Trouble with Lorentz transformations

[AdVen]

Did you read any of the replies you got in the thread you started about the twin paradox?

https://www.physicsforums.com/showthread.php?t=399741

Every solution is using SR only (because the problem is specified using SR only). That includes the two solutions you got from me, and the one you linked to yourself.

Dear Fredrik,

I was not aware that I had linked a solution to myself nor was I aware of the two solutions I got from you. Would you be so kind to tell me were exactly I can find these solutions?

It is my intention to derive the well-known formulas of SR, such as the formulas for proper length and proper time directly from the two formulas of the Lorentz transformation (see the two attached PDF files). I am planning to do something similar with the solution of the twin paradox, something like what Professor Park did at

http://kspark.kaist.ac.kr/Twin Paradox/Twin-Paradox Events and Transformations.htm

However, I am still not quite sure whether this solution is correct.

In the mean time I would appreciate it very much if you would read the two attached files just to check whether they do not contain any nonsense.

Thanks a lot for your information, Ad.

PS. I have asked the same question to some other guys of PhysicsForum.

 

[AdVen]

Adven has the solution - which he wrote but I guess he wanted some online text to refer to, so that is what I responded to.

I was not aware that I had a solution. Please, can you tell me where I can find the text?

Ad.

 

[AdVen]

Hi JesseM,

Could you check whether the following texts are correct:

http://www.socsci.ru.nl/~advdv/TimeDilatationFinal.pdf

and

http://www.socsci.ru.nl/~advdv/LengthContractionFinal.pdf

Thanks a lot for your time and effort, Ad.

 

[starthaus]

Hi JesseM,

Could you check whether the following texts are correct:

http://www.socsci.ru.nl/~advdv/TimeDilatationFinal.pdf

and

http://www.socsci.ru.nl/~advdv/LengthContractionFinal.pdf

Thanks a lot for your time and effort, Ad.

both files are correct now.

 

[starthaus]

I was not aware that I had a solution. Please, can you tell me where I can find the text?

Ad.

Here

 

[Fredrik]

I just gave Adven an online source for a lot of things about SR including the twin paradox.
...
I guess he wanted some online text to refer to, so that is what I responded to.

You don't have to explain yourself to me. The things I said were for AdVen, not you. (And so are the things below this).

I was not aware that I had linked a solution to myself nor was I aware of the two solutions I got from you. Would you be so kind to tell me were exactly I can find these solutions?

Now you're really confusing me. I included a link to the thread you started, so it must have been obvious that I was referring to my posts in that thread, and to your posts in that thread.

...something like what Professor Park did at

http://kspark.kaist.ac.kr/Twin Paradox/Twin-Paradox Events and Transformations.htm

I don't know how you can say "I was not aware that I had linked a solution" and then immediately link to it again. It must have been clear that that's the link I meant, since I included a link to the thread where you posted it and asked for comments. One of the comments you got was from me:

It looks good. I don't like that he says "is in S" when he should be saying something like "has velocity 0 in S", but the explanation is fine.

 

[AdVen]

You don't have to explain yourself to me. The things I said were for AdVen, not you. (And so are the things below this).


Now you're really confusing me. I included a link to the thread you started, so it must have been obvious that I was referring to my posts in that thread, and to your posts in that thread.

I don't know how you can say "I was not aware that I had linked a solution" and then immediately link to it again. It must have been clear that that's the link I meant, since I included a link to the thread where you posted it and asked for comments. One of the comments you got was from me:

I am very sorry for the confusion. Now it is clear to me. We both were referring to Park's solution. If I understand you well this solution is oké except for some minor phrasing, such as:

"instead of "is in S" he should be saying something like "has velocity 0 in S":

Thanks again, Ad.

 

[AdVen]

Here

I am going to look into it very carefully. Thanks for the information.

 

[AdVen]

Here

In this text they use acceleration and deceleration. SR is only about inertial systems. It looks as if GR is used here or am I wrong?

 

[starthaus]

In this text they use acceleration and deceleration. SR is only about inertial systems. It looks as if GR is used here or am I wrong?

You are wrong, this is sadly a very common misconception. SR deals with accelerated frames. See the many attachments in my blog on this very subject.

