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#1 tar

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Posted 3 July 2011 - 02:26 AM

Swansont,

Don't know who you are referring to as gas bags, hoping to overturn relativity theory, but I would like to check in as someone who does not understand what relativity theory is saying about the universe. I see an experiment where two in sync clocks are removed from each other, one follows one path into another inertial frame, and when rejoined the clocks are no longer in sync. I just want to know what happened, where it happened, when it happened and why it happened, so I can fit the forces, laws and combinations, into my model of the world. I can take ratios and make analogies and transforms, and such, in a general, uneducated, natural way. I can't do the math.

Just looking for the explanations. Just need things to fit together in my model, in the same manner that they fit together, for real.

For instance if all matter in the universe is in actuality the same age, that is t zero being the big bang, and t "age of the universe" being the age of any matter in it now, I do not know the meaning of our near C traveler coming back 5 years younger. Does that mean that the matter in the ship and body of the traveler is "age of the universe" minus 5 years old? If so, then the universe would be filled with matter of different ages, if matter can leave an inertial frame, and return to it.

Just looking for a point of reference from which to understand the rest.

Regards, TAR2
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#2 tar

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Posted 4 July 2011 - 01:01 PM

P.S.

By the way, how does the high speed twin know when to turn around and come back?

P.P.S

Let's say the traveliing twin was instructed to go to Alpha Centauri 4.5 light years distant, turn around and come back. It would take him about 5 years to get there, he would be running his engines for 5 years, and he would be five years older when he got there. He would run his engines for 5 years to get back. And by my thinking would be 10 years older when he got back. It would not matter that he was seeing the Earth age very slowly as he was outrunning the photons on the way out, and that he would see the Earth in fast motion on the way back, it would still add up to 10 years of travel. Probably also would "see" what was in front of him in higher frequencies/shorter wavelengths than normal and what he was moving away from in lower than normal frequencies/longer wavelengths.

Edited by tar, 4 July 2011 - 01:06 PM.

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#3 imatfaal

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Posted 4 July 2011 - 02:46 PM

Tar - here is a very good site with three analyses of the twin situation (I refuse to say paradox cos it aint one) and three common probelms with understanding

http://www.desy.de/u...in_paradox.html

The Physics Faqs are well maintained and good stuff. If you have any problems with them some one will be able to help you out
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#4 swansont

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Posted 4 July 2011 - 05:21 PM

Let's say the traveliing twin was instructed to go to Alpha Centauri 4.5 light years distant, turn around and come back. It would take him about 5 years to get there, he would be running his engines for 5 years, and he would be five years older when he got there. He would run his engines for 5 years to get back. And by my thinking would be 10 years older when he got back. It would not matter that he was seeing the Earth age very slowly as he was outrunning the photons on the way out, and that he would see the Earth in fast motion on the way back, it would still add up to 10 years of travel. Probably also would "see" what was in front of him in higher frequencies/shorter wavelengths than normal and what he was moving away from in lower than normal frequencies/longer wavelengths.

You always have to state the frame of reference with which you are making the measurement. If a spaceship travels at 0.866c as measured by an earth observer (gamma=2), the earth observer will see the ship take 5.2 years to get there and 5.2 years to get back, with the distance being 4.5 LY. The earth observer will be 10.4 years older when the ship returns. (This ignores all accelerations)

The rocket pilot, however, sees the distance contracted by a factor of 2, and he measures the 2.25 LY trip as taking only 2.6 years out and the same on return, for a total of 5.2 years. His clock, as measured by an earth observer, ran half as fast as an earth-bound clock. The space pilot is 5.2 years younger than things on earth. While they disagree on the measurements, there is an underlying consistency of the relativity: the length contraction measured in one frame manifests itself as time dilation in the other frame.
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#5 Janus

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Posted 4 July 2011 - 06:03 PM

P.S.

By the way, how does the high speed twin know when to turn around and come back?

P.P.S

Let's say the traveliing twin was instructed to go to Alpha Centauri 4.5 light years distant, turn around and come back. It would take him about 5 years to get there, he would be running his engines for 5 years, and he would be five years older when he got there. He would run his engines for 5 years to get back. And by my thinking would be 10 years older when he got back.

