A MACHO is passing the solar system at the velocity of .5c.

Click For Summary

Discussion Overview

The discussion revolves around the concept of time dilation as experienced by a MACHO (Massive Compact Halo Object) traveling at 0.5c relative to the solar system. Participants explore the implications of special relativity (SR) and general relativity (GR) on time perception between different frames of reference, particularly focusing on the example of a person on Pike's Peak compared to someone at sea level.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant asserts that the MACHO experiences time dilation, suggesting a factor of 4:3, which is later corrected to approximately 1000:866.
  • Another participant clarifies that the MACHO does not experience time dilation in its own frame, but sees the Earth experiencing dilation, and vice versa.
  • A participant introduces the idea that time dilation is reflexive between inertial frames, supported by Lorentz transformations.
  • Discussion arises regarding the "extra second" experienced by a person at a higher altitude (Pike's Peak) due to relativistic effects, questioning whether this is solely an SR effect.
  • Participants note that the "extra second" may be a net result of both SR and GR effects, with one participant emphasizing that the perception of time differs between observers in different frames.
  • There is a contention regarding whether the situation resembles the twins paradox, with some arguing that it does not apply here as only one observer experiences the "extra second" when considering SR alone.

Areas of Agreement / Disagreement

Participants express differing views on the nature of time dilation between frames, particularly regarding the implications of SR and GR. There is no consensus on whether the "extra second" experienced by the person on Pike's Peak is an effect of SR alone, and the discussion remains unresolved regarding the relationship between accelerated frames and inertial frames in this context.

Contextual Notes

Participants note that the discussion involves assumptions about inertial versus accelerated frames and the complexities of applying SR in non-inertial contexts. The mathematical details of time dilation factors and the specific conditions under which they apply are also acknowledged as relevant but not fully resolved.

OneEye
Okay, everyone, I know that this is sounds like a set-up question. And that's because it is. But please humor me, because I'm trying to get this straight:

A MACHO is passing the solar system at the velocity of .5c.

Therefore, the MACHO experiences a time dilation. Its time is slowed by a factor of 4:3.

Right?
 
Physics news on Phys.org
The MACHO doesn't experience any time dilation in its own frame. It sees the Earth experiencing that dilation, and of course Earth sees the MACHO's time dilated.
 
selfAdjoint said:
The MACHO doesn't experience any time dilation in its own frame. It sees the Earth experiencing that dilation, and of course Earth sees the MACHO's time dilated.

Excellent. This is exactly the point that I was trying to set up. Thank you!

So, then, we have a principle which says that time dilation between any two comoving reference frames is always collateral: Both frames see the other as experiencing time dilation. Correct?

(BTW, got my math wrong. 0.5c produces a dilation factor of about 1000:866, not 4:3. Forgot to sqrt.)
 
Comoving is the wrong word here. Two frames are comoving if the velocity difference between them is (instantaneously) zero. Like a car driving along beside a train and going the same speed.

Now the two frames in your example, in order for the dilations to be valid, have to be inertial, which essentailly means not accelerated. So with that proviso, what you say is true; the dilations are reflexive. This is shown by the Lorentz transformations, which are matrices. If you use some L.T. [tex]A[/tex] to transform from the Earth frame to the MACHO frame, then to transform in the other direction you use [tex]A^{-1}[/tex].

So now, on to the punch line. And it better not be about twins! :wink:
 
Selfadjoint - thanks for the terminological clarification. Also, thanks for the substantiation.

No, the punchline is not about twins. It is this: It is well-remarked that a person living in the Rocky Mountains will experience an "extra second" or so of life because of the relativistic effect associated with the greater tangential velocity resulting from the constant rotational velocity of the earth.

Surely, given what we have discussed above, this cannot be an effect of special relativity. Right?

Also, years ago, when I worked on GPS, it was common for the officers to breathlessly remark how that it was necessary to compensate for relativistic effects when calculating one's position and time from the satellite signals. Someone on the board just recently pointed out that this was due to both SR and GR effects, and that the GPS clock actually appeared faster than those on the earth.

So, the punchline is this: Does the fellow on top of Pike's Peak really get that "extra second" relative to the sea-level population of the earth. If so, is that really an SR effect?
 
OneEye said:
So, the punchline is this: Does the fellow on top of Pike's Peak really get that "extra second" relative to the sea-level population of the earth. If so, is that really an SR effect?
He gets a little due to GR and gives a little back due to SR. The "extra second" (if that's accurate) is the net result.

edit, clarification: a person on Pikes Peak notices no change in lifespan, its just that he thinks he's a second or two older than a guy near sea level.
 
Last edited:
...because, if we are considering only SR, then the guy on Pike's Peak gets his second from the perspective of a guy in New York, but the guy in New York gets a second from the perspective of the guy on Pike's Peak.

Right?
 
OneEye said:
...because, if we are considering only SR, then the guy on Pike's Peak gets his second from the perspective of a guy in New York, but the guy in New York gets a second from the perspective of the guy on Pike's Peak.

Right?

The point here is to remember that both are in acceleratedframes (they are both traveling in circles and circular motion is accelerated motion). SR can deal with accelerated frames but the application is somewhat different than that when dealing with inertial frames.
 
OneEye said:
...because, if we are considering only SR, then the guy on Pike's Peak gets his second from the perspective of a guy in New York, but the guy in New York gets a second from the perspective of the guy on Pike's Peak.

Right?
It sounds like you're trying to create a twins paradox (sorry, SA). None exists here. Only one gets a second and it isn't just because of SR. If you want to limit it to just SR, then neiter gets a second.
 

Similar threads

Undergrad Are Special Relativity effects valid for angular velocity?
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Twin Paradox with accelerated Motion
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad New Developments In The Search For Planet X
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Doppler like effect affecting observed time for a moving object
  • · Replies 1 ·
Replies
1
Views
1K
High School Reciprocal time dilation
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Comparing Clock Rates in Accelerated vs Constant Velocity Frames
  • · Replies 14 ·
Replies
14
Views
2K
Python Building a Solar System simulation with python
  • · Replies 2 ·
Replies
2
Views
4K
Could we make a practical solar fridge?
  • · Replies 30 ·
2
Replies
30
Views
5K
Undergrad Disproving Velocity's Effect on Space-Time
  • · Replies 1 ·
Replies
1
Views
1K
Is my fictional Solar System stable and realistic?
  • · Replies 21 ·
Replies
21
Views
7K