View Full Version : Tensors and Time Dilation?

tommac

2010-Jul-02, 03:36 PM

One thing that has been confusing me is how can there only be one time dimension?

If I curve space in X direction ... then I would need to dilate time to keep the speed of light constant for a beam of light that is travelling along the X axis. Right?

But how does that effect the Y direction? So if time is dilated as above but space is not curved in the Y direction then how can the speed of light stay constant?

I have a gut feeling that it is addressed in the ricci tensor ... but really not sure how ... firstly is that right? Secondly can someone explain how this issue is addressed?

korjik

2010-Jul-02, 03:41 PM

it is handled in the v^2 term in SR. Takes the directional dependence out of the equation.

There is a reason that all those little vector symbols are used in physics.

grapes

2010-Jul-02, 04:24 PM

If I curve space in X direction ... then I would need to dilate time to keep the speed of light constant for a beam of light that is travelling along the X axis. Right? I'm not exactly sure what you mean by "curve space in the X direction" but one thing that may clear up the confusion is that light follows a geodesic in spacetime--if space is curved, light will follow the curvature. Light would not be able to go in a straight line, in that sense.

tommac

2010-Jul-02, 06:06 PM

it is handled in the v^2 term in SR. Takes the directional dependence out of the equation.

There is a reason that all those little vector symbols are used in physics.

Can you go into this a little bit?

tommac

2010-Jul-02, 06:09 PM

I'm not exactly sure what you mean by "curve space in the X direction" but one thing that may clear up the confusion is that light follows a geodesic in spacetime--if space is curved, light will follow the curvature. Light would not be able to go in a straight line, in that sense.

OK ... say that I was either travelling quickly towards a point along the x axis or towards the center of a black hole ...

my time would warp and space in the direction of travel would warp ...

but ... if I shine a flashlight along the y or z access or in a tangent to the EH of a black hole then space should NOT be curved in that direction right? But since there is only one time ... then time would the same regardless of the direction that I shine the light ( x axis or y axis )

Andrew D

2010-Jul-02, 06:41 PM

OK ... say that I was either travelling quickly towards a point along the x axis or towards the center of a black hole ...

my time would warp and space in the direction of travel would warp ...

but ... if I shine a flashlight along the y or z access or in a tangent to the EH of a black hole then space should NOT be curved in that direction right? But since there is only one time ... then time would the same regardless of the direction that I shine the light ( x axis or y axis )

does not compute.

tommac

2010-Jul-02, 08:59 PM

does not compute.

x------->------>------->------>wall

If I am traveling along the x axis ( lets assume 2d space ( x,y ) + time ) ....

and I shined a flashlight in the direction of movement my space with respect to a wall, space in the direction of travel would be warped, but only in the direction of travel, correct?

Nereid

2010-Jul-02, 09:04 PM

x------->------>------->------>wall

If I am traveling along the x axis ( lets assume 2d space ( x,y ) + time ) ....

and I shined a flashlight in the direction of movement my space with respect to a wall, space in the direction of travel would be warped, but only in the direction of travel, correct?

No.

Mass-energy has an effect on all of space-time; or, in Wheeler's words "spacetime tells mass how to move, while mass tells spacetime how to curve".

loglo

2010-Jul-02, 09:08 PM

The lack of time dilation in the directions transverse to travel comes straight from SR. No need to invoke tensors.

tommac

2010-Jul-02, 09:19 PM

The lack of time dilation in the directions transverse to travel comes straight from SR. No need to invoke tensors.

Great ... can you show some more detail about how this works I am confused about it.

Tensor

2010-Jul-03, 04:16 AM

Great ... can you show some more detail about how this works I am confused about it.

Transverse Doppler Equations Derivation (http://www.mrelativity.net/Equations/Equations7.htm)

tusenfem

2010-Jul-03, 09:48 AM

OK ... say that I was either travelling quickly towards a point along the x axis or towards the center of a black hole ...

Yeah, where else would you be travelling ....

but ... if I shine a flashlight along the y or z access or in a tangent to the EH of a black hole then space should NOT be curved in that direction right? But since there is only one time ... then time would the same regardless of the direction that I shine the light ( x axis or y axis )

You are thinking flatland, wrong wrong wrong.

The black hole is a sphere and thus shining your light transverse to your trajectory will also pass through curved space.

How about you really start reading an introductory book on special relativity? It is quite obvious you don't understand a word of basic freshman physics.

tommac

2010-Jul-06, 08:49 PM

OK here is an easier and hopefully clear example.

You have 3 points in space at a right angle to each other

X

YZ

Lets assume that X is signifigantly further away from Y than Z is ( although I dont think this is needed ). Lets assume that x is far enough away that even though it is in a right angle formation with Y and Z ... XY =~ XZ

At t=0 X,Y,Z confirm through many experiments that their clocks are all in sync with each other.

Then Z rushes at near the speed of light directly towards Y.

X notices that Z is moving to Y but relative to X, Y didnt move that much.

Z then rendezvous with Y.

Z and Y compare their clocks and they are significantly off.

then they take a very slow journey together with X and compare their clocks.

What do their clocks say? Who's clocks are the same ( X and Y did not move ( except very slowly ) relative to each other )? But Y and Z should be off significantly. Who is right?

Maybe I have a simple freshman mistake here but I am somewhat confused about this seemingly freshman problem in SR and looking for clarification.

Yeah, where else would you be travelling ....

You are thinking flatland, wrong wrong wrong.

The black hole is a sphere and thus shining your light transverse to your trajectory will also pass through curved space.

How about you really start reading an introductory book on special relativity? It is quite obvious you don't understand a word of basic freshman physics.

tommac

2010-Jul-06, 08:53 PM

Transverse Doppler Equations Derivation (http://www.mrelativity.net/Equations/Equations7.htm)

This looks to be what I am asking for. Thanks ... but can you answer probably a very dumb question which I dont get at a quick look ... what is "s" in figure 1? I thought at first it was source ... but source is already noted.

tommac

2010-Jul-06, 09:01 PM

You are thinking flatland, wrong wrong wrong.

I am not thinking flatland ... what I am saying is that the curvature is in the direction of the singularity. I would assume, please correct me if I am wrong ... that a photon fired in the direction of the singularity would behave differently than the photon fired in a perpendicular direction.

The black hole is a sphere and thus shining your light transverse to your trajectory will also pass through curved space. Of course it is a sphere.

I make no assumptions that it is not going to travel through curved space ... just that it is travelling at a different angle with respect to the curvature. Not sure why you are adding this assumption to the question.

Nereid

2010-Jul-06, 09:18 PM

tommac, are you asking about SR, or GR?

Your question in #13 seems pure SR, but your comment in #15 implies full GR.

Tensor

2010-Jul-06, 09:49 PM

This looks to be what I am asking for. Thanks ... but can you answer probably a very dumb question which I dont get at a quick look ... what is "s" in figure 1? I thought at first it was source ... but source is already noted.

It's the position of the source when a wavelength is emitted. The end of the vector labeled v is where the next wavelength is emitted. The vector v represents the velocity of the scorce. c is, of course, the distance light travels in the time the source travels v. Although not specifically stated, the distances represented by the vectors is the distance traveled in one second.

tommac

2010-Jul-07, 12:52 AM

tommac, are you asking about SR, or GR?

Your question in #13 seems pure SR, but your comment in #15 implies full GR.

Really either ... I believe there to be examples in both SR and GR ...

tommac

2010-Jul-07, 12:55 AM

It's the position of the source when a wavelength is emitted. The end of the vector labeled v is where the next wavelength is emitted. The vector v represents the velocity of the scorce. c is, of course, the distance light travels in the time the source travels v. Although not specifically stated, the distances represented by the vectors is the distance traveled in one second.

Thanks ... can we look at "Recession B" in figure 2. Say we used that diagram ... however say "s" simultaneously released 2 photons ... one directly at where the word "source" is and the other at the detector. That would be the foundation for my question.