Ah, but according to him, the distance between Earth and Alpha C is length contracted to 1.96 ly, which takes him 2.18 years to travel at 0.9c for a total round trip time of 4.36 years round trip by his clock.

It would not matter that he was seeing the Earth age very slowly as he was outrunning the photons on the way out, and that he would see the Earth in fast motion on the way back, it would still add up to 10 years of travel. Probably also would "see" what was in front of him in higher frequencies/shorter wavelengths than normal and what he was moving away from in lower than normal frequencies/longer wavelengths.


the Relativistic Doppler shift ratio is:

sqrt((1+B)/(1-B))

where

B=v/c

Thus, while heading away from Earth, he will see the Earth age at a rate of 1/4.36 his own rate and accumulate 2.18/4.36 =0.5 years.
on the return trip, he will see the Earth age at a rate 4.36 his own and accumulate 4.36x2.18 = 9.5 years for a total of 10 yrs.

Thus he will measure 4.36 years pass on his clock while watching a total of 10 yrs pass on the Earth.

Edited by Janus, 4 July 2011 - 06:05 PM.

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#6 tar

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Posted 4 July 2011 - 08:08 PM

Janus and Swansont,

Thus he will measure 4.36 years pass on his clock while watching a total of 10 yrs pass on the Earth.


But then he would know his clock was wrong, because he had covered 9 light years distance, in 4.36 years?
He would clock himself going over twice the speed of light! Presumably when he was halfway to Alpha Centuri with the Sun and Alpha Centuri both 2.25 light years away, he would know it would take him, at 0.866c, which is 1.155 years/light year, 2.6 more years to make it to Alpha Centuri, and would know he thus had travelled for 2.6 years, and could recalibrate his faulty clock.

Swansont,

I understand that different "here and nows" will see the rest of the universe differently. The order of events, for instance, and the passage of time on a distant moving clock, but I was using the twins to investigate the nature of time, that is why I posted in the time thread. And I understand that you have to define the reference frames you are using to discuss what is happening when. But there is a hypothetical reference frame in which all points in the universe are the same age. This frame itself, cannot actually be witnessed, because the points in it are separated by distance, and an event in one spot does not actually occur in another spot, until the photons announcing the event arrive.

So for the twins, I think it important for each twin, to on their own, reference this hypothetical reference frame, where all points are the age of the universe, including themselves, and with that knowledge, and their knowledge of the distance between themselves and another point, be able to figure how long events will take to make the trip between, and how long they will take, at the speed they themselves are going, to make the trip.

Regards, TAR2

P.S. Not related directly to this thread, but since, this discussion has been moved, I will stick it here. Were the 4 Cesium clocks that were flown around the world, westward and eastward and so on, positioned in the plane in different orientations, or were they all facing the same way, in relation to the direction of the plane.

I don't remember seeing a description of how they were placed. It might matter, considering the photon travel time between the cesium atom and the detector. Would it matter if the detector was foward in the plane to the cesium atom, or the cesium atom ahead of the detector? Or the photon travelling UP rather than DOWN to the detector?

Edited by tar, 5 July 2011 - 02:26 AM.

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#7 Janus

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Posted 4 July 2011 - 08:44 PM

Janus and Swansont,



But then he would know his clock was wrong, because he had covered 9 light years distance, in 4.36 years?
He would clock himself going over twice the speed of light! Presumably when he was halfway to Alpha Centuri with the Sun and Alpha Centuri both 2.25 light years away, he would know it would take him, at 0.866c, which is 1.155 years/light year, 2.6 more years to make it to Alpha Centuri, and would know he thus had travelled for 2.6 years, and could recalibrate his faulty clock.


As I already pointed out in the previous post, for him, the distance between Earth and Alpha C is not 4.5 lys, but somewhat less than 1/2 that distance (in my example he was traveling at 0.9c). And that distance is just as "real" as the distance as measured from the Earth. There is nothing faulty with his clock or his method of the distance, they are just as good as those used by the Earth and th results they give are just as valid.

