Who Truly Experiences Slower Time in the Paradox of Time Dilation?

Click For Summary
The discussion centers on the concept of time dilation in the context of special relativity, particularly through the lens of the twin paradox. It highlights that while both twins perceive each other's clocks as running slow during their separation, the twin who accelerates (turns around) experiences less accumulated time due to the change in inertial frames. The conversation emphasizes that the aging difference is determined by the paths taken through spacetime, which can be calculated using proper time metrics. The importance of acceleration in breaking the symmetry of the situation is underscored, as it allows for a definitive comparison of ages upon reunion. Ultimately, the discussion reaffirms that Einstein's postulate regarding relative motion remains valid, even when considering acceleration.
  • #91


swerdna said:
In my opinion this is the actual or absolute reality of the relative movement of non-accelerating things and I don’t understand why Relativity only considers only an abstract part off this reality.

It's not abstract; it's real.

When something is accelerated, the acceleration is felt. You are pushed back in your seat. The cutlery rattles. The pencil rolls across the table. Things fall over.

A theory of science, like relativity, is not some abstract thought experiment, but a description of the real world, which has definite consequences, and can be falsified if wrong.

Unaccelerated motion is in a straight line at constant velocity. It turns out that the laws of physics really don't take any account of different straight line motions. It really and truly makes no difference to the laws of physics whether you treat A as moving and B at rest, or B as moving but A at rest. This is a discovery about the world... one that was initially very surprising.

When it was found that the laws of physics -- Maxwell's equations, in fact -- implied a particular velocity for the speed of light, it was a natural reaction to think that here was something that would allow you identify absolute movement. Someone would be absolutely at rest if the speed of light had this value relative to them. Surprisingly, this is not true. It really and truly is the case that two individuals who are moving relative to each other still measure the same velocity for the same ray of light.

Some people can't accept that, but it is true. Any real description of the real world has to deal with this.

The solution is relativity.

Relativity is not an abstract philosophical notion that "everything is relative". It is a definite, concrete account of precisely WHAT is relative and how. Velocity is relative. Time is relative. Position is relative. Distance is relative. Acceleration is not relative. Rotation is not relative.

You can use relativity to calculate how various things relate to each other, like the measurements of a clock. The reason relativity is used for this is because it is a concrete, well tested, accurate account of what happens to clocks in reality.

You are continuously suggesting that things "ought" to be different. They aren't.

Now in fact, there are cases where you need more general physics. You need general relativity to deal with gravity. You need quantum mechanics to deal with very small scale phenomena and wave effects. There will be other changes as well to deal with extremes we are still unclear about -- like conditions in the very early universe or approaching the singularity of a black hole. All of those factors are going to clash EVEN WORSE with your own intuitions.

It remains the case that special relativity is a concrete, accurate, well tested and measured mathematical account of what really happens with clocks and motions.

Acceleration is not relative. The description is not "equal and opposite" for two particles... if one particle accelerates, and the other doesn't, there's no ambiguity. One particle really is the one that is accelerating, not the other.

Cheers -- sylas
 
Last edited:
Physics news on Phys.org
  • #92


swerdna said:
By equal and opposite mean that the relative movement of non-accelerating things can’t be correctly attributed to one thing and not the other, regardless that one or both may have previously accelerated.
If I'm understanding you right, that's already true in relativity. Motion is always relative, there is no objective truth about which of the two objects is moving, regardless of whether either one accelerated previously.
swerdna said:
The movement is between the things not of the things. In my opinion this is the actual or absolute reality of the relative movement of non-accelerating things and I don’t understand why Relativity only considers only an abstract part off this reality.
I don't understand what you mean by "Relativity only considers an abstract part of this reality".
 
  • #93


swerdna said:
When I tell a theist that I don’t accept their claim that a god exists they invariably start quoting from the bible. This is totally pointless as the bible is only valid if a god exists. When I tell people that I don’t accept Relativity because I can’t accept some of the basic building blocks it’s constructed on then it’s equally pointless to use Relativity to validate the building blocks.

One such building block I don’t accept is the way Relativity uses frames. A frame and the things in it only represent an abstract part of existence and a frame can’t and doesn’t exist independently from a possible infinite number of other frames and things they contain that are of equal importance. When considering two things moving relative to each other I don’t see how it’s valid to arbitrarily give either frame any preference or quality that is different to the other. I don’t see that any number of periods of acceleration attribute any actual (absolute) definition of movement to a thing other than how it moves relative to something else.