Andrew D

2010-Jul-07, 02:56 AM

But Y and Z should be off significantly. Who is right?

Don't get stuck here; there is no "right", because there is no global time. The clocks vary, but each measurement is correct by the clock with which it is measured.

Tensor

2010-Jul-07, 03:21 AM

Thanks ... can we look at "Recession B" in figure 2. Say we used that diagram ... however say "s" simultaneously released 2 photons ... one directly at where the word "source" is and the other at the detector. That would be the foundation for my question.

First you need to look at the link, then look at the titles of the sections, in that link, that are numbered and bolded. Then, look at the your question I quoted here and tell me what is wrong the with question. I'm not sure what the foundation for any other question would be.

WayneFrancis

2010-Jul-07, 03:21 AM

OK here is an easier and hopefully clear example.

You have 3 points in space at a right angle to each other

X

YZ

Lets assume that X is signifigantly further away from Y than Z is ( although I dont think this is needed ).

Okay...so useless information but more information is better then less with your scenarios I've found.

Lets assume that x is far enough away that even though it is in a right angle formation with Y and Z ... XY =~ XZ

ok so like this

http://users.on.net/~waynefrancis/tommacxyz.png

At t=0 X,Y,Z confirm through many experiments that their clocks are all in sync with each other.

Then Z rushes at near the speed of light directly towards Y.

X notices that Z is moving to Y but relative to X, Y didnt move that much.

Z then rendezvous with Y.

Z and Y compare their clocks and they are significantly off.

then they take a very slow journey together with X and compare their clocks.

And X would see the same discrepancy as Y would

What do their clocks say?

Let me ask you a question. Do you think Z's acceleration/deceleration would cause a shift between X and Y's frames and why?

Who's clocks are the same ( X and Y did not move ( except very slowly ) relative to each other )?

Well the shift between X and Y's clocks is dependant on the rate of acceleration/deceleration and the the time of that acceleration/deceleration.

But Y and Z should be off significantly. Who is right?

You think there will be a discrepancy that can't be accounted for but this is because you don't understand the first step.

I know this will probably fall on deaf ears but here it goes. Tommac have you plugged in ANY numbers to see what X,Y & Z would see for the first step?

Maybe I have a simple freshman mistake here but I am somewhat confused about this seemingly freshman problem in SR and looking for clarification.

My guess is either you not actually doing the maths to see what the answer would be or you did what you think is the maths and for some reason got something wrong. My first guess is you are "gut feeling" this and that is where the confusion starts.

How about this I put some numbers to it all

X→Y = 1.5ly

Y→Z = 1ly

X→Z ≈ 1.8ly

X,Y & Z's clocks are synchronised and at the same rate.

IE they all observe each others clocks tick at the same rate and adjusting for distance they all agree on the time. Note you can't get all 3 clocks to read the same time. IE you can't get them all to see each others clocks read the same ... not possible...maybe this is your first mistake in understanding clock synchronisation.

So when X's clock reads 1.5 years it will see Y's clock at 0 and not see Z's clock yet.

when X's clock reads ~1.8 years it will see's Y's clock at about .3 and Z's clock at 0

Z sees Y's clock at 2 years and X's clock ~.2 years and their own clock reads at 3 years

Z accelerates/decelerates to a rate of ~.99c nearly instantly towards Y

Z's thinks the trip took ~52 days so their clock is now at 3.143 years but sees Y's clock reads 4 years

Looking at X both Z & Y see X's clock read at 2.5 years. So now we have 3 clocks ticking at the same rate again. What will X see Y & Z's clock as? Well X will see Z accelerate towards Y when X's clock reads 4.8 years. Z's clock will read 3 years and Y's clock will read 3.3 years.

X and Y will both see Z's clock start to run at a different rate as Z will also see X&Y run at different rates.

So now we have X,Y & Z seeing each other's clocks again tick at the same rate. X will observe that Y & Z's clocks are not synchronised (but truly X never see's Y&Z's clock agree on the time so this is not a big deal)

The fact that the clocks have times shifted doesn't matter...You can't synchronise even 2 separated clocks to both read the same time to local observers at both points. The larger the distance the more obvious the shift in time.

For example if we had 2 points and they synchronised their clock with a light pulse from 1/2 way between them they'd still see the others clock shifted by an amount determined by the distance between them.

Nereid

2010-Jul-07, 05:21 AM

tommac, are you asking about SR, or GR?

Your question in #13 seems pure SR, but your comment in #15 implies full GR.Really either ... I believe there to be examples in both SR and GR ...

Thanks for that.

I think it would help - you mostly - if you would clearly state the theoretical framework (SR or GR, not both!) within which you ask each question. I expect you'll find the SR-based questions a lot easier to get answers to ... and that if you are having extended difficulty with SR, you should probably postpone any and all questions on GR, at least until you've developed a good, working understanding of SR. In my experience, SR is child's play compared to GR.

macaw

2010-Jul-07, 06:06 AM

Transverse Doppler Equations Derivation (http://www.mrelativity.net/Equations/Equations7.htm)

Excuse me, Tensor but the "Millenium" website and its owner, Joseph Rybzyck are 100% crank. There are much better places to get an explanation of the transverse doppler effect.

macaw

2010-Jul-07, 06:09 AM

Excuse me, Tensor but the "Millenium" website and its owner, Joseph Rybzyck are 100% crank. There are much better places to get an explanation of the transverse doppler effect.

Here (http://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Motion_in_an_arbitrary _direction) is a much better post on the subject.

macaw

2010-Jul-07, 06:10 AM

I have a gut feeling that it is addressed in the ricci tensor ... but really not sure how ... firstly is that right?

nope, it isn't

tusenfem

2010-Jul-07, 07:01 AM

You have 3 points in space at a right angle to each other

X

YZ

Lets assume that X is signifigantly further away from Y than Z is ( although I dont think this is needed ). Lets assume that x is far enough away that even though it is in a right angle formation with Y and Z ... XY =~ XZ

At t=0 X,Y,Z confirm through many experiments that their clocks are all in sync with each other.

Then Z rushes at near the speed of light directly towards Y.

X notices that Z is moving to Y but relative to X, Y didnt move that much.

And this (the bolded) is EXACTLY why I always ask you to THINK before you write something.

If Z rushes to Y, without any comments to the contraty we can assume that Y remains at rest.

Not only does 'Y didnt move that much" but in fact Y didnt move AT ALL.

tommac

2010-Jul-09, 03:12 AM

Don't get stuck here; there is no "right", because there is no global time. The clocks vary, but each measurement is correct by the clock with which it is measured.

OK ... so what are the readings on the clocks?

tommac

2010-Jul-09, 03:14 AM

Thanks for that.

I think it would help - you mostly - if you would clearly state the theoretical framework (SR or GR, not both!) within which you ask each question. I expect you'll find the SR-based questions a lot easier to get answers to ... and that if you are having extended difficulty with SR, you should probably postpone any and all questions on GR, at least until you've developed a good, working understanding of SR. In my experience, SR is child's play compared to GR.

OK .. SR then

tommac

2010-Jul-09, 03:17 AM

And this (the bolded) is EXACTLY why I always ask you to THINK before you write something.

If Z rushes to Y, without any comments to the contraty we can assume that Y remains at rest.

Not only does 'Y didnt move that much" but in fact Y didnt move AT ALL.

Sorry for the typo ... I obviously meant z ...

X notices that Z is moving to Y but relative to X, Z didnt move that much

tommac

2010-Jul-09, 03:21 AM

Why are you talking about seeing clocks if they all are standing next to each other? They can just look over and read the guys watch ... like when I ask someone in the subway what time it is.

Okay...so useless information but more information is better then less with your scenarios I've found.

ok so like this

http://users.on.net/~waynefrancis/tommacxyz.png

And X would see the same discrepancy as Y would

Let me ask you a question. Do you think Z's acceleration/deceleration would cause a shift between X and Y's frames and why?

