Relativity - Oh dear, here we go again!

[ynot]

Huh!? Your claims are getting weirder. Pick any object that isn't accelerating. There's definitely an inertial frame in which that object's world line coincides with the time axis. In fact, there's an infinite number of them. (Hint: rotations). If you believe otherwise, you have no idea what an inertial frame is.

Any of these inertial frames can be called "rest frames" of that object, since the spatial coordinates of the object are (0,0,0) the whole time.

An object that isn't accelerating isn’t an object that is stationary. To define an object that isn't accelerating as being stationary is an abstract definition. To express anything mathematically is to express it abstractly. Math is abstract.

Rotation - now there’s a things that really puzzles me, but I don’t want to get sidetracked.

So? You can think of that "o" as a feather in space if you'd like.

You were the one that was putting importance on using the Earth (you even bolded it)

 

[BillyJoe]

Not so. I just don’t accept your understanding of this. More precisely, I’m questioning the validity of the methods you (and others) use to reach your understanding. I realise that they are the same methods that have been used by many clever people for many years, and that my questioning is most likely to be proven groundless. But until that time, the little voice in my head keeps asking the questions

The smilie says that I was joking....I think
I'm sure you are determined to understand it. It just that it seems as if you are blocking off every possible way of understanding it.

By defining o as a rest frame you are automatically making it a universal rest frame. o is no more a rest frame than a, b or c. To put your finger on any object and call it a rest frame is “playing god” with the universe (no I‘m not a theist). If you arbitrarily define an object as being a rest frame, you have only created an abstract concept of a rest frame. Any conclusions that result from an abstract concept are abstract conclusions.

Case in point:
The subject is called "relativity", meaning everything is relative to everything else, meaning every frame of reference can be taken arbitrarily as the rest frame and the motions of all the other objects can be calculated from that rest frame. And the answers you get are all equally legitimate and consistent.

You can take o as the rest frame and work out how all the other frames, a, b and c move relative to o.
You can take a as the rest frame and work out how all the other frames, o, b and c move relative to a.
You can take b as the rest frame and work out how all the other frames, o, a and c move relative to b.
You can take c as the rest frame and work out how all the other frames, a, b and c move relative to c.

This is what relativity is all about.

The Earth is no more concrete than a feather floating in space. I don’t like using the Earth as a rest frame as we (humans) live with the illusion that it is. There is no such thing as an actual rest frame, why pretend that there is?

That's why I didn't call it the Earth in the first place!
That's why I had all the interacting bodies (a, b and c) moving instead of having one of them as the rest frame!
Sometimes you can't win!
Anyway, let's call o a feather, then, if you will, it doesn't matter.

 

[BillyJoe]

An object that isn't accelerating isn’t an object that is stationary.

You cannot say "an object that is stationary".
You must say "an object that is stationary relative to [fill in the blank]"

To define an object that isn't accelerating as being stationary is an abstract definition.

I am stationary relative to my son who is sitting at the computer next to mine playing computer games.
There is nothing abstract about that.

To express anything mathematically is to express it abstractly. Math is abstract.

If I have one apple and someone gives me another apple, I have two apples. I mean I really do have two apples. The mathematical expression 1 + 1 = 2 is an abstraction, but that doesn't prevent me from applying it to a concrete example.

 

[BillyJoe]

Respectfully, Myriad, we are just trying to demonstarte to ynot that time dilation is real. I chose to demonstrate that two clocks which, in classical physics, would show the same time, actually do show different times when relativity is taken into account. That is all.

You get the same result using c as the rest frame as I do using o as the rest frame. So, really, we are saying the same thing. Ynot disagrees with both of us.

 

[Fredrik]

An object that isn't accelerating isn’t an object that is stationary.

In a way it is, because there's always a class of inertial frames in which it is stationary.

To define an object that isn't accelerating as being stationary is an abstract definition. To express anything mathematically is to express it abstractly. Math is abstract.

I agree. But how is that a problem? You dismissed what BillyJoe said because he was using these "abstract concepts", i.e. because he was using mathematics. Are you dismissing all of mathematics, or just inertial frames? What exactly is it that troubles you?

You were the one that was putting importance on using the Earth (you even bolded it)

That was BillyJoe, not me. And nothing he said implies that it's important to use the Earth. He actually said "o is just intended to be an arbitrary rest frame for the purposes of this illustration. The spaceships a, b and c are moving relative to this arbitrary rest frame. It could be the Earth for example". This is the exact opposite of saying that it's important to use the Earth.

Rotation - now there’s a things that really puzzles me, but I don’t want to get sidetracked.

