Angular velocity & impossible situation of relativity

[radicalsymmetry]

Person-a travels on circumference c1.

Person-b travels on circumference c2.

 

There will be time-dilation. Person-b will age more slowly relative to Person-a.

 

However... say that Person-a & Person-b can look at each other throughout the rotation, and light travels between them at c, do we not have an impossible situation of relativity?

 

Please explain in plain English.

 

[Strange]

What speeds are a and b moving at?

 

What exactly do you think is impossible?

 

Note that this might not be explainable using special relativity, because of the acceleration involved.

[ajb]

Note that this might not be explainable using special relativity, because of the acceleration involved.

You can handle both accelerated objects and non-inertial frames ("accelerated frames") in special relativity.

[Strange]

You can handle both accelerated objects and non-inertial frames ("accelerated frames") in special relativity.

 

OK. I wasn't sure.

[radicalsymmetry]

What speeds are a and b moving at?

 

What exactly do you think is impossible?

 

 

 

Less than c, I don't think it really matters for the puzzle, and they're both moving at the same angular velocity.

 

The problem is that person a and person b can see each other, via the constant speed of light, yet time slows down for person a because they are traveling through space-time at a higher velocity.

 

Let's say that they both spin around the centre for a few years until the outer (person b) is 24 hours younger than the inner (person a). For argumants sake let's say the "master clock" is in the centre. How could this be possible if they are also able to observe each other the whole time at the speed of light ? There exists a conflict in transmission of information...That's the topic of the OP.

 

 

( note: points p1, p2 & p3 are to be regarded distinctly from person a & person b. I apologise for any confusion caused by my labelling. )

 

Edited July 27, 2014 by radicalsymmetry

[swansont]

Their clocks don't agree. What other "problems" are you thinking exist?

[Strange]

Less than c, I don't think it really matters for the puzzle, and they're both moving at the same angular velocity.

 

OK. That was the missing bit of information.

 

 

The problem is that person a and person b can see each other, via the constant speed of light, yet time slows down for person a because they are traveling through space-time at a higher velocity.

 

I don't see why you think that is a problem. It happens. GPS receivers have to take it into account.

 

I am not sure how the acceleration would be taken into account, but if we consider just the relative velocity, then they will both see the other's clocks running slow. (Person a is only travelling faster from some external frame of reference.)

[radicalsymmetry]

So if we put an optical fibre cable at the centre and ran it out radially, with break-out points at each circumference, and the cable moves round the circumference(s) under the travellers feet, are we to presume that the travellers perceive an increased frequency of light ? i.e the frequency of light increases dependant on the observers movement in space-time, even if the path which the light takes remains fixed ?

Edited July 27, 2014 by radicalsymmetry

[xyzt]

 

 

Less than c, I don't think it really matters for the puzzle, and they're both moving at the same angular velocity.

 

The problem is that person a and person b can see each other, via the constant speed of light, yet time slows down for person a because they are traveling through space-time at a higher velocity.

 

Let's say that they both spin around the centre for a few years until the outer (person b) is 24 hours younger than the inner (person a). For argumants sake let's say the "master clock" is in the centre. How could this be possible if they are also able to observe each other the whole time at the speed of light ? There exists a conflict in transmission of information...That's the topic of the OP.

 

 

( note: points p1, p2 & p3 are to be regarded distinctly from person a & person b. I apologise for any confusion caused by my labelling. )

 

time dilation conflict 2d _ 2.jpg

This is exactly the situation solved by GPS. The clocks on the ground would disagree with the clocks in the satellites UNLESS the frequency of the satellite clocks is pre-adjusted at launch. This is exactly what happens and the frequency adjustment is done according to GR. I could post for you the exact derivation.

[radicalsymmetry]

How can the light "know" that it should increase in frequency when travelling in a fixed system ?

 

It can't obviously.

 

Using the example provided in my previous post, i.e an optical fibre cable, is there a compression on the radial length of the cable for those (people) moving at a radial velocity?

 

Makes me think that space is nothing more than a rarefaction of time.

[swansont]

How can the light "know" that it should increase in frequency when travelling in a fixed system ?

 

It can't obviously.

 

 

Obviously. Don't anthropomorphize nature. She hates that.

 

You might as well ask "How does an object "know" to fall down when its center-of-mass is not over some buttressing structure?"

 

Things behave according to the laws of nature, and relativity is one of those laws. Time is not an absolute.

[xyzt]

How can the light "know" that it should increase in frequency when travelling in a fixed system ?

It doesn't. Don't project your crackpoterry on the laws of nature. It is time that is affected, GR explains exactly how. I pffered to post the explanation but it involves understanding of basic GR, something that you obviously lack. Besides, you asked for a "touchy-feely" explanation.

 

You can get the ratio of clock rates relatively easily by knowing GR.