You draw a straight line on a piece of paper. The straight line is real. Is it horizontal or vertical? The choice of whether to call it horizontal or vertical is like a free choice of inertial frame in flat spacetime. You can even choose coordinates in which the straight line is "wavy" - that is making your life hard - like choosing a non-inertial frame in flat spacetime. In flat spacetime, the assertion that inertial frames exist is just the idea that there are coordinates which make straight lines "straight", and which make your life easy. Why should it be possible to make life easy? - that you have to ask God :-p - and in fact maybe it can't always be done, since gravity exists :smile:
 
Last edited:
  • #94


Hello swerdna.

Picking a frame is not just picking a part of "reality". By picking different frames you just measure things differently. The results in all frames are equally valid. Every frame contains all the objects in the universe but each object is at rest in only one frame.

Matheinste
 
  • #95


Written in layman-speak . . .

An inertial frame is defined by non-accelerating things that don’t move relative to each other.

No inertial frame can be stationary relative to any other inertial frame. It follows therefore that all inertial fames move relative to all other inertial frames.

There is absolutely no evidence that anything can ever be absolutely stationary. It follows therefore that no inertial frame can be absolutely stationary.

In other words inertial frames are always relatively and absolutely in motion.

Anything wrong with any of this?
 
  • #96


swerdna said:
An inertial frame is defined by non-accelerating things that don’t move relative to each other.

omit "that don't move relative to each other". Non-accelerating things can still move relative to each other just fine.

No inertial frame can be stationary relative to any other inertial frame. It follows therefore that all inertial fames move relative to all other inertial frames.

False... two inertial reference frames can differ only by the location of the origin. Neither frame moves with respect to the other.

There is absolutely no evidence that anything can ever be absolutely stationary. It follows therefore that no inertial frame can be absolutely stationary.

It's not that there's no "evidence". Say rather that physics provides no basis for singling out anyone inertial frame as an "absolute" frame. All inertial frames have the same standing, in physics. Physics does not use a concept of "absolute" motion.

Cheers -- sylas
 
  • #97


sylas said:
omit "that don't move relative to each other". Non-accelerating things can still move relative to each other just fine.
Are you saying that accelerating things can be in inertial frames?

sylas said:
False... two inertial reference frames can differ only by the location of the origin. Neither frame moves with respect to the other.
So things in one inertial frame don’t move relative to each other, and things in another inertial frame don’t move relative to each other, and these two frames don’t move relative to each other? Doesn’t this mean that the things in one frame don’t move relative to things in the other frame, and doesn’t this make the two frames the same frame?

sylas said:
It's not that there's no "evidence". Say rather that physics provides no basis for singling out anyone inertial frame as an "absolute" frame. All inertial frames have the same standing, in physics. Physics does not use a concept of "absolute" motion.

Cheers -- sylas
Is that physics per se or just theoretical psychics referring to Relativity? I think it’s a self-evident fact of reality that nothing can ever be absolutely stationary so it automatically follows that everything is absolutely moving. If there is any credible proof that this is incorrect I would love to see it (non-mathematical).
 
  • #98


swerdna said:
sylas said:
omit "that don't move relative to each other". Non-accelerating things can still move relative to each other just fine.
Are you saying that accelerating things can be in inertial frames?

I am saying that non-accelerating things can move with respect to each other. It's written right there, you just quoted it!

"Being in" a reference frame is awkward phrasing. In SR, everything is in every reference frame. A "thing" can define a reference frame by tracing out the time axis... we make a reference frame by making this thing always at location zero. If the thing is accelerating, then the associated reference frame is not inertial. That is... accelerating things do not define inertial reference frames.

So things in one inertial frame don’t move relative to each other, and things in another inertial frame don’t move relative to each other, and these two frames don’t move relative to each other? Doesn’t this mean that the things in one frame don’t move relative to things in the other frame, and doesn’t this make the two frames the same frame?

If by frame you mean a particular set of co-ordinates, and by inertial you mean inertial, then no, it doesn't. Two inertial frames, or co-ordinate systems, with no relevative motion between them, may still have a different origin.