To grasp Relativity you are going to have to throw away some notions you probably have about the nature of time and distance.

Let's say you have two men one faces in one direction and the other faces in the opposite. The second man is the the right of the first man as seen by the first man. The second man say's that the first man is to his right. Add a third man who faces at a 90į angle to the first two. According to him, neither man is to the right or left of the other. Who's correct? who is really to the right of the other, or is neither? There is no one absolute correct answer.

The same is true with the measurement of time and distance. The time that elapses between two events or the distance between two points, depends upon who is doing the measuring.
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#8 DrRocket

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Posted 4 July 2011 - 10:14 PM

Swansont,

Don't know who you are referring to as gas bags, hoping to overturn relativity theory, but I would like to check in as someone who does not understand what relativity theory is saying about the universe. I see an experiment where two in sync clocks are removed from each other, one follows one path into another inertial frame, and when rejoined the clocks are no longer in sync. I just want to know what happened, where it happened, when it happened and why it happened, so I can fit the forces, laws and combinations, into my model of the world. I can take ratios and make analogies and transforms, and such, in a general, uneducated, natural way. I can't do the math.

Just looking for the explanations. Just need things to fit together in my model, in the same manner that they fit together, for real.

For instance if all matter in the universe is in actuality the same age, that is t zero being the big bang, and t "age of the universe" being the age of any matter in it now, I do not know the meaning of our near C traveler coming back 5 years younger. Does that mean that the matter in the ship and body of the traveler is "age of the universe" minus 5 years old? If so, then the universe would be filled with matter of different ages, if matter can leave an inertial frame, and return to it.

Just looking for a point of reference from which to understand the rest.

Regards, TAR2



The most fundamental aspect of relativity, both special and general is that the metric that determines the spacetime interval is the same for all observers, it is invariant.

In special relativity this means that c^2 \Delta t^2- \Delta x^2- \Delta y^2-\Delta z^2 is the same in all inertial reference frames. In general relativity it means that The Lorentzian metric (aka inner product) which is locally <(t_1,x_1,y_1,z_1),(t_2,x_2,y_2,z_2)>=c^2t_1t_2-x_1x_2-y_1y_2-z_1z_2 is the same for all observers.

A path in spacetime for a particle or body is called its world line. The length of that (time like) world line is the time (multiplied by c), called proper time, experienced by the body. Length is determined using the Lorentzian metric. It is a fact that a geodesic path in the Lorentzian geometry of spacetime has a length, proper time, that is a maximum among all timelike curves joining two given end points. It is also a result of general relativity that a body in free fall has a worldline that is a geodesic.

So, suppose that two twins start and later meet again at coincident points in spacetime. One twin (the "stay at home twin") remains in free fall (sat at the South Pole of the Earth). The other uses a rocket to break out of free fall, travel to a nearby star and return. The "stay at home twin has followed a geodesic spacetime path, and therefore has experienced the maximum possible proper time. The traveling twin has followed a non-geodesic path, and is therefore younger.

There is no "when" this occurred. There is no "where" this occurred either. General relativity does not allow the comparison of clocks at different spatial points -- "time here" vs "time there" loses meaning. There are approximations, but only approximations that permit a sort of comparison between separated clocks (approximating general relativity locally with special relativity). There is no "mechanism" causing clocks to run differently. What GR provides is an entirely different notion of the very nature of time from the Newtonian ideal, and even something fundamentally different from special relativity. Special relativity is merely a local approximation (really the linear approximation on the tangent space) to general relativity.


Unfortunately there is no adequate way to describe all of this without used of differential geometry. For a complete explanation see Gravitation by Misner, Thorne and Wheeler.

Edited by DrRocket, 4 July 2011 - 10:21 PM.

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#9 IM Egdall

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Posted 4 July 2011 - 11:22 PM

Swansont,

Just looking for the explanations. Just need things to fit together in my model, in the same manner that they fit together, for real.

For instance if all matter in the universe is in actuality the same age, that is t zero being the big bang, and t "age of the universe" being the age of any matter in it now, I do not know the meaning of our near C traveler coming back 5 years younger. Does that mean that the matter in the ship and body of the traveler is "age of the universe" minus 5 years old? If so, then the universe would be filled with matter of different ages, if matter can leave an inertial frame, and return to it.