Well the shift between X and Y's clocks is dependant on the rate of acceleration/deceleration and the the time of that acceleration/deceleration.

You think there will be a discrepancy that can't be accounted for but this is because you don't understand the first step.

I know this will probably fall on deaf ears but here it goes. Tommac have you plugged in ANY numbers to see what X,Y & Z would see for the first step?

My guess is either you not actually doing the maths to see what the answer would be or you did what you think is the maths and for some reason got something wrong. My first guess is you are "gut feeling" this and that is where the confusion starts.

How about this I put some numbers to it all

X→Y = 1.5ly

Y→Z = 1ly

X→Z ≈ 1.8ly

X,Y & Z's clocks are synchronised and at the same rate.

IE they all observe each others clocks tick at the same rate and adjusting for distance they all agree on the time. Note you can't get all 3 clocks to read the same time. IE you can't get them all to see each others clocks read the same ... not possible...maybe this is your first mistake in understanding clock synchronisation.

So when X's clock reads 1.5 years it will see Y's clock at 0 and not see Z's clock yet.

when X's clock reads ~1.8 years it will see's Y's clock at about .3 and Z's clock at 0

Z sees Y's clock at 2 years and X's clock ~.2 years and their own clock reads at 3 years

Z accelerates/decelerates to a rate of ~.99c nearly instantly towards Y

Z's thinks the trip took ~52 days so their clock is now at 3.143 years but sees Y's clock reads 4 years

Looking at X both Z & Y see X's clock read at 2.5 years. So now we have 3 clocks ticking at the same rate again. What will X see Y & Z's clock as? Well X will see Z accelerate towards Y when X's clock reads 4.8 years. Z's clock will read 3 years and Y's clock will read 3.3 years.

X and Y will both see Z's clock start to run at a different rate as Z will also see X&Y run at different rates.

So now we have X,Y & Z seeing each other's clocks again tick at the same rate. X will observe that Y & Z's clocks are not synchronised (but truly X never see's Y&Z's clock agree on the time so this is not a big deal)

The fact that the clocks have times shifted doesn't matter...You can't synchronise even 2 separated clocks to both read the same time to local observers at both points. The larger the distance the more obvious the shift in time.

For example if we had 2 points and they synchronised their clock with a light pulse from 1/2 way between them they'd still see the others clock shifted by an amount determined by the distance between them.

tommac

2010-Jul-09, 03:27 AM

First you need to look at the link, then look at the titles of the sections, in that link, that are numbered and bolded. Then, look at the your question I quoted here and tell me what is wrong the with question. I'm not sure what the foundation for any other question would be.

Are you talking about the title:

The Classical Transverse Doppler Effect for Initial Wavelengths

Are you saying the problem is because this is for the initial wavelength? Sorry ... not understand what you are hinting at.

WayneFrancis

2010-Jul-10, 01:49 AM

Sorry for the typo ... I obviously meant z ...

I think I understand one of your problems. You are transposing some of the effects from the accelerated observer to the non accelerated observer.

WayneFrancis

2010-Jul-10, 02:33 AM

Why are you talking about seeing clocks if they all are standing next to each other? They can just look over and read the guys watch ... like when I ask someone in the subway what time it is.

Ummm My reply was in response to this post. Also I didn't say they where standing next to each other. They are 1ly, 1.5ly & ~1.8ly apart. Though the experiment could be done at 10m, 15m & 18m....the variations in the clocks would just be a LOT smaller.

OK here is an easier and hopefully clear example.

You have 3 points in space at a right angle to each other

X

YZ

Lets assume that X is signifigantly further away from Y than Z is ( although I dont think this is needed ). Lets assume that x is far enough away that even though it is in a right angle formation with Y and Z ... XY =~ XZ

At t=0 X,Y,Z confirm through many experiments that their clocks are all in sync with each other.

Then Z rushes at near the speed of light directly towards Y.

X notices that Z is moving to Y but relative to X, Y didnt move that much.

Z then rendezvous with Y.

Z and Y compare their clocks and they are significantly off.

then they take a very slow journey together with X and compare their clocks.

What do their clocks say? Who's clocks are the same ( X and Y did not move ( except very slowly ) relative to each other )? But Y and Z should be off significantly. Who is right?

Maybe I have a simple freshman mistake here but I am somewhat confused about this seemingly freshman problem in SR and looking for clarification.

When I, and others, talk about "clocks" in these thought experiments we don't mean like wrist watches. Normally it is some type of light clock where the observers would count ticks.

You seem to be suggesting that when X,Y&Z come together that they would not be able to reconcile their clocks using SR because there are 3 of them and the initial trip of Z would cause X&Y to disagree on what Z's clock would be when it arrived at Y.

If this isn't the case then please think before you write and write a thought experiment that clearly states the thought experiment, providing numbers would be a good start. I tell my clients all the time if you have a very ambiguous set of requirements for a system then you won't get a system that does what you want 99% of the time.

Nereid

2010-Jul-10, 06:57 AM

OK here is an easier and hopefully clear example.

You have 3 points in space at a right angle to each other

X

YZ

Lets assume that X is signifigantly further away from Y than Z is ( although I dont think this is needed ). Lets assume that x is far enough away that even though it is in a right angle formation with Y and Z ... XY =~ XZ

At t=0 X,Y,Z confirm through many experiments that their clocks are all in sync with each other.

Then Z rushes at near the speed of light directly towards Y.

X notices that Z is moving to Y but relative to X, Y didnt move that much.

Z then rendezvous with Y.

Z and Y compare their clocks and they are significantly off.

then they take a very slow journey together with X and compare their clocks.

What do their clocks say? Who's clocks are the same ( X and Y did not move ( except very slowly ) relative to each other )? But Y and Z should be off significantly. Who is right?

Maybe I have a simple freshman mistake here but I am somewhat confused about this seemingly freshman problem in SR and looking for clarification.

Here's a variant of your thought experiment (assuming you have specified X, Y, and Z properly - I see in a later post you say you'd mixed at least one up).

At the start of the experiment there are clocks everywhere, 1mm apart if necessary.

These clocks are all synchronised (you need to say how, in considerable detail, this is done, in your experiment).

In step 1, Z moves ("rushes"); let's assume we have synchronised clocks everywhere, moving at the velocity Z reaches, relative to X and Y.

In step 2 - "Z then rendezvous with Y" - we have Z decelerating to zero (i.e. not moving wrt X and Y).

In step 3 - "[Y and Z] take a very slow journey together with X" (I presume you mean Y and Z move, at a very slow speed, towards X, and stop when they reach X; do you?) - is unnecessary. Can you see why?

You can now ask your questions in a more simple, direct fashion - what are they?

tommac

2010-Jul-10, 03:24 PM

OK ... so what are the results on the clocks?

I dont think the second rendezvous ( where X Y and Z meetup in the end ) is needed BUT just wanted to have all of the clocks in one place.

Here's a variant of your thought experiment (assuming you have specified X, Y, and Z properly - I see in a later post you say you'd mixed at least one up).

At the start of the experiment there are clocks everywhere, 1mm apart if necessary.

These clocks are all synchronised (you need to say how, in considerable detail, this is done, in your experiment).

In step 1, Z moves ("rushes"); let's assume we have synchronised clocks everywhere, moving at the velocity Z reaches, relative to X and Y.

In step 2 - "Z then rendezvous with Y" - we have Z decelerating to zero (i.e. not moving wrt X and Y).

In step 3 - "[Y and Z] take a very slow journey together with X" (I presume you mean Y and Z move, at a very slow speed, towards X, and stop when they reach X; do you?) - is unnecessary. Can you see why?

You can now ask your questions in a more simple, direct fashion - what are they?

tommac

2010-Jul-10, 03:28 PM

the second rendezvous in my question ... is to make sure all of the clocks were at the same place at the same time in the same frame.