Is that physics per se or just theoretical psychics referring to Relativity? I think it’s a self-evident fact of reality that nothing can ever be absolutely stationary so it automatically follows that everything is absolutely moving. If there is any credible proof that this is incorrect I would love to see it (non-mathematical).

No, it does not "automatically" follow that everything is absolutely moving. There is no absolute, either for absolute movement or for absolute stationary.

You CAN be at rest with respect to something else. REALLY at rest with respect to something else. And your view is just as good as anyone else's... therefore things are not "absolutely moving" either.

In my view, the lack of any absolute frame of reference is a genuine discovery. There's nothing self-evident about it. The ancients considered it "self-evident" that the Earth provided a fixed absolute reference frame. Turns out that this is an arbitrary choice, as far as physics is concerned, which was highly counter intuitive at first.

Much of this is convention. There's nothing to stop someone from defining for some reason a particular reference frame as the absolute basis for deciding what is and is not stationary. What physics says... and this is a discovery; not a self-evident truth ... is that this choice is arbitrary in the sense that the laws of physics can't be used to single out a frame.

Cheers -- sylas
 
Last edited:
  • #99


sylas said:
swerdna said:
An inertial frame is defined by non-accelerating things that don’t move relative to each other.
omit "that don't move relative to each other". Non-accelerating things can still move relative to each other just fine.
But swerdna was talking about how an inertial frame is defined, i.e. a single one. A single frame is indeed defined in terms of a set of non-accelerating rulers and clocks which don't move relative to each other.
sylas said:
swerdna said:
There is absolutely no evidence that anything can ever be absolutely stationary. It follows therefore that no inertial frame can be absolutely stationary.
It's not that there's no "evidence". Say rather that physics provides no basis for singling out anyone inertial frame as an "absolute" frame. All inertial frames have the same standing, in physics. Physics does not use a concept of "absolute" motion.
Well, saying there's "no basis for singling out anyone inertial frame" is the same as saying there's no evidence for a violation of Lorentz-symmetry which would be the only conceivable basis for defining a preferred frame. To put it another way, all the evidence supports the idea that the fundamental laws of physics are locally Lorentz-symmetric, meaning that their equations will remain unchanged when you transform from one frame in SR to another using the Lorentz transformation.
 
  • #100


JesseM said:
But swerdna was talking about how an inertial frame is defined, i.e. a single one. A single frame is indeed defined in terms of a set of non-accelerating rulers and clocks which don't move relative to each other.

Ah! Thanks JesseM, and my apologies to you, swerdna!

I made a very silly reading of your text. By "An inertial frame is defined by non-accelerating things that don’t move relative to each other", I had taken you to mean that different non-accelerating things with different frames don't move in relation to each other. My fault for a dumb reading.

Yes, I agree. An inertial frame is defined by a collection of things that are not accelerating and not moving in relation to each other.

Well, saying there's "no basis for singling out anyone inertial frame" is the same as saying there's no evidence for a violation of Lorentz-symmetry which would be the only conceivable basis for defining a preferred frame. To put it another way, all the evidence supports the idea that the fundamental laws of physics are locally Lorentz-symmetric, meaning that their equations will remain unchanged when you transform from one frame in SR to another using the Lorentz transformation.

Yes. Nicely expressed.

Cheers -- sylas
 
  • #101


JesseM said:
But swerdna was talking about how an inertial frame is defined, i.e. a single one. A single frame is indeed defined in terms of a set of non-accelerating rulers and clocks which don't move relative to each other.
Thanks for clarifying and confirming.

JesseM said:
Well, saying there's "no basis for singling out anyone inertial frame" is the same as saying there's no evidence for a violation of Lorentz-symmetry which would be the only conceivable basis for defining a preferred frame. To put it another way, all the evidence supports the idea that the fundamental laws of physics are locally Lorentz-symmetric, meaning that their equations will remain unchanged when you transform from one frame in SR to another using the Lorentz transformation.
Don’t immediately understand that. Is my second statement also correct? -“all (single) inertial fames move relative to all other (single) inertial frames”
(single) added for clarity.
 
  • #102


sylas said:
Ah! Thanks JesseM, and my apologies to you, swerdna!