Just looking for a point of reference from which to understand the rest.

Regards, TAR2


The age of the universe is measured in "cosmic time". See link:

http://ncse.com/evol...ing-cosmic-time
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#10 tar

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Posted 5 July 2011 - 04:21 AM

DrRocket,

Thank you for the description, but although I understand what you are saying, I am finding it hard to accept a reality, without a mechanism. With our imaginations, and formulae, we can build models that work, that do not necessarily have to actually fit reality. It seems very strange to me, for instance, that you can say that we figured the universe pretty much out, down to how old it is and how much stuff is in it, and what the nature of the stuff is. All this from observing photons telling us what the universe used to be like. Which is fine, we are pretty smart, and able to make ratios and analogies, map one thing to another, and put ourselves in another location and time and imagine what it must be like. But only because we understand the mechanisms involved. And have built back a model that we "predict" should be the way the entire universe is "now".

The Newtonian "notion" of space and time, past and future, here and there, is how I appear to understand things, as a human. I can not "pretend" to understand them elsewise. I can slow things down, speed them up, make them larger and smaller, scale this way and that, but I don't know the meaning, of "coming back aged less". Compared to what? Number of heartbeats was smaller? Would the traveller "feel" like she was forshortened? What are the implications of such a voyage? Would the photons her ship is running into, eminating from Alpha Centuri (if that was her turn around point) be mostly of the x-ray and gamma and cosmic ray variety? Would they burn her up? Would they "age" her? Wrinkle her skin? Make her come back looking like she had aged 100 years? (not to mention how long it would take to get up to that speed at an acceleration that would not tear her apart.) Would the "light pressure" of the high energy photons from Alpha Centuri, hitting her forward shields impede her progress, causing her to have to maintain a constant acceration, through their electromagnetic field? How would this affect her clock, and the equations?

In my book, reality fits together, is always true, and always is at least a little more complex than the model of it we hold in our heads. For you to say that I can not properly model reality, without understanding differential geometry is counter intuitive. It is the equations that are not complete. Reality is already complete. And if reality is doing something, there is a reason for it, a mechanism involved, a way that that thing fits into the whole picture. If something doesn't make sense, its because there is an aspect of what is going on that I don't understand. I can accept that I do not know differential equations, but I cannot accept that there is not an explanation of the who, where, when, why and how of a journey that takes place within my view, within my lifetime. There must be mechanisms that cause the effects. Otherwise, they wouldn't happen.

Regards, TAR2

Edited by tar, 5 July 2011 - 04:37 AM.

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#11 DrRocket

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Posted 5 July 2011 - 07:14 AM

DrRocket,

Thank you for the description, but although I understand what you are saying, I am finding it hard to accept a reality, without a mechanism. With our imaginations, and formulae, we can build models that work, that do not necessarily have to actually fit reality. It seems very strange to me, for instance, that you can say that we figured the universe pretty much out, down to how old it is and how much stuff is in it, and what the nature of the stuff is. All this from observing photons telling us what the universe used to be like. Which is fine, we are pretty smart, and able to make ratios and analogies, map one thing to another, and put ourselves in another location and time and imagine what it must be like. But only because we understand the mechanisms involved. And have built back a model that we "predict" should be the way the entire universe is "now".

The Newtonian "notion" of space and time, past and future, here and there, is how I appear to understand things, as a human. I can not "pretend" to understand them elsewise. I can slow things down, speed them up, make them larger and smaller, scale this way and that, but I don't know the meaning, of "coming back aged less". Compared to what? Number of heartbeats was smaller? Would the traveller "feel" like she was forshortened? What are the implications of such a voyage? Would the photons her ship is running into, eminating from Alpha Centuri (if that was her turn around point) be mostly of the x-ray and gamma and cosmic ray variety? Would they burn her up? Would they "age" her? Wrinkle her skin? Make her come back looking like she had aged 100 years? (not to mention how long it would take to get up to that speed at an acceleration that would not tear her apart.) Would the "light pressure" of the high energy photons from Alpha Centuri, hitting her forward shields impede her progress, causing her to have to maintain a constant acceration, through their electromagnetic field? How would this affect her clock, and the equations?