I am not suggesting anything ... just not sure what the answer is .... it is a question. But it seems that nobody here can answer it.

Ummm My reply was in response to this post. Also I didn't say they where standing next to each other. They are 1ly, 1.5ly & ~1.8ly apart. Though the experiment could be done at 10m, 15m & 18m....the variations in the clocks would just be a LOT smaller.

When I, and others, talk about "clocks" in these thought experiments we don't mean like wrist watches. Normally it is some type of light clock where the observers would count ticks.

You seem to be suggesting that when X,Y&Z come together that they would not be able to reconcile their clocks using SR because there are 3 of them and the initial trip of Z would cause X&Y to disagree on what Z's clock would be when it arrived at Y.

If this isn't the case then please think before you write and write a thought experiment that clearly states the thought experiment, providing numbers would be a good start. I tell my clients all the time if you have a very ambiguous set of requirements for a system then you won't get a system that does what you want 99% of the time.

Nereid

2010-Jul-10, 04:08 PM

OK ... so what are the results on the clocks?

I dont think the second rendezvous ( where X Y and Z meetup in the end ) is needed BUT just wanted to have all of the clocks in one place.

Here's a variant of your thought experiment (assuming you have specified X, Y, and Z properly - I see in a later post you say you'd mixed at least one up).

At the start of the experiment there are clocks everywhere, 1mm apart if necessary.

These clocks are all synchronised (you need to say how, in considerable detail, this is done, in your experiment).

In step 1, Z moves ("rushes"); let's assume we have synchronised clocks everywhere, moving at the velocity Z reaches, relative to X and Y.

In step 2 - "Z then rendezvous with Y" - we have Z decelerating to zero (i.e. not moving wrt X and Y).

In step 3 - "[Y and Z] take a very slow journey together with X" (I presume you mean Y and Z move, at a very slow speed, towards X, and stop when they reach X; do you?) - is unnecessary. Can you see why?

You can now ask your questions in a more simple, direct fashion - what are they?

One step at a time tommac, one step at a time.

If you're OK with my 'clocks everywhere' variant of your thought experiment, you certainly don't need the step 3/second rendezvous (can you see why not?). How do you work out what Y's, and Z's, clocks show, when Z meets Y, without having them travel back to X?

Before proceeding, do you mind if I ask why you have step 2/Z decelerating? I mean, don't you simply want to know what Z's clock reads (and Y's) at the instant they meet?

Nereid

2010-Jul-10, 04:11 PM

the second rendezvous in my question ... is to make sure all of the clocks were at the same place at the same time in the same frame.

I am not suggesting anything ... just not sure what the answer is .... it is a question. But it seems that nobody here can answer it.

If I may hazard a guess as to why ("it seems that nobody here can answer it"): your thought experiment is poorly specified, or ambiguous; you have not said - clearly - what you are trying to do, and no one could, in fact, conduct your thought experiment! A basic requirement of a thought experiment is that it is not ambiguous; it could be done by anyone, independently, and the results would be the same ... you have not set up such an experiment.

WayneFrancis

2010-Jul-10, 04:41 PM

OK here is an easier and hopefully clear example.

You have 3 points in space at a right angle to each other

X

YZ

Lets assume that X is signifigantly further away from Y than Z is ( although I dont think this is needed ). Lets assume that x is far enough away that even though it is in a right angle formation with Y and Z ... XY =~ XZ

At t=0 X,Y,Z confirm through many experiments that their clocks are all in sync with each other.

Then Z rushes at near the speed of light directly towards Y.

X notices that Z is moving to Y but relative to X, Y didnt move that much.

Z then rendezvous with Y.

Z and Y compare their clocks and they are significantly off.

then they take a very slow journey together with X and compare their clocks.

What do their clocks say? Who's clocks are the same ( X and Y did not move ( except very slowly ) relative to each other )? But Y and Z should be off significantly. Who is right?

Maybe I have a simple freshman mistake here but I am somewhat confused about this seemingly freshman problem in SR and looking for clarification.

the second rendezvous in my question ... is to make sure all of the clocks were at the same place at the same time in the same frame.

I am not suggesting anything ... just not sure what the answer is .... it is a question. But it seems that nobody here can answer it.

I did half the work for you in post #22 (http://www.bautforum.com/showthread.php/105552-Tensors-and-Time-Dilation?p=1757113#post1757113) already after filling in info that was needed to give an answer.

Again give us some numbers to work with.

How far apart are all the members at the beginning of the thought experiment?

How are the clocks being synchronised?

How fast does Z accelerate and for how long? How fast does Z decelerate? (I'm assuming Z will stop at Y.)

How fast does Y & Z accelerate towards X and for how long? How fast do they decelerate?

The clocks final reading depend on all those parameters ... if you don't provide numbers then how is anyone suppose to give you an answer.

tommac

2010-Jul-13, 06:44 PM

If I may hazard a guess as to why ("it seems that nobody here can answer it"): your thought experiment is poorly specified, or ambiguous; you have not said - clearly - what you are trying to do, and no one could, in fact, conduct your thought experiment! A basic requirement of a thought experiment is that it is not ambiguous; it could be done by anyone, independently, and the results would be the same ... you have not set up such an experiment.

Yes but it seems like you re-worded it perfectly. But I am looking for the answers.

tommac

2010-Jul-13, 06:49 PM

At some point I would like all of the clocks in the same place, so thre is no significant distance between the clocks and that all of the clocks eventually end up in the same frame.

One step at a time tommac, one step at a time.

If you're OK with my 'clocks everywhere' variant of your thought experiment, you certainly don't need the step 3/second rendezvous (can you see why not?). How do you work out what Y's, and Z's, clocks show, when Z meets Y, without having them travel back to X?

Before proceeding, do you mind if I ask why you have step 2/Z decelerating? I mean, don't you simply want to know what Z's clock reads (and Y's) at the instant they meet?

WayneFrancis

2010-Jul-14, 02:30 AM

Yes but it seems like you re-worded it perfectly. But I am looking for the answers.

And we still can't give you "an answer" if you don't ask us a proper question. Its like asking "How long will I have to drive to get to my destination on my next holiday?" Well...that would depend on where your next holiday is, where you are going from how fast you will drive, etc.

tommac

2010-Jul-14, 04:32 PM

And we still can't give you "an answer" if you don't ask us a proper question. Its like asking "How long will I have to drive to get to my destination on my next holiday?" Well...that would depend on where your next holiday is, where you are going from how fast you will drive, etc.

Use any numbers you want really ...

Arbitrarily lets choose

Starting

X at 10,0

Y at 0,0

Z at 0,5

Z accelerates quickly to near the speed of light relative to Y when z is at 0,4 and begins a quick decelleration at 0,1 all in the direction of Y

At Y & Z rendezvous

X at 10,0

Y at 0,0

Z at 0,0

Y & Z travel slowly to X

At X,Y & Z rendezvous:

X at 10,0

y at 10,0

z at 10,0

WayneFrancis

2010-Jul-14, 04:57 PM

Use any numbers you want really ...

Arbitrarily lets choose

Starting

X at 10,0

Y at 0,0

Z at 0,5

What are your units? Light years?

Z accelerates quickly to near the speed of light relative to Y when z is at 0,4 and begins a quick decelleration at 0,1 all in the direction of Y

Read that Tommac...you're still ambiguous in you description

Does Z take 1 unit to accelerate to "near the speed of light"? What speed exactly does Z accelerate to?

At Y & Z rendezvous

X at 10,0

Y at 0,0

Z at 0,0

Y & Z travel slowly to X

At X,Y & Z rendezvous:

X at 10,0

y at 10,0

z at 10,0

Give ACTUAL units.

Once again we need the following

1) Rate of acceleration for Z

2) Top speed of Z

3) Rate of deceleration for Z if different then the rate of acceleration

4) distance between the 3 observers, include the metric.