I made a very silly reading of your text. By "An inertial frame is defined by non-accelerating things that don’t move relative to each other", I had taken you to mean that different non-accelerating things with different frames don't move in relation to each other. My fault for a dumb reading.

Yes, I agree. An inertial frame is defined by a collection of things that are not accelerating and not moving in relation to each other.



Yes. Nicely expressed.

Cheers -- sylas
Thanks - Good to know that I’m not the only one who can make mistakes.
 
  • #103


sylas said:
No, it does not "automatically" follow that everything is absolutely moving. There is no absolute, either for absolute movement or for absolute stationary.

You CAN be at rest with respect to something else. REALLY at rest with respect to something else. And your view is just as good as anyone else's... therefore things are not "absolutely moving" either.

In my view, the lack of any absolute frame of reference is a genuine discovery. There's nothing self-evident about it. The ancients considered it "self-evident" that the Earth provided a fixed absolute reference frame. Turns out that this is an arbitrary choice, as far as physics is concerned, which was highly counter intuitive at first.

Much of this is convention. There's nothing to stop someone from defining for some reason a particular reference frame as the absolute basis for deciding what is and is not stationary. What physics says... and this is a discovery; not a self-evident truth ... is that this choice is arbitrary in the sense that the laws of physics can't be used to single out a frame.

Cheers -- sylas
Yes you CAN be REALLY stationary RELATIVE to something else but this is ONLY a RELATIVE stationary and NOT an ABSOLUTE stationary. In other words, RELATIVE stationary isn’t REALLY stationary in an ABSOLUTE or universal sense. Given that there is ABSOLUTELY no evidence that a thing can ever be ABSOLUTELY stationary then (by default if nothing else) it must be concluded that everything is REALLY always moving in an ABSOLUTE sense (IMHO).

Don’t forget - “Written in layman-speak“
 
Last edited:
  • #104


If object A is at rest relative to object B and is therefore absolutely moving then what is object A's absolute speed?
 
  • #105


swerdna said:
Yes you CAN be REALLY stationary RELATIVE to something else but this is ONLY a RELATIVE stationary and NOT an ABSOLUTE stationary. In other words, RELATIVE stationary isn’t REALLY stationary in an ABSOLUTE or universal sense. Given that there is ABSOLUTELY no evidence that a thing can ever be ABSOLUTELY stationary then (by default if nothing else) it must be concluded that everything is REALLY always moving in an ABSOLUTE sense (IMHO).

Don’t forget - “Written in layman-speak“

Relativity is a consequence of the speed of light not being infinite. If it were infinite, then
there would be only one reference frame and Lorentz invariance would rule.
But in quantum entangled state correlations, 'things' can move at infinite speed. There is only one reference frame then. But the 'things' are quantum state information and not particels/mass etc.
 
  • #106


DaleSpam said:
If object A is at rest relative to object B and is therefore absolutely moving then what is object A's absolute speed?
Absolute movement of any parfticluar thing can’t be measured because there is no absolute stationary to measure it against. A thing is always stationary relative to itself but a single thing alone can’t be used to measure it’s own movement. The only movement that can be measured therefore is relative movement. That relative movement exists proves that movements exists. That nothing can be absolutely stationary establishes that all things move in an absolute or universal sense.
 
Last edited:
  • #107


p764rds said:
Relativity is a consequence of the speed of light not being infinite. If it were infinite, then
there would be only one reference frame and Lorentz invariance would rule.
But in quantum entangled state correlations, 'things' can move at infinite speed. There is only one reference frame then. But the 'things' are quantum state information and not particels/mass etc.
Sorry but none of that makes any sense to me.
 
  • #108


swerdna said:
Yes you CAN be REALLY stationary RELATIVE to something else but this is ONLY a RELATIVE stationary and NOT an ABSOLUTE stationary. In other words, RELATIVE stationary isn’t REALLY stationary in an ABSOLUTE or universal sense. Given that there is ABSOLUTELY no evidence that a thing can ever be ABSOLUTELY stationary then (by default if nothing else) it must be concluded that everything is REALLY always moving in an ABSOLUTE sense (IMHO).

Don’t forget - “Written in layman-speak“
Can't you see that if "absolutely stationary" makes no sense, then "absolutely moving" makes no sense either?