Start with the Schwarzschild solution to EFE:

 

[math]ds^2=(1-r_s/r) (cdt)^2-\frac{dr^2}{1-r_s/r}-(rd\theta)^2[/math]

 

Use the fact that

 

[math]ds=c d\tau[/math]

 

Then:

 

[math](c d\tau)^2=(1-r_s/r) (cdt)^2-\frac{dr^2}{1-r_s/r}-(rd\theta)^2[/math]

 

produces, by division with [math](cdt)^2[/math]:

 

[math](\frac{d\tau}{dt})^2=(1-r_s/r)-\frac{(v/c)^2}{1-r_s/r}-(\frac{r \omega}{c})^2[/math]

 

Write the above for two locations , at radial distances [math]r_1[/math] and [math]r_2[/math] and you get:

 

 

[math](\frac{d\tau_1}{dt})^2=(1-r_s/r_1)-\frac{(v_1/c)^2}{1-r_s/r_1}-(\frac{r_1 \omega_1}{c})^2[/math]

[math](\frac{d\tau_2}{dt})^2=(1-r_s/r_2)-\frac{(v_2/c)^2}{1-r_s/r_2}-(\frac{r_2 \omega_2}{c})^2[/math]

 

Divide the two:

 

[math](\frac{d\tau_2}{d \tau_1})^2=\frac{1-r_s/r_2-\frac{(v_2/c)^2}{1-r_s/r_2}-(\frac{r_2 \omega_2}{c})^2}{1-r_s/r_1-\frac{(v_1/c)^2}{1-r_s/r_1}-(\frac{r_1 \omega_1}{c})^2}[/math]

 

where [math]v_i= \frac{d r_i}{dt}[/math] i=1,2. If the orbit is circular, then [math]v_i=0[/math] but this is not the usual case.

 

The above equation relates the proper times of two clocks , located at different radial distances and moving at different angular speeds. It is the foundation of the calculations for setting up the frequencies of the GPS clocks (such that they are synched up).

 

[math]\displaystyle \frac{d\tau_2}{d \tau_1}=\sqrt{\frac{1-r_s/r_2-\frac{(v_2/c)^2}{1-r_s/r_2}-(\frac{r_2 \omega_2}{c})^2}{1-r_s/r_1-\frac{(v_1/c)^2}{1-r_s/r_1}-(\frac{r_1 \omega_1}{c})^2}}[/math]

 

Since the above (exact) formula is rather complicated, the GPS calculations use a power series approximation, making use of the fact that [math]r_s<<r[/math]. The formula encapsulates the effects in:

 

1. gravitational potential difference , via the term in [math]\frac{r_s}{r_i}[/math]

2. radial speed difference (if it exists), via the term in [math]v_i[/math]

3. angular speed difference, via the term in [math]r_i \omega_i[/math]

 

In general, the formula is expressed in terms of ratios of frequencies, not clock rates:

 

[math]\displaystyle \frac{f_1}{f_2}= \sqrt{\frac{1-r_s/r_2-\frac{(v_2/c)^2}{1-r_s/r_2}-(\frac{r_2 \omega_2}{c})^2}{1-r_s/r_1-\frac{(v_1/c)^2}{1-r_s/r_1}-(\frac{r_1 \omega_1}{c})^2}}[/math]

 

 

 

 

Using the example provided in my previous post, i.e an optical fibre cable, is there a compression on the radial length of the cable for those (people) moving at a radial velocity?

 

No, there is no "compression"

 

 

 

Makes me think that space is nothing more than a rarefaction of time.

 

Time passage is a complex function of the gravitational potential and of relative motion. Do you have GPS in your car, mobile phone? How do you think it works? Not through crank misconceptions, that much is sure.

Edited July 27, 2014 by xyzt

[Sensei]

It doesn't. Don't project your crackpoterry on the laws of nature.

(...)

Not through crank misconceptions, that much is sure.

 

Can't you write single post without being rude?

 

If forum activity makes you so much angry, you should find other hobby..

 

People here want to help others, not to insult them..

[Janus]

So if we put an optical fibre cable at the centre and ran it out radially, with break-out points at each circumference, and the cable moves round the circumference(s) under the travellers feet, are we to presume that the travellers perceive an increased frequency of light ? i.e the frequency of light increases dependant on the observers movement in space-time, even if the path which the light takes remains fixed ?

 

First consider a hollow tube extending from Pa to Pb. Pa puts a marble in his end and lets go. What happens? the marble will travel along the tube gaining speed relative to it until it comes out with PB measuring it as moving at some speed. The marble gains energy from the spinning disk as it moves outward.

 

Replace the tube with a fiber-optic cable and send a pulse of light along it. The pulse, just like the marble must gain energy from the spinning disk as it move from Pa to Pb. However, light cannot gain speed. When Pa emits it, it is moving at c, When it reaches Pb it is moving at c. However, it still must have an energy difference between Pa and Pb, and since the energy of light is related to its frequency, Pb measures an increase in frequency as compared to Pa.

[Enthalpy]

Don't anthropomorphize nature. She hates that.