5) Rate of acceleration for Y&Z towards X

6) Top speed of Y&Z

7) Rate of deceleration for Z if different then the rate of acceleration

Again you might as well say "My Uncle bob lives 10 away and I want to drive there fast. How long will it take me?"

Nereid

2010-Jul-14, 06:50 PM

If I may hazard a guess as to why ("it seems that nobody here can answer it"): your thought experiment is poorly specified, or ambiguous; you have not said - clearly - what you are trying to do, and no one could, in fact, conduct your thought experiment! A basic requirement of a thought experiment is that it is not ambiguous; it could be done by anyone, independently, and the results would be the same ... you have not set up such an experiment.Yes but it seems like you re-worded it perfectly. But I am looking for the answers.

No worries.

A good first step would be to say how the clocks, in each frame, will be synchronised. Or you could simply say they are, and leave it at that.

Next? As has subsequently been pointed out, you need to be more specific about Z's acceleration ... what you have written is too vague to work with. But! Why do you need Z to accelerate at all? Why not have Z move at velocity {details} wrt X, and set the clocks in both frames to zero when Z is at {initial position}?

tommac

2010-Jul-15, 02:31 PM

OK ... lets assume that I take both of your suggestions ...

No worries.

A good first step would be to say how the clocks, in each frame, will be synchronised. Or you could simply say they are, and leave it at that.

Next? As has subsequently been pointed out, you need to be more specific about Z's acceleration ... what you have written is too vague to work with. But! Why do you need Z to accelerate at all? Why not have Z move at velocity {details} wrt X, and set the clocks in both frames to zero when Z is at {initial position}?

tommac

2010-Jul-15, 02:35 PM

Does the metric matter? All I want to know is whose clock shows the most progression in time. why would the metric matter? lets say 10 light years

Also the rest of the stuff should be able to be derived from the question.

Assume constant acceleration:

0-.99999999999999999 c in 1 second

same for decelleration

What are your units? Light years?

Read that Tommac...you're still ambiguous in you description

Does Z take 1 unit to accelerate to "near the speed of light"? What speed exactly does Z accelerate to?

Give ACTUAL units.

Once again we need the following

1) Rate of acceleration for Z

2) Top speed of Z

3) Rate of deceleration for Z if different then the rate of acceleration

4) distance between the 3 observers, include the metric.

5) Rate of acceleration for Y&Z towards X

6) Top speed of Y&Z

7) Rate of deceleration for Z if different then the rate of acceleration

Again you might as well say "My Uncle bob lives 10 away and I want to drive there fast. How long will it take me?"

Nereid

2010-Jul-15, 02:47 PM

OK ... lets assume that I take both of your suggestions ...

No worries.

A good first step would be to say how the clocks, in each frame, will be synchronised. Or you could simply say they are, and leave it at that.

Next? As has subsequently been pointed out, you need to be more specific about Z's acceleration ... what you have written is too vague to work with. But! Why do you need Z to accelerate at all? Why not have Z move at velocity {details} wrt X, and set the clocks in both frames to zero when Z is at {initial position}?

Now you have to specify Z's velocity and initial position.

tommac

2010-Jul-15, 03:37 PM

Now you have to specify Z's velocity and initial position.

Starting 1 unit = 10 light years

X at 10,0

Y at 0,0

Z at 0,5

Z's velocity = .999999999999999999999 c

forrest noble

2010-Jul-15, 07:18 PM

tommac,

Tensors and Time Dilation?

One thing that has been confusing me is how can there only be one time dimension?

If I curve space in X direction ... then I would need to dilate time to keep the speed of light constant for a beam of light that is traveling along the X axis. Right?

But how does that effect the Y direction? So if time is dilated as above but space is not curved in the Y direction then how can the speed of light stay constant?

I have a gut feeling that it is addressed in the Ricci tensor ... but really not sure how ... firstly is that right? Secondly can someone explain how this issue is addressed?

I think the two factors you are addressing "tensors" and "time dilation" to be best understood should not be considered together. Time dilation might be best understood by considering individual atoms within the "time dilated" entity/ reference frame being considered. Those entities being time dilated would accordingly be moving relative to the prevailing gravitational field.

As to time dilation: One might consider a single atom as a kind of clock. Although a simplification, consider atoms of a specific type whereby its electron(s) are orbiting the nucleus at a constant velocity in each shell relative to the nucleus which is also spinning on its axis relative to the background field. In each shell electrons move at different velocities relative to the other shells. As you pointed out, when moving in a direction relative to the center of gravity at a point, direction X, electrons will slow down in the direction of that motion. When moving in the opposite direction electrons will not slow down. When moving in the "Y' direction (perpendicular to its linear motion at that point as you questioned) such motion as a ratio to the speed of light is also unchanged so there would be no change in velocity due to time dilation. To the atoms themselves all speeds remain the same in all time frames, but to a "stationary" (little or no motion relative to the center of gravity) outside observer electron velocities seem to slow down in the direction of motion meaning they accordingly can't exceed the speed of light within that field. So from an outside observer's perspective the amount of total revolutions of a particular electron per time period decreases in direct relation to the atoms velocity relative to the prevailing gravitational field. Since all atomic matter is made up of atoms the slowing of time of a person or clock can be calculated just by knowing the velocity relative to the prevailing gravitational field. Having no motion relative to this field, time will progress at its fastest possible rate. Although simplified, this idea might make time dilation more understandable.

As to tensors: Tensors can be considered coordinate vectors at any given point. Take a directional vector in direction X. "Tensor" is used in place of the word vector when a directional analysis of a vector direction (actual direction) of an object is being analyzed. Cartesian tensors can be arbitrarily set up giving the directional forces in X, Y, Z directions along with a T coordinate for time calculating changes in velocity and direction over time. Tensors are also used in matrices, square or rectangular table-like listings of tensors such as 2 by 2, 2 by 3, 3 by 4, or any combination or quantity. Such a table of tensors can be mathematically manipulated to make calculations concerning acceleration changes due to gravity, for instance, or for changing the reference frame.

The "Ricci Tensor" in General Relativity is a partial differential (calculus) equation where the "tensors" in the equation are accordingly used to calculate the warping (curving) of space-time. This equation, of the 10 total of General Relativity, has null effect on time dilation if the vector motion of the matter being evaluated is solely linear relative to the reference frame for any calculated time period. This may be the case if the matter is moving directly toward the center of gravity in a given field. With the numerous gravitational influences of our solar system, for instance, this would seemingly never be the case for any sustained time period.

Bottom line I suggest that the two, time dilation and tensors be thought of as unrelated entities. Only one time dimension, isn't that much easier? My opinion is that to complicate theoretical physics is relatively easy, to theoretically simplify physics is more difficult but in the long run I think will ultimately be much more productive and valid.

Hope I shed some light; if this posting begs more questions than it provides answers please ignore it.

Nereid

2010-Jul-15, 07:27 PM

Starting 1 unit = 10 light years

X at 10,0

Y at 0,0

Z at 0,5

Z's velocity = .999999999999999999999 c

You've given Z's speed, not its velocity.

Velocity is a vector quantity, it has magnitude and direction.

What is Z's velocity?

tommac

2010-Jul-15, 08:40 PM

You've given Z's speed, not its velocity.

Velocity is a vector quantity, it has magnitude and direction.

What is Z's velocity?

Please read the thread ... it is clearly stated in the problem.

Starting

X at 10,0

Y at 0,0

Z at 0,5

Z accelerates quickly to near the speed of light relative to Y when z is at 0,4 and begins a quick decelleration at 0,1 all in the direction of Y

At Y & Z rendezvous

X at 10,0

Y at 0,0

Z at 0,0

So ... if Z starts at 0,5 and ends at 0,0 then it would seem that the direction of travel and acceleration would be along the Y axis right?

