at some given instant of the TRAVELER'S life. The equation says that, at some given instant in the traveler's life, the home twin will conclude that their separation is TWICE as great as what the traveler concludes.

There is ANOTHER, DIFFERENT length contraction result, that relates the distances at some given instant of the HOME TWIN'S life. That DIFFERENT equation says that, at some given instant in the HOME TWIN'S life, the home twin will conclude that their separation is HALF as great as what the traveler concludes. I.e., that DIFFERENT equation would be written

D_H(tau) = D_T(tau) / gamma ,

where tau is any given instant in the HOME TWIN'S life. Note that I've use a capital D for the distances in this latter equation, different from the lower-case d that I used in the first equation, because they are different FUNCTIONS, taking a DIFFERENT argument.

For example, take tau = 20 years (the instant in the HOME TWIN'S life when she is 20 years old).

The home twin says that, since the traveler has been moving at 0.866c for 20 years, that his distance from her must be 0.866*20 = 17.32 lightyears.

The traveler says that he was 40 when she was 20. So he says that he has been moving at 0.866c for 40 years, and therefore their separation must be 0.866*40 = 34.64 lightyears, which agrees with the above equation.

The fact that there are TWO DIFFERENT length contraction equations, as described above, is why BOTH the traveler AND the home twin can EACH legitimately and consistently maintain that a moving rod (stationary in the other's frame) is only half as long as the other twin says it is.

Mike Fontenot