Consider an analogy. Someone on Earth might say "the Moon is above the Earth". An astronaut on the Moon might say "the Earth is above the Moon". Which one is above the other depends on which direction you decide is "up". I hope you will agree, therefore, that the Moon is not absolutely above the Earth. But it doesn't follow that the Moon is absolutely below the Earth.

It is a simple matter of linguistic logic

NOT (absolutely stationary) ≠ absolutely (NOT stationary)​
 
  • #109


DrGreg said:
Can't you see that if "absolutely stationary" makes no sense, then "absolutely moving" makes no sense either?

Consider an analogy. Someone on Earth might say "the Moon is above the Earth". An astronaut on the Moon might say "the Earth is above the Moon". Which one is above the other depends on which direction you decide is "up". I hope you will agree, therefore, that the Moon is not absolutely above the Earth. But it doesn't follow that the Moon is absolutely below the Earth.

It is a simple matter of linguistic logic

NOT (absolutely stationary) ≠ absolutely (NOT stationary)​
The opposite of nonsense is sense. The opposite of absolute stationary is absolute moving . If absolute stationary is “nonsense” then absolute moving is “sense”. If a thing isn’t stationary it’s moving there is no third alternative. That absolute stationary makes no sense establishes that absolutely moving makes sense as it‘s the only thing left.

The relationship between the Earth and the Moon is completely relative. In an absolute or universal sense nothing is ever up, down, faster, slower, etc.
 
Last edited:
  • #110


swerdna said:
... The opposite of absolute stationary is absolute moving. ...

It is a logical fallacy to take the refutation of a certain claim as the affirmation of an opposite claim. It's a false dichotomy.

If you want "opposite", then take the opposite of "absolute"; not of "stationary". You really really want to use the word "absolute" here for some reason, and so you set up two absolute alternatives. Neither one is correct.

The real situation is that the state of being stationary or in motion is not absolute at all. There is no absolute. Not for being stationary, not for being in motion. Whether an object is in motion or stationary is relative.

Cheers -- sylas
 
  • #111


sylas said:
It is a logical fallacy to take the refutation of a certain claim as the affirmation of an opposite claim. It's a false dichotomy.

If you want "opposite", then take the opposite of "absolute"; not of "stationary". You really really want to use the word "absolute" here for some reason, and so you set up two absolute alternatives. Neither one is correct.

The real situation is that the state of being stationary or in motion is not absolute at all. There is no absolute. Not for being stationary, not for being in motion. Whether an object is in motion or stationary is relative.

Cheers -- sylas
Seems to be turning into a semantic debate. I’m happy to use the term “universal” rather than “absolute” if that’s more acceptable.

If things didn’t move relative to other things then everything would be universally stationary. The reality is however that things do move relative to other things and that means there is nothing that is universally stationary. Everything is always moving relative to something else universally.

There can be relative movement and relative stationary but there can’t be universal stationary. There is always movement universally regardless that some things are relatively stationary.
 
Last edited:
  • #112


swerdna said:
Seems to be turning into a semantic debate. I’m happy to use the term “universal” rather than “absolute” if that’s more acceptable.

I'll stick with the word "relative". Motion is only meaningful relative to something else.

... Everything is always moving relative to something else universally.

You are much better just to leave out the word "universally". It leads you into inconsistency.

Your first sentence makes good sense if you leave off that redundant word.
Everything is always moving relative to something else.

The reason you should omit that additional word is because EXACTLY THE SAME THING holds for being stationary.
Everything is always stationary relative to something else.

There can be relative movement and relative stationary but there can’t be universal stationary. ...

There's your inconsistency. The only sense in which there is "universal motion" applies just as well to say "universal stationary". Just like everything is always moving relative to something else, so too everything is always stationary relative to something else.
 
  • #113


sylas said:
The real situation is that the state of being stationary or in motion is not absolute at all. There is no absolute. Not for being stationary, not for being in motion. Whether an object is in motion or stationary is relative.

sylas said:
I'll stick with the word "relative". Motion is only meaningful relative to something else.



You are much better just to leave out the word "universally". It leads you into inconsistency.

Your first sentence makes good sense if you leave off that redundant word.
Everything is always moving relative to something else.

The reason you should omit that additional word is because EXACTLY THE SAME THING holds for being stationary.
Everything is always stationary relative to something else.