Nereid

2010-Jul-15, 08:43 PM

Please read the thread ... it is clearly stated in the problem.

The "problem" has been reformed, restated, re-reformed, re-restated, etc many times.

Consequently I have no idea which, of the many, often quite different, versions of "the problem" you are referring to.

tommac, people here are trying to help you understand stuff; please cooperate.

Please re-state the problem, in a complete and unambiguous form.

tommac

2010-Jul-15, 08:58 PM

Yes this is very good information. Can I ask a follow up?

Lets forget about tensors .... and focus as you suggest on Time Dilation.

Lets assume 3 observers, A, B and C ... each of which produce a pulse of light in all directions at 1 second intervals local time.

If C travels directly in the direction of A, but at roughly a tangent to B ... and A and B dont move relative to each other ... how does each observer observe the other two? Lets just have 3 variables F for faster than it views its own puls, S for slower than its own pulse and E for equal to its own pulse

Here is how I think it should work ... however I am near positive that I am wrong but looking for a correction:

X|B|C

A|E|S

So ... A is Equal to ** pulse but A views C's pulse as being slow compared to his

X|A|C

B|E|?

B sees A's pulse as being equal to his not sure how B views C's pulse

X|A|B

C|F|?

C observes A's Pulse as being Faster than its own ... not sure how it views B's Pulse

tommac,

I think the two factors you are addressing "tensors" and "time dilation" to be best understood should not be considered together. Time dilation might be best understood by considering individual atoms within the "time dilated" entity/ reference frame being considered. Those entities being time dilated would accordingly be moving relative to the prevailing gravitational field.

As to time dilation: One might consider a single atom as a kind of clock. Although a simplification, consider atoms of a specific type whereby its electrons are moving at a constant velocity in each shell relative to the nucleus of the atom which is also spinning on its axis relative to the background field. In each shell electrons move at different velocities relative to the other shells. As you pointed out, when moving in a direction relative to the center of gravity at a point, direction X, electrons will slow down in the direction of that motion. When moving in the opposite direction electrons will not slow down. When moving in the "Y' direction (perpendicular to its linear motion at that point as you questioned) such motion as a ratio to the speed of light is also unchanged so there would be no change in velocity due to time dilation. To the atoms themselves all speeds remain the same in all time frames, but to a "stationary" (little or no motion relative to the center of gravity) outside observer electron velocities seem to slow down in the direction of motion meaning they accordingly can't exceed the speed of light within that field. So from an outside observer's perspective the amount of total revolutions of a particular electron per time period decreases in direct relation to the atoms velocity relative to the prevailing gravitational field. Since all atomic matter is made up of atoms the slowing of time of a person or clock can be calculated just by knowing the velocity relative to the prevailing gravitational field. Having no motion relative to this field, time will progress at its fastest possible rate. Although simplified, this idea might make time dilation more understandable.

As to tensors: Tensors can be considered coordinate vectors at any given point. Take a directional vector in direction X. "Tensor" is used in place of the word vector when a directional analysis of a vector direction (actual direction) of an object is being analyzed. Cartesian tensors can be arbitrarily set up giving the directional forces in X, Y, Z directions along with a T coordinate for time calculating changes in velocity and direction over time. Tensors are also used in matrices, square or rectangular table-like listings of tensors such as 2 by 2, 2 by 3, 3 by 4, or any combination or quantity. Such a table of tensors can be mathematically manipulated to make calculations concerning acceleration changes due to gravity, for instance, or for changing the reference frame.

The "Ricci Tensor" in General Relativity is a partial differential (calculus) equation where the "tensors" in the equation are accordingly used to calculate the warping (curving) of space-time. This equation, of the 10 total of General Relativity, has null effect on time dilation if the vector motion of the matter being evaluated is solely linear relative to the reference frame for any calculated time period. This may be the case if the matter is moving directly toward the center of gravity in a given field. With the numerous gravitational influences of our solar system, for instance, this would seemingly never be the case for any sustained time period.

Bottom line I suggest that the two, time dilation and tensors be thought of as unrelated entities. Only one time dimension, isn't that much easier? My opinion is that to complicate theoretical physics is relatively easy, to theoretically simplify physics is more difficult but in the long run I think will ultimately be much more productive and valid.

Hope I shed some light; if this posting begs more questions than it provides answers please ignore it.

tommac

2010-Jul-15, 08:59 PM

It is clearly stated in the post that you quoted.

The "problem" has been reformed, restated, re-reformed, re-restated, etc many times.

Consequently I have no idea which, of the many, often quite different, versions of "the problem" you are referring to.

tommac, people here are trying to help you understand stuff; please cooperate.

Please re-state the problem, in a complete and unambiguous form.

Starting

X at 10,0

Y at 0,0

Z at 0,5

Z accelerates quickly to near the speed of light relative to Y when z is at 0,4 and begins a quick decelleration at 0,1 all in the direction of Y

At Y & Z rendezvous

X at 10,0

Y at 0,0

Z at 0,0 So ... if Z starts at 0,5 and ends at 0,0 then it would seem that the direction of travel and acceleration would be along the Y axis right?

slang

2010-Jul-15, 10:24 PM

It is clearly stated in the post that you quoted.

No it isn't! Maybe it's clear to you, filling in the details in your mind. Are they all supposed to be in one line? Is Y an object? You speak of an Y axis, which suggest they are not in one line. Your post is most definitely NOT unambiguous, and I don't understand why you deny it when told so by a scholar who is trying to help you.

forrest noble

2010-Jul-15, 10:26 PM

Tommac,

If C travels directly in the direction of A, but at roughly a tangent to B ... and A and B don't move relative to each other ... how does each observer observe the other two? Lets just have 3 variables F for faster than it views its own pulse, S for slower than its own pulse and E for equal to its own pulse.

Since all observers perceive light in their own reference frame as moving at light speed, the observation of light originating in another reference frame into your own, of course would still appear to be moving at light speed upon your observation. If you are looking at a different reference frame conceptually, you would consider the speed of light in all other reference frames as moving faster than light in the direction of their relative motion to you and slower than light speed in the opposite direction. The time interval between light pulses would be directly proportional to the time dilation, if any, rather than the conceptual light speed.

To determine their relative time dilation, on the other hand, you would need to know how each reference frame is moving relative to a common primary gravitational influence if there is one. If there is no common center of gravity concerning the primary cause of time dilation, then to conceptually compare two reference frames with differing centers of gravity, the time dilation of each would first need to be calculated. Following that one might compare the time in the two reference frames to a common center of gravity or reference frame (such as the sun for instance) if such commonality exists, otherwise such conceptual time comparisons of time dilations accordingly would only be speculative and would not result in the certain validity of any conclusion.

macaw

2010-Jul-15, 11:46 PM

If C travels directly in the direction of A, but at roughly a tangent to B ...

Howzat? Can you attach a drawing. Because, from your prose, it is not comprehensible.

WayneFrancis

2010-Jul-16, 01:24 AM

Does the metric matter?

Well if you want the correct answer to what the clocks read then YES.

All I want to know is whose clock shows the most progression in time.

Well tommac you never asked "Which clock shows the most progression in time?"

The answer to that is easy....it is X

why would the metric matter? lets say 10 light years

The metric matters because your question when this X,Y,Z triangle thought experiments started said

...

What do their clocks say? Who's clocks are the same ( X and Y did not move ( except very slowly ) relative to each other )? But Y and Z should be off significantly. Who is right?

...

Notice the bolded question asks what their clocks will read not just simply "who's clock accumulated the most time".

This is the problem tommac. You constantly ask ambiguous questions and often your questions mutate over time then you seem to get offended when people ask for clarification.

To boot almost always when people ask you for clarification they state exactly why the clarification is needed, ie explaining how your question is ambiguous, then you often just regurgitate that you don't think it matters which show us that not only do you not understand the original concept but you seem to have some aversion to accepting what the reasoning behind the concept is all about.