 

[JesseM]

In this text they use acceleration and deceleration. SR is only about inertial systems. It looks as if GR is used here or am I wrong?

Accelerated motion can be analyzed just fine from the perspective of an inertial frame (and technically a modern physicist would generally say that even if you use a non-inertial frame with a pseudo-gravitational field as discussed here, this is still 'SR' if spacetime is not curved). Any smoothly-curve path in spacetime can be approximated as a polygonal path made up of a series of straight segments of constant velocity joined by instantaneous accelerations, and if you take the limit (in the calculus sense) as the segments become shorter and shorter (and the number of segments becomes greater and greater), this should approach perfect agreement with the original smooth path. If a given straight segment has a velocity v as seen in the inertial observer's frame, and the time between the beginning and end of the segment in the inertial observer's frame is dt, then the proper time along that segment should be $$\sqrt{1 - v^2/c^2} dt$$. So, if you have a smoothly-curved path where the velocity as a function of time in the inertial observer's frame is some function v(t), the proper time along this path between two moments t₀ and t₁ (which could be the moments of departing from and reuniting with a twin, for example) would be given by the integral $$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2}\,dt$$ (because in calculus an integral is just the limiting case of a sum in which the size of each segment dt becomes arbitrarily short)

 

[AdVen]

You are wrong, this is sadly a very common misconception. SR deals with accelerated frames. See the many attachments in my blog on this very subject.

Where can I find your blog?

 

[AdVen]

Accelerated motion can be analyzed just fine from the perspective of an inertial frame (and technically a modern physicist would generally say that even if you use a non-inertial frame with a pseudo-gravitational field as discussed here, this is still 'SR' if spacetime is not curved). Any smoothly-curve path in spacetime can be approximated as a polygonal path made up of a series of straight segments of constant velocity joined by instantaneous accelerations, and if you take the limit (in the calculus sense) as the segments become shorter and shorter (and the number of segments becomes greater and greater), this should approach perfect agreement with the original smooth path. If a given straight segment has a velocity v as seen in the inertial observer's frame, and the time between the beginning and end of the segment in the inertial observer's frame is dt, then the proper time along that segment should be $$\sqrt{1 - v^2/c^2} dt$$. So, if you have a smoothly-curved path where the velocity as a function of time in the inertial observer's frame is some function v(t), the proper time along this path between two moments t₀ and t₁ (which could be the moments of departing from and reuniting with a twin, for example) would be given by the integral $$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2}\,dt$$ (because in calculus an integral is just the limiting case of a sum in which the size of each segment dt becomes arbitrarily short)

Thank you very much for your clear explanation.

 

[AdVen]

Here

Hello starthaus,

I copied from the Twin Paradox in Wikipedia the following part:

Consider a spaceship traveling from Earth to the nearest star system outside of our solar system: a distance $$d = 4.45$$ light years away, at a speed $$v = 0.866c$$ (i.e., 86.6 percent of the speed of light). The Earth-based mission control reasons about the journey this way (for convenience in this thought experiment the ship is assumed to immediately attain its full speed upon departure): the round trip will take $$t = 2d/v = 10.28$$ years in Earth time (''i.e.'' everybody on Earth will be 10.28 years older when the ship returns). The amount of time as measured on the ship's clocks and the aging of the travelers during their trip will be reduced by the factor $$\epsilon = \sqrt{1 - v^2/c^2}$$, the reciprocal of the (Lorentz factor). In this case $$\epsilon = 0.500 \,$$ and the travelers will have aged only 0.500*10.28 = 5.14 years when they return.

The ship's crew members also calculate the particulars of their trip from their perspective. They know that the distant star system and the Earth are moving relative to the ship at speed $$v$$ during the trip. In their rest frame the distance between the Earth and the star system is $$\epsilon d = 0.5d$$ = 2.23 light years ((length contraction)), for both the outward and return journeys. Each half of the journey takes $$2.23/v$$ = 2.57 years, and the round trip takes 2*2.57 = 5.14 years. Their calculations show that they will arrive home having aged 5.14 years. The travelers' final calculation is in complete agreement with the calculations of those on Earth, though they experience the trip quite differently.