In my book, reality fits together, is always true, and always is at least a little more complex than the model of it we hold in our heads. For you to say that I can not properly model reality, without understanding differential geometry is counter intuitive. It is the equations that are not complete. Reality is already complete. And if reality is doing something, there is a reason for it, a mechanism involved, a way that that thing fits into the whole picture. If something doesn't make sense, its because there is an aspect of what is going on that I don't understand. I can accept that I do not know differential equations, but I cannot accept that there is not an explanation of the who, where, when, why and how of a journey that takes place within my view, within my lifetime. There must be mechanisms that cause the effects. Otherwise, they wouldn't happen.

Regards, TAR2


Implicit in your search for a "mechanism" is the assumption that this mechanism is describable in terms of something that you find familiar, presumably the usual Newtonian view of the universe. But the whole point of relativity is that the Newtonian perspective is simply wrong except as a low speed local approximation to that which is the actual reality.

There is no universal notion of "where" or "when", so you are basically screwed in you search. Yes, it is counter-intuitive when your intuition is based on the Newtonian model.. That intuition is worthless in this setting.

Physics is not philosophy, ordinary words are no substitute for the actual language of the subject, and that language is mathematics.
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#12 Vilas Tamhane

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Posted 5 July 2011 - 01:32 PM

As I already pointed out in the previous post, for him, the distance between Earth and Alpha C is not 4.5 lys, but somewhat less than 1/2 that distance (in my example he was traveling at 0.9c). And that distance is just as "real" as the distance as measured from the Earth. There is nothing faulty with his clock or his method of the distance, they are just as good as those used by the Earth and th results they give are just as valid.



I donít think that the question raised by tar is replied satisfactorily. Traveler on reaching Alpha C stops and finds that original distance in earthís frame is restored. According to tar traveler is fully justified in using his time and the distance to find out the velocity with which he traveled. It is about 1.7c.

You may say that once the traveler is in the earthís frame, he should use coordinates of that frame. But it may also mean that calculated time in the moving frame is wrong and bears no real significance.

There is one more thing I wish to know. When traveler stops at Alpha C, what happens to the space-time diagram? Coordinates of the travelerís frame coincide with those of earthís. Distance that was half for traveler goes on increasing till it is 4.5 light years. This is definitely the case as the contracted distance cannot remain hanging somewhere. After all it is the same space for both the frames.

If the space axis rotates till it coincides with the space axis of the earth then time axis should also rotate and coincide with the orthogonal time axis of earth. As traveler starts decelerating to stop at Alpha C, he will find that the distance goes on expanding till it becomes 4.5Ly. Similarly his clock should go on running fast till the travelerís clock and stationary clock show the same time. What is applicable to distance should also be applicable to clock.


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#13 swansont

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Posted 5 July 2011 - 03:35 PM

I donít think that the question raised by tar is replied satisfactorily. Traveler on reaching Alpha C stops and finds that original distance in earthís frame is restored. According to tar traveler is fully justified in using his time and the distance to find out the velocity with which he traveled. It is about 1.7c.


No, the traveller is not justified in doing this. Relativity is quite clear on this point: times and distances are not invariant under a transformation between frames.

There is one more thing I wish to know. When traveler stops at Alpha C, what happens to the space-time diagram? Coordinates of the travelerís frame coincide with those of earthís. Distance that was half for traveler goes on increasing till it is 4.5 light years. This is definitely the case as the contracted distance cannot remain hanging somewhere. After all it is the same space for both the frames.

If the space axis rotates till it coincides with the space axis of the earth then time axis should also rotate and coincide with the orthogonal time axis of earth. As traveler starts decelerating to stop at Alpha C, he will find that the distance goes on expanding till it becomes 4.5Ly. Similarly his clock should go on running fast till the travelerís clock and stationary clock show the same time. What is applicable to distance should also be applicable to clock.