Also the rest of the stuff should be able to be derived from the question.

Assume constant acceleration:

0-.99999999999999999 c in 1 second

same for decelleration

Ok for once can you state the full question...you've still missed out bits or you've changed the question in your mind again and neglected to tell the rest of us.

Your question was Z accelerates quickly to Y then Y and Z accelerate slowly towards X but yet you've only given 1 set of acceleration/deceleration.

I'm also wondering why you wrote "0-.99999999999999999" what is the minus sign for.

But since you changed the question above, which basically boils down to "What clock accumulated the most time?" then the answer is X. But again I question your motives because giving you an answer never seems to lead to you accepting said answer with or without the maths.

WayneFrancis

2010-Jul-16, 01:37 AM

Please read the thread ... it is clearly stated in the problem.

No tommac, the thread does NOT clearify. Not only have you still left out needed information that I explicitly asked for in post #45 (http://www.bautforum.com/showthread.php/105552-Tensors-and-Time-Dilation?p=1761914#post1761914) but you've seemingly changed the question too.

So ... if Z starts at 0,5 and ends at 0,0 then it would seem that the direction of travel and acceleration would be along the Y axis right?

Yes but you still need to provide the vector rate and duration of the acceleration for Y&Z towards X.

Honestly ground your self and in 1 post clearly articulate your thought experiment because if we are forced to fish through all these posts to come up with a thought experiment then not only will we get contradictory attributes but we'll still be left with an ambiguous thought experiment.

WayneFrancis

2010-Jul-16, 01:41 AM

The "problem" has been reformed, restated, re-reformed, re-restated, etc many times.

Consequently I have no idea which, of the many, often quite different, versions of "the problem" you are referring to.

tommac, people here are trying to help you understand stuff; please cooperate.

Please re-state the problem, in a complete and unambiguous form.

100% agreement here. Even if you think I'm being unreasonable with you tommac I'm not the only one point this stuff out to you.

Being involved in scientific discussions in other areas of science has made me very weary when people don't like to fully state a question in one place. It is often a sign they are trying to leave them selves some wiggle room and less obvious to the causal observer what exactly is being asked and answered. For a casual observer reading this post might think no one could answer your "simple" question if we didn't constantly point out that you haven't provided enough information to answer said question.

WayneFrancis

2010-Jul-16, 02:03 AM

Yes this is very good information. Can I ask a follow up?

This should be good...lets change gears again before the other question is answered.

Lets forget about tensors .... and focus as you suggest on Time Dilation.

Lets assume 3 observers, A, B and C ... each of which produce a pulse of light in all directions at 1 second intervals local time.

OK

If C travels directly in the direction of A, but at roughly a tangent to B ... and A and B dont move relative to each other ... how does each observer observe the other two? Lets just have 3 variables F for faster than it views its own puls, S for slower than its own pulse and E for equal to its own pulse

Ok so like this

http://users.on.net/~waynefrancis/tommac_te3.png

Here is how I think it should work ... however I am near positive that I am wrong but looking for a correction:

X|B|C

A|E|S

So ... A is Equal to ** pulse but A views C's pulse as being slow compared to his

X|A|C

B|E|?

HOLD IT! STOP! Where are you getting "X" from?

Your thought experiment has 3 points A,B,C and three comparisions (F)aster,(S)lower,(E)qual. No X....nor do you define what you mean by X. This is the problem tommac...you ask questions and people are left asking themselves "Have I missed something? What is tommac really saying here?"

B sees A's pulse as being equal to his not sure how B views C's pulse

X|A|B

C|F|?

C observes A's Pulse as being Faster than its own ... not sure how it views B's Pulse

C will observe B & A's pulse faster then its pulse while C is in motion towards A.

I see the problem here you have a discrepancy on how A&B can see their clock in synch while C sees them out of synch while C is in motion. This is the classical situation of different observers don't observe events happening at the same time.

WayneFrancis

2010-Jul-16, 02:08 AM

It is clearly stated in the post that you quoted.

Starting

X at 10,0

Y at 0,0

Z at 0,5

Z accelerates quickly to near the speed of light relative to Y when z is at 0,4 and begins a quick decelleration at 0,1 all in the direction of Y

At Y & Z rendezvous

X at 10,0

Y at 0,0

Z at 0,0 So ... if Z starts at 0,5 and ends at 0,0 then it would seem that the direction of travel and acceleration would be along the Y axis right?

No tommac it doesn't. That post only says the distance over which the acceleration/deceleration happened and was missing the rate of said acceleration/deceleration. Later you just said "0-.99999999999999999 c in 1 second" but left out all information about Y&Z acceleration/deceleration to X AND to boot you changed the question anyway. The only person the question is "clear" to, and I even question that because the question keeps mutating from post to post, is you.

tommac

2010-Jul-16, 04:03 AM

No tommac it doesn't. That post only says the distance over which the acceleration/deceleration happened and was missing the rate of said acceleration/deceleration. Later you just said "0-.99999999999999999 c in 1 second" but left out all information about Y&Z acceleration/deceleration to X AND to boot you changed the question anyway. The only person the question is "clear" to, and I even question that because the question keeps mutating from post to post, is you.

You can derive it.

tommac

2010-Jul-16, 04:05 AM

100% agreement here. Even if you think I'm being unreasonable with you tommac I'm not the only one point this stuff out to you. .

Not necessarily unreasonable ... just obsessive ... It seems that instead of just ignoring the question you need to post 20 + times on the thread

tommac

2010-Jul-16, 04:06 AM

This should be good...lets change gears again before the other question is answered..

This question wasnt for you .... you still didnt answer the other question.

tommac

2010-Jul-16, 04:22 AM

Howzat? Can you attach a drawing. Because, from your prose, it is not comprehensible.

http://www.spacetimeandtheuniverse.com/members/tom-albums-tommacs-guide-universe-picture13-abc.jpg

There is only 1 object moving ...

tommac

2010-Jul-16, 04:35 AM

Lets ignore gravity ... or GR ....

This is a pure SR question ... no GR involved.

I am confused with what I think is a simultaneity issue.

Tommac,

Since all observers perceive light in their own reference frame as moving at light speed, the observation of light originating in another reference frame into your own, of course would still appear to be moving at light speed upon your observation. If you are looking at a different reference frame conceptually, you would consider the speed of light in all other reference frames as moving faster than light in the direction of their relative motion to you and slower than light speed in the opposite direction. The time interval between light pulses would be directly proportional to the time dilation, if any, rather than the conceptual light speed.

To determine their relative time dilation, on the other hand, you would need to know how each reference frame is moving relative to a common primary gravitational influence if there is one. If there is no common center of gravity concerning the primary cause of time dilation, then to conceptually compare two reference frames with differing centers of gravity, the time dilation of each would first need to be calculated. Following that one might compare the time in the two reference frames to a common center of gravity or reference frame (such as the sun for instance) if such commonality exists, otherwise such conceptual time comparisons of time dilations accordingly would only be speculative and would not result in the certain validity of any conclusion.

forrest noble

2010-Jul-16, 06:01 AM

Tommac,

Lets ignore gravity ... or GR ....

This is a pure SR question ... no GR involved.

I am confused with what I think is a simultaneity issue.

For reference frames moving relative to each other based upon SR alone without knowledge of a mutual center of gravity, such knowledge or calculations of simultaneity cannot be made. Even when using GR, calculations are very difficult and the best bet may be to have clocks in both reference frames continuously re-calibrated by the same distant pulsar. Such clocks seemingly could come close to recordings and realizations of simultaneity. Eventually I think our satellites and space robots will be controlled by such clocks where precision timing is required.