There's your inconsistency. The only sense in which there is "universal motion" applies just as well to say "universal stationary". Just like everything is always moving relative to something else, so too everything is always stationary relative to something else.
What about acceleration? There’s nothing relative about acceleration.

As diazona said in post #37 - “something can be assumed to be moving in an absolute sense, if it is accelerating”. You seemed to agree with him/her at the time.
 
  • #114


swerdna said:
What about acceleration? There’s nothing relative about acceleration.

Whether you are in motion or stationary is relative.
Whether you are accelerating or inertial is absolute.

This is not hard.

I got to ask, what is the point here? Are you just trying to twist things into contradictions, or are you seriously still not understanding basic relativity?

The measurement of acceleration as a number is still relative to an observer; but you can define a "proper" acceleration as being the acceleration of an object as measured in the inertial frame where it is (instantaneously) with a velocity of zero. That still leaves the direction of acceleration as relative, but it does give an unambiguous absolute magnitude for "proper acceleration".
 
  • #115


sylas said:
Whether you are in motion or stationary is relative.
Whether you are accelerating or inertial is absolute.

This is not hard.

I got to ask, what is the point here? Are you just trying to twist things into contradictions, or are you seriously still not understanding basic relativity?

The measurement of acceleration as a number is still relative to an observer; but you can define a "proper" acceleration as being the acceleration of an object as measured in the inertial frame where it is (instantaneously) with a velocity of zero. That still leaves the direction of acceleration as relative, but it does give an unambiguous absolute magnitude for "proper acceleration".
It’s not so much a difficulty of understanding basic Relativity. It’s a difficulty in accepting the validity of one of the basic building blocks that Relativity is founded on. If I could accept that the building block was valid I don’t see that I would have much difficulty in accepting basic Relativity. It’s more to do with accepting than understanding. Although I guess it’s more than likely that my lack of acceptance is a result of my lack of understanding. I’m not trying to be clever or difficult. I’m trying find out what the truth is.

When you are accelerating you are absolutely in motion (no relativeness required).
When you are inertial you are not absolutely stationary.
 
  • #116


swerdna said:
When you are accelerating you are absolutely in motion (no relativeness required).
When you are inertial you are not absolutely stationary.

Are you aware that this is true in Newtonian physics, not just special relativity?

Also, are you aware that the statements mean:
1. When you are accelerating you are absolutely in motion (no relativeness required). = When you are accelerating relative to a particular inertial frame, you are accelerating relative to all inertial frames.
2. When you are inertial you are not absolutely stationary. = When you are stationary relative to a particular inertial frame, you are not stationary relative to all inertial frames.
 
Last edited:
  • #117


atyy said:
Are you aware that this is true in Newtonian physics, not just special relativity?

Also, are you aware that the statements mean:
1. When you are accelerating you are absolutely in motion (no relativeness required). = When you are accelerating relative to a particular inertial frame, you are accelerating relative to all inertial frames.
2. When you are inertial you are not absolutely stationary. = When you are stationary relative to a particular inertial frame, you are not stationary relative to all inertial frames.
Yes, but I don’t understand the point of your question. Care to explain it?
 
  • #118


swerdna said:
Yes, but I don’t understand the point of your question. Care to explain it?

So those are the 2 statements you can't accept?
 
  • #119


atyy said:
Are you aware that this is true in Newtonian physics, not just special relativity?

Also, are you aware that the statements mean:
1. When you are accelerating you are absolutely in motion (no relativeness required). = When you are accelerating relative to a particular inertial frame, you are accelerating relative to all inertial frames.
Yes.
atyy said:
2. When you are inertial you are not absolutely stationary. = When you are stationary relative to a particular inertial frame, you are not stationary relative to all inertial frames.
Yes. You can only ever be stationary to one particular inertial frame at at time because all inertial frames always move relatrive to all other inerttial frames. This was covered and agreed earlier in the thread.
 
  • #120


atyy said:
So those are the 2 statements you can't accept?
No. I fully accept both statements. I made them. I don't accept sylas’s claim that - “Whether you are in motion or stationary is relative”.
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 9 ·
Replies
9
Views
653
  • · Replies 16 ·
Replies
16
Views
2K
Replies
27
Views
2K
  • · Replies 24 ·
Replies
24
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 45 ·
2
Replies
45
Views
6K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
Replies
12
Views
2K