As the speed changes, the amount of contraction and dilation changes. Upon a return to the earth frame, the lengths will be the same as will the rates of the clocks (i.e. the frequency). The accumulated phase difference (i.e. time difference) will remain.
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#14 Vilas Tamhane

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Posted 5 July 2011 - 03:56 PM

No, the traveller is not justified in doing this. Relativity is quite clear on this point: times and distances are not invariant under a transformation between frames.


As the speed changes, the amount of contraction and dilation changes. Upon a return to the earth frame, the lengths will be the same as will the rates of the clocks (i.e. the frequency). The accumulated phase difference (i.e. time difference) will remain.



Yes, you made a very good point. But now both the clocks are in the same frame. Distance is back to normal and so according to earthís clock speed of the traveler was 0.866c and according to travelerís clock it was 1.7c


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#15 swansont

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Posted 5 July 2011 - 04:07 PM

Yes, you made a very good point. But now both the clocks are in the same frame. Distance is back to normal and so according to earthís clock speed of the traveler was 0.866c and according to travelerís clock it was 1.7c


But you have changed frames and times and distances are not invariant under a transformation between frames. We know this, so we know that answer is incorrect. Ignorance of the law is no excuse.
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#16 Vilas Tamhane

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Posted 5 July 2011 - 04:24 PM

But you have changed frames and times and distances are not invariant under a transformation between frames. We know this, so we know that answer is incorrect. Ignorance of the law is no excuse.



I donít get you. Can you elaborate your statement? I thought case is very simple because now earth and the traveler are in the same frame.




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#17 swansont

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Posted 5 July 2011 - 06:50 PM

I donít get you. Can you elaborate your statement? I thought case is very simple because now earth and the traveler are in the same frame.


They are not in the same frame as when the measurements were valid. You are trying to use a clock that recorded an elapsed time in a moving frame with a length measurement in the rest frame. That's mixing frames, and that's a no-no. You have to be consistent in using measurements from a single frame, because times and distances are not invariant under a transformation between frames.
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#18 J.C.MacSwell

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Posted 5 July 2011 - 08:42 PM

Yes, you made a very good point. But now both the clocks are in the same frame. Distance is back to normal and so according to earthís clock speed of the traveler was 0.866c and according to travelerís clock it was 1.7c


As long as you recognize what it is that you measuring, average speed in terms of the traveler's moving and accelerating reference frame, while displacing a distance measured in their starting and final inertial frame; then you can make that claim. It is certainly valid for the traveler. There is no limitation of 1.0 c when measured this way.

...and it still is 0.866c measured in the inertial frame where the less than 1.0 c speed limit applies.
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#19 Vilas Tamhane

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Posted 6 July 2011 - 09:48 AM

As long as you recognize what it is that you measuring, average speed in terms of the traveler's moving and accelerating reference frame, while displacing a distance measured in their starting and final inertial frame; then you can make that claim. It is certainly valid for the traveler. There is no limitation of 1.0 c when measured this way.

...and it still is 0.866c measured in the inertial frame where the less than 1.0 c speed limit applies.


I think there is a contradiction. You say that measurement of the velocity of the traveler is valid and there is no limitation to the velocity of light. What it means is that the traveler was cruising with a speed more than that of light. In any case, in relativity what is common and same is the measurement of velocity v of the traveler. Both the observers agree that velocity Ďví of the traveler is same. If traveler uses his clock, then not only that he finds his velocity to be more than light but there is disagreement about the velocity v.


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#20 J.C.MacSwell

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Posted 6 July 2011 - 01:18 PM

I think there is a contradiction. You say that measurement of the velocity of the traveler is valid and there is no limitation to the velocity of light. What it means is that the traveler was cruising with a speed more than that of light. In any case, in relativity what is common and same is the measurement of velocity v of the traveler. Both the observers agree that velocity ‘v’ of the traveler is same. If traveler uses his clock, then not only that he finds his velocity to be more than light but there is disagreement about the velocity v.


That is not what I said.

Other than that, only your last sentence, if velocity is taken in the context that I specifically stated, is correct. Everything else is wrong.

Edited by J.C.MacSwell, 6 July 2011 - 01:19 PM.

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