I like that one.

[radicalsymmetry]

Thanks for your input, Janus.

 

In the case of the marble there's centrifugal force but a photon will spend most of it's journey n free-space and not as a particle being subjected to (side wall) angular rotation.

 

Therefore I don't agree "The pulse, just like the marble must gain energy from the spinning disk" is as clear-cut as you've portrayed it to be.

[xyzt]

 

Can't you write single post without being rude?

 

If forum activity makes you so much angry, you should find other hobby..

 

People here want to help others, not to insult them..

Nope, see his response to Janus' excellent post.

Edited July 28, 2014 by xyzt

[Mordred]

roflmao, by the way your post on the math relations is excellent as well as Janus post. Unfortunately not everyone can relate to math sad but true none the less. After 10+years answering questions on various forums a certain amount of patience is required

Edited July 28, 2014 by Mordred

[xyzt]

roflmao, by the way your post on the math relations is excellent as well as Janus post. Unfortunately not everyone can relate to math sad but true none the less. After 10+years answering questions on various forums a certain amount of patience is required

This is not a problem with him not being able to relate to mainstream math. The real problem is with him accepting mainstream science. As evidence, see his response to Janus' excellent post. I call them the way they ARE.

[Mordred]

np problem mate our job is to teach the mainstream, though that does get frustrating lol. if they cannot accept the mainstream teachings more often than not that is their loss not ours. As long as we are satisfied that we have provided the most accurate answer then how they accept that answer is up to them and their loss not ours.

 

quite frankly it would be wrong to change our answers to conform to the OPS thinking (deviations from mainstream textbook answers), that being said its often difficult to convince others the main stream is correct. However if I can convince 1 person out of 20 to learn the main stream then I'm happy. I accomplished something

 

as they say fight the battles you can win and don't give a second thought to those you cannot

your answer is correct, its up to the OP to understand it

Edited July 28, 2014 by Mordred

[xyzt]

np problem mate our job is to teach the mainstream, though that does get frustrating lol

You can't teach hardened cranks. Whether you are nice, like Janus or not so much, like me.

[Mordred]

true I find it a challenge myself, as frustrating as it is

Edited July 28, 2014 by Mordred

[radicalsymmetry]

I believe I'm asking perfectly rational questions;

such as...

 

 

the frequency of light increases dependant on the observers movement in space-time, even if the path which the light takes remains fixed ?

 

i.e space-time has remained unchanged. Light has changed.

 

~ vs ~

 

is there a compression on the radial length of the cable for those (people) moving at a radial velocity?

 

i.e space-time has changed. Light has remained unchanged.

 

 

When, by Janus, an example is provided that alludes to the (first) example above, by way of a marble in a tube, I question the validity of the example by stating that which I see as very obvious...

 

 

...a photon will spend most of it's journey n free-space and not as a particle being subjected to (side wall) angular rotation.

 

This isn't the line of thinking of a crank. Far from it. I'm a logical person who wishes to understand the world around him. I welcome any further discussion which is on-topic. Thank You.

 

p.s. If you wish to discuss me, or make speculations about me as a person, I suggest that this thread, titled "Angular velocity & impossible situation of relativity", is not the appropiate place to do so.

Edited July 28, 2014 by radicalsymmetry

[imatfaal]

!

Moderator Note

 

OK - everyone stop the comments about one and other. Please keep it friendly and keep it science.

 

RadicalSymmetry - this is a science forum; arguments from a preconceived and purely imaginary standpoint are frowned upon. Arguments from incredulity, ignorance, and incomprehension are pretty much worthless. XYZT has given a mathematical solution and others have explained in a more textual manner. Take another look at the explanations and if you do not understand them ask for clarification.

 

You claim to be merely asking questions in a rational and logical sense - yet all the experiments and real world situations we observe back up the ideas of relativity but your lack of understanding means you are happy to declare an "impossible situation". This is not rational. If you wish to explore the ideas of Einstein and learn why we believe they are correct then please do so - that is the reason for this forum; however, if you wish to show through ill-conceived gedanken that relativity is incorrect - then we will be moving this thread to Speculations and your ideas will receive short-shrift.

 

[radicalsymmetry]

Thanks, imatfaal.

In the OP I had thought that two different points at the same angular velocity, where the travellers can see each other, creates an impossible situation.

However; this thread is now at the stage where some reasons are being given to explain the nature of a relative time-dilation. Namely; change in frequency of wave vector.

 

I do recognise that some detailed maths, relevant to the OP, has been provided but I do not wish to thank the poster as he/she provided said information with unnecessary insinuations and personal remarks.

 

I'm not here to argue. I want to comprehend. To that end, in my previous post, I've posted my perspective and seek dialog on the subject in layman’s terms.

[/modtip]

if you wish to show through ill-conceived gedanken that relativity is incorrect...

 

This is certainly not my intention.

Edited July 28, 2014 by radicalsymmetry