Trouble with Lorentz transformations

In summary, the conversation discusses using Lorentz transformations to derive the "length contraction" result. It is noted that the incorrect result is obtained because the measurements are not simultaneous in the unprimed frame. The correct result is then derived using the equations x' = γ(x - vt) and t' = γ(t - vx/c²). This leads to the conclusion that L' = γL, where L' is the length measured by the primed frame and L is the length measured by the non-primed frame.
  • #141
stevmg said:
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".
 
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  • #142
starthaus said:
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
 
  • #143
stevmg said:
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.
 
  • #144
starthaus said:
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".

Shackleford said:
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.
 
  • #145
Shackleford said:
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
Shackleford said:
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.
 
  • #146
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.
 
  • #147
stevmg said:
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."
 
  • #148
AdVen said:
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."
 
  • #149
JesseM said:
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.
 
  • #150
I completely agree!
 

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