Symetry, time dilation, twin paradox and all that stuff

Click For Summary
SUMMARY

The discussion centers on the twins paradox in the context of special relativity, specifically addressing the mathematical principles that explain time dilation and proper time. The key takeaway is that symmetry is broken due to one twin accelerating and changing inertial frames during the journey, while the other remains in a single inertial frame. The proper time, defined as the time measured by a clock moving along a worldline, varies between the twins due to relativistic effects, which can be calculated using the Lorentz transformation equations. The discussion also highlights the importance of understanding these equations to resolve apparent contradictions in time measurements between different reference frames.

PREREQUISITES
  • Understanding of special relativity concepts, including time dilation and inertial frames.
  • Familiarity with Lorentz transformation equations and their applications.
  • Knowledge of proper time and its significance in relativistic physics.
  • Basic grasp of spacetime diagrams and worldlines in relativity.
NEXT STEPS
  • Study the Lorentz transformation equations in detail to understand their derivation and applications.
  • Explore the concept of proper time and its implications in both special and general relativity.
  • Investigate experimental validations of time dilation, such as the Hafele-Keating experiment with atomic clocks.
  • Learn about spacetime diagrams and how they visually represent events and the effects of relativity.
USEFUL FOR

Students of physics, educators teaching relativity, and anyone interested in the mathematical foundations of time dilation and the twins paradox will benefit from this discussion.

  • #31
"and there is just no way to tell what it is, you can also understand the question of their relative ages not to have an objective frame-independent answer at all"

But that's why I said, that to me, this has something of the 'flavour' of QM - the 'not knowing' in an objective sense - until one actually meets (which to me is like opening the box and making an observation)

It may not have any real physical similarity but I seem to find it easier to accept when I can see parallels/analogies. Some people have a lot of difficulty dealing with QM and it's apparently odd interpretations and all the uncertainty and etc. I have personally never found it hard to swallow QM ideas, but for some reason I do find these 'apparent paradoxes' in relativity excruciatingly difficult.

Thanks for your help though - I am beginning, I think, to make more sense of this thanks to you.

Cheers

Peter
 
Physics news on Phys.org
  • #32
If the twin paradox were like QM, assuming that a twin even had a definite age would lead to logical contradictions.

SR is really a lot simpler than QM. A twin has a "proper age" as measured in their own frame of reference (one can call this a writwatch age). This is a definite number, not one of those quantum things that is forbidden to have a definte value.

The only thing that's a bit odd about the behavior if this age is due to the fact that space and time are interconnected. Experimentally, one finds that when one twin moves around, his wristwatch age or proper age is not the same as that of the other twin when they meet again. And that's really all there is to it. If you move a clock around in a loop, it won't read the same as a clock that stays put. This is a fundamental feature of physics.
 
  • #33
resurgance2001 said:
"and there is just no way to tell what it is, you can also understand the question of their relative ages not to have an objective frame-independent answer at all"

But that's why I said, that to me, this has something of the 'flavour' of QM - the 'not knowing' in an objective sense - until one actually meets (which to me is like opening the box and making an observation)
But in QM, one can make a measurement of some variable like position and get an objective answer which would be true for everyone. In relativity, questions like the relative age of two separated twins have no objective answer, they are just frame-dependent. Would you also say that velocity in Newtonian physics is QM-like because there is no objective answer about an object's velocity, it depends on what frame you use? Would you say that the slope of a line on a 2D plane is QM-like, because the value of the slope depends on how you orient your coordinate axes? Would you say that the x-coordinate of an object in space is QM-like because it depends on where you choose to place the origin of your coordinate system? I really think the geometric analogy is best here, and few would argue that just because things like x-coordinate or slope have no single coordinate-independent value, that implies that we somehow can't have a totally objective picture of reality, whereas QM poses more of a real problem for those who want such an objective picture (although various 'interpretations' of QM do allow an objective description of the world independently of what we choose to measure).
resurgance2001 said:
Some people have a lot of difficulty dealing with QM and it's apparently odd interpretations and all the uncertainty and etc. I have personally never found it hard to swallow QM ideas
That may mean you don't understand it well enough! For example, would you agree that a measuring device should obey the same fundamental laws as the system it's measuring, since they're both just collections of the same type of fundamental particles? Would you say the fundamental laws of physics should be able to describe the entire universe, without the need for an external measuring device? QM poses difficulties for these notions, in a way that is unlike all non-quantum theories.
 

Similar threads

  • · Replies 43 ·
2
Replies
43
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 70 ·
3
Replies
70
Views
7K
  • · Replies 115 ·
4
Replies
115
Views
9K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 35 ·
2
Replies
35
Views
3K
  • · Replies 54 ·
2
Replies
54
Views
4K
  • · Replies 24 ·
Replies
24
Views
2K
  • · Replies 20 ·
Replies
20
Views
3K