You're right, we should deal with as few issues as possible. I think it was also a mistake to start talking about the twin paradox before the original issue had been resolved, but that can of worms is already open. Did you read post #162 in this thread? You haven't said anything about it.

 

[ynot]

In a way it is, because there's always a class of inertial frames in which it is stationary.

Yes, and that way is the abstract way. Which is fine if it’s not presented as being reality.

I agree. But how is that a problem? You dismissed what BillyJoe said because he was using these "abstract concepts", i.e. because he was using mathematics. Are you dismissing all of mathematics, or just inertial frames? What exactly is it that troubles you?

I have no problem with abstract concepts, or that mathematics is abstract, or brainstorming the most ridiculous ideas to get out of the rut of linear thinking. I have a problem when abstract concepts and mathematics are presented as being actual.

That was BillyJoe, not me. And nothing he said implies that it's important to use the Earth. He actually said "o is just intended to be an arbitrary rest frame for the purposes of this illustration. The spaceships a, b and c are moving relative to this arbitrary rest frame. It could be the Earth for example". This is the exact opposite of saying that it's important to use the Earth.

Sorry about that (you look so much alike . The part of BillyJoe’s post that I was responding to was . . .
“Let's be more concrete still and call o the Earth so that a, b and c are moving relative to the Earth. Can you make sense of the scenario now?“.
Not the part you quoted.

You're right, we should deal with as few issues as possible. I think it was also a mistake to start talking about the twin paradox before the original issue had been resolved, but that can of worms is already open. Did you read post #162 in this thread? You haven't said anything about it.

Yes I read your post #162. Sorry I didn’t respond. Unfortunately I don’t have the time to respond to all posts. I’m self employed and very busy. I didn’t understand the first part. I thought the whole point of the twins paradox was that one twin ages more than the other. I think that saying “aging at a slower rate“ is essentially the same as saying “aging less“. The rest I could pretty much follow and understand. I think math is a very clever and useful tool that ranks right up there with the wheel and sliced bread. I don’t think however that everything that can be expressed in the abstract world of math has actual existence in the world of reality. I’m not questioning the math of relativity, I’m only questioning the basis that it’s founded on

 

[ynot]

You cannot say "an object that is stationary".

You must say "an object that is stationary relative to [fill in the blank]"
I am stationary relative to my son who is sitting at the computer next to mine playing computer games.

I agree, but is relative real or abstract? I think it’s abstract.

If I have one apple and someone gives me another apple, I have two apples. I mean I really do have two apples. The mathematical expression 1 + 1 = 2 is an abstraction, but that doesn't prevent me from applying it to a concrete example.

I didn’t mean to imply that mathematics can’t express reality with a high degree of accuracy. What I meant was, just that because a thing can be expressed mathematically doesn’t mean that it is reality. Mathematics can be applied to reality, but it doesn’t create reality.

 

[ynot]

If you're speaking of hypothetical particles you are talking in abstractions. Try to overcome your disdain of them. You've titled your thread "Relativity..." - Reference frames come with the territory.

So if I create a thread titled “Bible . . .” I’m only allowed to communicate in “Bible speak”? << don't miss this.

E = mc^2 is true for particles of mass at velocity 0. I imagine particles have some velocity always - the universe seems to be in constant motion. Even a particle at a temperature of absolute zero on the Earth is moving with the Earth. Conceptualizing the "At Rest" reference frame allows you to work the problems without concern for what the universe is doing around your particle.

Massless particles at rest travel at the speed of light. That's their "at rest" reference frame. It may be abstract to you but it's true in Relativity.

I think you have to buy into the concept of reference frames to participate in complex discussions of relativistic interactions. If you can't or won't you should consider throwing in the towel.

Please remember that I’m only questioning the basis on which Relativity is founded. To me it seems to be founded on abstract concepts that are presented as being real. If I’m wrong, and the basic foundation is sound in reality, then I don’t think I would have much problem accepting Relativity as being more than an abstract concept.

Throw in the towel? You think I'm a quitter? I'll fight till the last drop of blood has dripped! (I know what you mean)

 

[ynot]

I suspect that many people (on this forum) share similar thoughts to mine regarding Relativity, but are reluctant to express those thoughts due to an “Emperor’s New Clothes complex“. If any have the courage to hold their hand up, I would appreciate some indication that they exist. Perhaps an anonymous poll would be the way to do it.

 

[PixyMisa]

An object that isn't accelerating isn’t an object that is stationary. To define an object that isn't accelerating as being stationary is an abstract definition.