If a pair of twins are born on the day the ship leaves, and one goes on the journey while the other stays on Earth, they will meet again when the traveler is 5.14 years old and the stay-at-home twin is 10.28 years old. The calculation illustrates the usage of the phenomenon of length contraction and time dilation to describe and calculate consequences and predictions of Einstein's (special theory of relativity).

and I finally understood the solution of the twin paradox. I am going to work this out with reference to the length contraction and time dilation formulas and will show you the result as soon as I am finished.

I am very grateful to you.

 

[starthaus]

Hello starthaus,

I copied from the Twin Paradox in Wikipedia the following part:



and I finally understood the solution of the twin paradox. I am going to work this out with reference to the length contraction and time dilation formulas and will show you the result as soon as I am finished.

I am very grateful to you.

You are welcome.

 

[starthaus]

Where can I find your blog?

Here : https://www.physicsforums.com/blog.php?u=241315

 

[stevmg]

starthaus -

I have read Taylor/Wheeler Spacetime Physics the First edition (1962 version) which is easier for a novice to comprehend than the later 2002 2nd edition as the later edition has too many bells and whistles. The First Edition is more to the point. Remember I have no one else around me to even discusss this subject matter with other than this Forum and so digesting the material can get slow.

The third chapter goes into GR. It explains the curvature of spacetime as the source of gravity. What is not explained in any text that I ever read or any comment anywhere is that what would make an object at rest (I know, there is no such thing as "at rest") appear to be pushed (curved worldline)?

Then it dawned on me - every object anywhere has a worldline that is forever growing and hence, other than the old general saying that "everything's in motion" and all frames of reference are relative to each other with no central one favored, there is the motion - presumably all the worldines would be traveling along a geodesic (I guess that's the right term) and there would always appear to be a "force" acting on them as all geodesics are curved.

I didn't have anybody here to tell me that and I never saw it anywhere else. All the 2D analogies which showed by bending a 2D world in a third dimension, objects would appear to be pushed together as they moved (page 184 of this 1st Edition), never showed why they would move in the first place.

In a 3D world, the unseen 4th dimension, time, makes them move (i.e. - the worldline.)

I hope I am correct.

 

[AdVen]

starthaus -
Remember I have no one else around me to even discusss this subject matter with other than this Forum and so digesting the material can get slow.

I am very curious about your situation:

starthaus -
I have no one else around me to even discusss this subject matter with other than this Forum.

Could you tell me more about it? Just for the record.

 

[stevmg]

I am a retired AF officer and delving into matters I never had time to do before. Have a math (not physics) background and my math degree is from 1963.

 

[stevmg]

I am very curious about your situation:


Could you tell me more about it? Just for the record.

I gave you the answer, now tell me the same about you...

 

[starthaus]

starthaus -

I have read Taylor/Wheeler Spacetime Physics the First edition (1962 version) which is easier for a novice to comprehend than the later 2002 2nd edition as the later edition has too many bells and whistles. The First Edition is more to the point. Remember I have no one else around me to even discusss this subject matter with other than this Forum and so digesting the material can get slow.

The third chapter goes into GR. It explains the curvature of spacetime as the source of gravity. What is not explained in any text that I ever read or any comment anywhere is that what would make an object at rest (I know, there is no such thing as "at rest") appear to be pushed (curved worldline)?

Then it dawned on me - every object anywhere has a worldline that is forever growing and hence, other than the old general saying that "everything's in motion" and all frames of reference are relative to each other with no central one favored, there is the motion - presumably all the worldines would be traveling along a geodesic (I guess that's the right term) and there would always appear to be a "force" acting on them as all geodesics are curved.

I didn't have anybody here to tell me that and I never saw it anywhere else. All the 2D analogies which showed by bending a 2D world in a third dimension, objects would appear to be pushed together as they moved (page 184 of this 1st Edition), never showed why they would move in the first place.

In a 3D world, the unseen 4th dimension, time, makes them move (i.e. - the worldline.)

I hope I am correct.

This is a tricky question. To my best knowledge there is one very good vizualization of the effect, it is a series of lectures produced at Caltech by Jim Blinn entitled "The Mechanical Universe".

 

[stevmg]

This is a tricky question. To my best knowledge there is one very good vizualization of the effect, it is a series of lectures produced at Caltech by Jim Blinn entitled "The Mechanical Universe".