WayneFrancis

2010-Jul-16, 06:02 AM

Not necessarily unreasonable ... just obsessive ... It seems that instead of just ignoring the question you need to post 20 + times on the thread

tommac, my style of posting is I read a thread post by post and comment on each post I feel I have something to comment on as I get it. If in the course of reading a thread I ask a question or make a comment that is answered/addressed in a post further on in the thread I acknowledge it. It just helps keep clear what my answers and comments are in relation too, hence my heavy use of quotes.

tommac

2010-Jul-16, 06:04 AM

tommac, my style of posting is I read a thread post by post and comment on each post I feel I have something to comment on as I get it. If in the course of reading a thread I ask a question or make a comment that is answered/addressed in a post further on in the thread I acknowledge it. It just helps keep clear what my answers and comments are in relation too, hence my heavy use of quotes.

For the most part this has not been helpful for me ...

WayneFrancis

2010-Jul-16, 06:08 AM

You can derive it.

No tommac, we can't. We can guess and fill in some numbers that you've left out but then our answers will be arbitrary.

WayneFrancis

2010-Jul-16, 06:11 AM

This question wasnt for you .... you still didnt answer the other question.

Questions posted here are generally for everyone to have a crack at. Even if I'm wrong with an answer I'm sure I'd be corrected and I to would learn from the thread.

Well to your thought experiment of

...

What do their clocks say? Who's clocks are the same ( X and Y did not move ( except very slowly ) relative to each other )? But Y and Z should be off significantly. Who is right?

...

You still have not provided all the information we need to answer that question.

To your changed question of

All I want to know is whose clock shows the most progression in time.

I answered in post #60 (http://www.bautforum.com/showthread.php/105552-Tensors-and-Time-Dilation?p=1762812#post1762812)

...

All I want to know is whose clock shows the most progression in time.

Well tommac you never asked "Which clock shows the most progression in time?"

The answer to that is easy....it is X

...

WayneFrancis

2010-Jul-16, 06:29 AM

Lets ignore gravity ... or GR ....

This is a pure SR question ... no GR involved.

I am confused with what I think is a simultaneity issue.

I tried to address this in post #22 (http://www.bautforum.com/showthread.php/105552-Tensors-and-Time-Dilation?p=1757113#post1757113)

r...You can't synchronise even 2 separated clocks to both read the same time to local observers at both points. The larger the distance the more obvious the shift in time...

There are 2 issues here 1 is you can NEVER synchronise 2 or more separated clocks so that all observers see all other clocks in agreement with their own without taking into account light travel time.

Because of this there can be more confusion when you try to see what other clocks read during and after one or more of the clocks has changed its reference frame.

IE synchronised clocks in the similar reference frames will not read the same time to any observer. The times will all be offset by an amount equal to the light travel time.

If we have a fully laid out thought experiment with all the variables needed then we can provide answers to what each observer will see every step of the thought experiment and it will be clearer why there is no inconsistencies.

tommac

2010-Jul-16, 12:29 PM

Ok so like this

http://users.on.net/~waynefrancis/tommac_te3.png

Yes like that.

Here is how I think it should work ... however I am near positive that I am wrong but looking for a correction:

X|B|C

A|E|S

So ... A is Equal to ** pulse but A views C's pulse as being slow compared to his

HOLD IT! STOP! Where are you getting "X" from?

My bad ... I used X as a place holder to keep the line formatted .... probably a bad choice ... however I think a space gets misformatted during posting:

|B|C

A|E|S

@|B|C

A|E|S

M|B|C

A|E|S

*|B|C

A|E|S

Your thought experiment has 3 points A,B,C and three comparisions (F)aster,(S)lower,(E)qual. No X....nor do you define what you mean by X. This is the problem tommac...you ask questions and people are left asking themselves "Have I missed something? What is tommac really saying here?"

C will observe B & A's pulse faster then its pulse while C is in motion towards A.

I see the problem here you have a discrepancy on how A&B can see their clock in synch while C sees them out of synch while C is in motion. This is the classical situation of different observers don't observe events happening at the same time.

Yes ... this is the question. When the clocks rendezvous ... what do they read and why?

WayneFrancis

2010-Jul-16, 04:38 PM

Yes like that.

My bad ... I used X as a place holder to keep the line formatted .... probably a bad choice ... however I think a space gets misformatted during posting:

|B|C

A|E|S

@|B|C

A|E|S

M|B|C

A|E|S

*|B|C

A|E|S

Ah I see what you are doing...

http://users.on.net/~waynefrancis/tommac_te3.png

At the start

red observing blue

A B C

A E E E

B E E E

C E E E

During C's trip to A

A B C

A E E F

B E E F

C S S E

While C&A travel to B together

A B C

A E S E

B F E F

C E S E

Yes ... this is the question. When the clocks rendezvous ... what do they read and why?

well what they read depends on how fast they all accelerate and decelerate and to what speed the reach and the distances they all travel.

tommac

2010-Jul-16, 09:01 PM

Ah I see what you are doing...

http://users.on.net/~waynefrancis/tommac_te3.png

At the start

red observing blue

A B C

A E E E

B E E E

C E E E

During C's trip to A

A B C

A E E F

B E E F

C S S E

While C&A travel to B together

A B C

A E S E

B F E F

C E S E

well what they read depends on how fast they all accelerate and decelerate and to what speed the reach and the distances they all travel.

So are you saying that the direction of travel relative to the source has no impact on time dilation?

WayneFrancis

2010-Jul-17, 02:55 AM

So are you saying that the direction of travel relative to the source has no impact on time dilation?

The off nadir angle will effect the frequency of the light but not the number of the pulses both A&B observe. IE Observers at different points will

observe the same number of pulses emitted by C during its trip. Don't mistake being able to considering yourself at rest with not being able to tell your not in an accelerated frame. The observers don't dictate the number of pulses release the emitter does. That is the ultimate arbitrator of the time elapsed.

IE In a journey for between any 2 points it is the body making the journey that dictates how long it takes them in their frame to make said journey.

If I travel from Earth to Alpha Centauri at .99c to me the trip will take 208 days. So if I pulse a non directional light source once a day the light will pulse 208 times and any observer anywhere in the universe would see only 208 days. The angle at which they are observing doesn't matter.

What I think you are doing is shifting your frame of reference but not shifting all the effects that go along with it which is causing you to think that the time dilation is observer dependant and not dependant on the emitter.

To emphasise this the ultimate arbitrator on how many times a clock ticks is the clock's frame not the observers frames.

tommac

2010-Jul-21, 03:01 PM

If I travel from Earth to Alpha Centauri at .99c to me the trip will take 208 days. So if I pulse a non directional light source once a day the light will pulse 208 times and any observer anywhere in the universe would see only 208 days. The angle at which they are observing doesn't matter.

.

But when will they see the pulse ... I understand theat they will see 208 pulses ... but the rate of the pulse will not be 1 pulse per day ...

My question is does the angle of travel make a difference when it comes to time dilation ... so if a pulse is done 1x per day in an accelerated frame ... does it matter the direction and angle ( with respect to an external observer ) of the acceleration as "the rate" of pulses that an external observer observes?

WayneFrancis

2010-Jul-21, 07:03 PM

But when will they see the pulse ... I understand theat they will see 208 pulses ... but the rate of the pulse will not be 1 pulse per day ...

My question is does the angle of travel make a difference when it comes to time dilation ... so if a pulse is done 1x per day in an accelerated frame ... does it matter the direction and angle ( with respect to an external observer ) of the acceleration as "the rate" of pulses that an external observer observes?

It will shift things a bit and that depends a lot on the speed and the total distance travel from the point of the non accelerated observers.

Observers in front of the accelerated traveller will see a different ... pattern then someone behind the traveller.

IE the Observer in front will see them spread over 4 years and a bit closer together in time. Observers behind will see them spread over about 8 years and obviously more spread out.

WayneFrancis

2010-Jul-22, 05:09 PM

Note that with my previous post this has nothing to do with SR and simply an issue with light travel time.

Powered by vBulletin® Version 4.2.3 Copyright © 2019 vBulletin Solutions, Inc. All rights reserved.