You have that precisely backwards.

 

[Thabiguy]

An object that isn't accelerating isn’t an object that is stationary.

Then what is an object that is stationary?

 

[Thabiguy]

Please remember that I’m only questioning the basis on which Relativity is founded. To me it seems to be founded on abstract concepts that are presented as being real.

Do you also feel the same way towards classical Newtonian mechanics? It is, after all, founded on these very same abstract concepts of time, velocity, acceleration - and also reference frames, inertial reference frames, and relativity (Galilean relativity).

Do you also have a hard time seeing classical mechanics as being more than an abstract concept?
If yes, then that still doesn't prevent you from relying on it in your real life on a daily basis, does it? Nor do you question its validity - or do you?
If not, if you are cool with classical mechanics, then what is the actual abstract concept that special relativity is founded on which you perceive not to be real, but only presented as such?

 

[BillyJoe]

Please remember that I’m only questioning the basis on which Relativity is founded. To me it seems to be founded on abstract concepts that are presented as being real. If I’m wrong, and the basic foundation is sound in reality, then I don’t think I would have much problem accepting Relativity as being more than an abstract concept.

Perhaps, then, we need to go right back and ask this question:
What do you think is being "presented as being real" that is not real?

 

[BillyJoe]

...Thabiguy, we cross-posted the same basic question.

 

[Ziggurat]

OK, I've got a spacetime diagram for you, YNOT:


The red line represents the earthbound twin's worldline. The blue line represents the traveling twin's worldline. The black lines at 45 degrees show the lightcone originating at the origin. The time axis is vertical, and the space axis is horizontal.

Now panel A shows the reference frame of the earthbound twin. In this frame, he is stationary, and the traveling twin is moving the entire time. Therefore in this frame, the traveling twin experiences time dilation while the earthbound twin does not, and so the earthbound twin ends up older. I've drawn this using a velocity of 0.707c for the outbound twin compared to the earthbound twin. This creates a time dilation factor of 0.707 as well (I chose that number for that reason - it's sqrt(0.5) ). We'll use a total time of 2 years in reference frame A, which means in this reference frame, the traveling twin turns around after 1 year in this frame (but because of time dilation, he experiences less time than that before he turns around).

Panel B shows the exact same events but now from the reference frame of the traveling twin when he is outbound. Note that panels A and B are both to scale. The earthbound twin is now moving, and experiences time dilation. If the earthbound twin ages 2 years from when the traveling twin leaves to when he returns, then in this outbound reference frame, those two events are separated by about 2.828 light years (because of the same time dilation factor that applied previously). Note carefully, though, that in this reference frame, the traveling twin is only stationary for PART of the time. And that part of the time is LESS than 1 year - in fact, only 0.707 years. Note further that when the traveling twin starts heading back towards earth, he's going much faster than 0.707c, and so for this part of the journey the time dilation factor is much larger. In this reference frame, it takes 2.121 years for the traveling twin to catch up to the earthbound twin. But because he's going so fast, he only experiences 0.707 years. So the proper time intervals (the time experienced along a given path) agree for both reference frames.

The third panel (C) again shows the same events, but this time in the reference frame of the inbound traveling twin. Again, the earthbound twin experiences time dilation. This time, it's the first leg of the traveling twin's journey that he's moving (much faster than the earthbound twin) at close to c for 2.121 years, but only experiences 0.707 years. For the last 0.707 years the traveling twin is stationary in this reference frame. He experiences a total of 1.414 years, the earthbound twin experiences 2 years, but the total time in this reference frame was 2.828 years. But again, the PROPER time intervals for both twins is the same in all these reference frames.

The point here is that time dilation DOES apply to any moving reference frame, relative to any other frame, but this does NOT create any contradictions when the transformations from one frame to another are handled correctly. You have so far definitely not understood relativity, because your objections center around the idea that there's some internal inconsistency with the theory. But there simply isn't. It's a beautifully self-consistent theory, and it's possible to determine this from a purely mathematical viewpoint. It's a separate question of whether or not the theory accurately describes reality (plenty of possible self-consistent theories have no connection to reality), though experiments have so far only confirmed it as correct. But if you're still not getting that the theory is self-consistent, then you really are not understanding it. And that isn't the fault of the theory.

 

[Fredrik]

The part of BillyJoe’s post that I was responding to was . . .
“Let's be more concrete still and call o the Earth so that a, b and c are moving relative to the Earth. Can you make sense of the scenario now?“.
Not the part you quoted.