Thank you for your quick reply. It seems that the more elementary we get (such as what initiates the movement of the parable of the two travelers cited in Spacetime Physics, 1st Edition) the more complex become the answers.

stevmg

 

[Shackleford]

Thank you for your quick reply. It seems that the more elementary we get (such as what initiates the movement of the parable of the two travelers cited in Spacetime Physics, 1st Edition) the more complex become the answers.

stevmg

Hasn't that been the case historically with physics? The more we learn the more complex it becomes and the less we realize we know.

 

[stevmg]

This is a tricky question. To my best knowledge there is one very good vizualization of the effect, it is a series of lectures produced at Caltech by Jim Blinn entitled "The Mechanical Universe".

Hasn't that been the case historically with physics? The more we learn the more complex it becomes and the less we realize we know.

One more dumb question with regard to this subject...

Am I "kind of right?" Is it conceivable that the motion of the ever lengthening wordlines is the movement of the various frames of reference which, as they travel over curved spacetime, can cause the "curvation" of these world lines which means "force" or even gravity. That parable of the two travelers as a specific example lends itself beautifully to such a concept and would be very easy to draw. Of course this would be a very, very artificial representation in 2D of a very, very specific 3D "universe" with time as one of the dimensions.

 

[AdVen]

Hasn't that been the case historically with physics? The more we learn the more complex it becomes and the less we realize we know.

About

complex

Always remember, that when somebody says 'this is complex', he/she actually is saying 'I do not know'. This custom has come into existence because many people think, that the reason why they do not understand something must be that many factors are involved. In reality, however, it may well be the case that only one rule or one principle may be the cause of the phenomenon under study. Take, for example, the following number sequence:

1 2 3 1 3 4 2 3 3 1 4 5 1 1 3 2 3 4 3 1 2 3 . . .

This sequence seems very 'complex', but it is actually governed by one rule. Therefore, if you do not understand something never say 'this is complex', but simply say 'I do not know'. If you cannot discover what the rule is, go to http://www.socsci.ru.nl/~advdv/fair98.html

How to live with 'I do not know' is the very core of philosophy.

 

[stevmg]

As described in "Choas" by Gleick.

Actually, I say "I do not know" all the time to my wife...

It is the safest answer. Trust me.

 

[AdVen]

As described in "Choas" by Gleick.

Actually, I say "I do not know" all the time to my wife...

It is the safest answer. Trust me.

Reading your reply I understand that you already know "How to live with: I do not know."

 

[JesseM]

Always remember, that when somebody says 'this is complex', he/she actually is saying 'I do not know'.

Sometimes it refers to unknowns, but not always. "Complex" can refer to phenomena that are understandable but whose behavior requires a lot of computing power to predict, like the predicting the weather a few days from now on a supercomputer, or calculating the large-scale behavior of a collection of water molecules from basic quantum physics (as was done here). It can also refer to things where understanding the answer requires you to have already gotten the training needed to understand a bunch of background concepts and mathematics that may be far from everyday experience (like the concepts and math involved in general relativity), which may have been the sort of thing stevmg was getting at when he said "It seems that the more elementary we get (such as what initiates the movement of the parable of the two travelers cited in Spacetime Physics, 1st Edition) the more complex become the answers."

 

[Shackleford]

Sometimes it refers to unknowns, but not always. "Complex" can refer to phenomena that are understandable but whose behavior requires a lot of computing power to predict, like the predicting the weather a few days from now on a supercomputer, or calculating the large-scale behavior of a collection of water molecules from basic quantum physics (as was done here). It can also refer to things where understanding the answer requires you to have already gotten the training needed to understand a bunch of background concepts and mathematics that may be far from everyday experience (like the concepts and math involved in general relativity), which may have been the sort of thing stevmg was getting at when he said "It seems that the more elementary we get (such as what initiates the movement of the parable of the two travelers cited in Spacetime Physics, 1st Edition) the more complex become the answers."

That's exactly what I meant by complex.

AdVen, I had to visit the website to discover the solution. lol. I'm not afraid to say I don't know. However, I'm very adamant when I do know.

 

[AdVen]

I completely agree!