Yes, I knew that when I replied. But even the part you quoted doesn't imply that the Earth has any special significance or that it's important to use the Earth. I quoted that part of his post to show you that he said so himself, in that same post.

Choosing a frame in which the Earth is stationary is no different than e.g. choosing to call the twins "Steve" and "Joe". If I had chosen to call them that, the reason would have been that I wanted to avoid expressions such as "the astronaut twin" and "the twin on Earth" in my explanation, it wouldn't have implied that their names are important.

Yes, and that way is the abstract way. Which is fine if it’s not presented as being reality.
...
I have a problem when abstract concepts and mathematics are presented as being actual.
...
I’m not questioning the math of relativity, I’m only questioning the basis that it’s founded on.

To me it seems to be founded on abstract concepts that are presented as being real. If I’m wrong, and the basic foundation is sound in reality, then I don’t think I would have much problem accepting Relativity as being more than an abstract concept.

I find these comments pretty strange. As Thabiguy pointed out, these abstract concepts (like inertial frames) are present in pre-relativity physics too. So why do you have a problem with relativity and not Newtonian mechanics?

It seems to me that you may have misunderstood what physics is, rather than just some detail in special relativity. There are several reasons that mathematics is used all the time, and the fact that mathematics makes it possible to calculate things is only one of them. Another reason, that's equally important, is that mathematics makes it possible to define things so that different physicists can know they're talking about the same thing. This makes the definitions "abstract", all the definitions. There isn't a single definition in a physical theory that isn't abstract!

That's what physics is. A theory is built from abstract concepts, and then you do experiments trying to prove that the theory isn't an accurate description of a certain aspect of reality.

In the case of SR, the abstract stuff is simply the mathematics of Minkowski space (which includes inertial frames). The physical theory is the claim that Minkowski space is an accurate representation of space and time. Only actual, physical, experiments (as opposed to thought experiments) can possibly prove it wrong.

I didn’t understand the first part. I thought the whole point of the twins paradox was that one twin ages more than the other. I think that saying “aging at a slower rate“ is essentially the same as saying “aging less“. The rest I could pretty much follow and understand.

The point is that at any time from when they separate until they meet again, except when the rocket turns around, they would both be correct saying "right now my twin is aging slower than me". That's time dilation. Actually, in a way they'd both be correct saying it during the acceleration phase as well. I'll get back to that later.

Right after the rocket has turned around, the twin on Earth can say "That's weird. During a short time, my brother's aging rate increased. For an instant, it actually caught up with mine. Then it started to decrease again". This is also just time dilation. There is less time dilation going on during the acceleration phase since their relative velocity is smaller.

What the astronaut twin can say right after the rocket has turned around is "Wtf!? my brother just aged several years in a very short time!". That's not time dilation. It's relativity of simultaneity (the tilting of simultaneity planes).

So why did I claim that it would still make sense for both of them to say "right now my twin is aging slower than me" during the acceleration phase as well? I did because the time dilation is going on the whole time, except at the the precise moment when their relative velocity is zero, and there's no way to reverse its effect. The relativity of simultaneity effect is however reversible at this point. All the astronaut would have to do to be older than his brother again is to turn the ship around again. My point is just that this makes it reasonable to say that we shouldn't use terms like "aging rate" to describe what happens when the simultaneity planes get tilted the other way.

If you didn't understand the first part of #162, you probably didn't understand the rest either, because the rest is the explanation of the first part.

 

[ynot]

You have that precisely backwards.

So you’re saying everything that isn’t accelerating is stationary? In other words, Everything that isn’t accelerating isn’t moving relative to anything else. I don’t think so. Perhaps my terminology isn’t correct in the language of Relativity.

 

[robinson]

Then what is an object that is stationary?

That is a good question. Seems that objects are not stationary, unless the observer is in the same trajectory. So the observer determines what is moving or still, and that "stationary" means "moving in the same motion/trajectory/velocity as I am".

Which seems to be an assumption we just accept, in order to be able to calculate stuff. I checked, and this is nothing new, what with it being brought up long ago in regards to Newton's first law and relativity as well.

But it gets complicated quick, and my head already exploded once thinking about this. So let us ignore motion within the frame of the observer, so there will be no more cranial over-expansion tonight.

Oh dear, oh dear, space time stuff is hard.

 

[ynot]

Then what is an object that is stationary?[/size][/font]

I don‘t believe that any object is truly, actually stationary. "an object that is stationary" doesn't actually exist in reality, it only exists as an abstract concept. If anyone can give me just one example (actual, not abstract) of a stationary object then I would change my mind on this in a heartbeat.

 

[robinson]

We must have cross posted.