Relativity - Oh dear, here we go again!

[Fredrik]

The word "theory" has many meanings, so even in a philosophical conversation, it can be used ambiguously. A theory can become a scientific law, or it can be disproved, or it can be argued over on a message board.

I'm not going to debate you on everything you said, because it would take us too far from the topic of this thread. I will make a few comments though.

Yes, the word "theory" is often used like that, mainly by people who have never studied science. (E.g. creationists who believe that the name "the theory of evolution" implies uncertainty). But it's certainly not used like that by physicists. There are lots of examples of theories in physics that are known to not really describe anything in the real world, and they are still called theories. And not even the very best theories in physics have "become scientific laws". It's still called the theory of relativity for example.

You are simply wrong about how the word theory is used. Yes, it's used the way you say by most people, but not by actual theorists.

Many many people talk directly about reality, and do things with reality, in reality, all the time, every day. That you think it can't be done is absurd.

They don't ever define have to define the concepts they're using, not rigorously anyway. That's why they can do it. Most people never have to rigorously define anything, but theoretical physicists do. When they talk about the things they have defined, they are definitely not talking about the real universe. They are talking about a fictional universe that is very much like the real one, but not quite the same.

 

[sphenisc]

What the twins could say to each other when the astronaut twin is back on Earth is "during the whole trip, except for that brief moment when the rocket turned around, you were aging at a slower rate than me". This is however not the same thing as "you have aged less than me" (which, at least to me, means exactly "you are now younger than me").

The reason why these two claims are not equivalent can be seen in this space-time diagram (taken from the Wikipedia article about the twin paradox):

[qimg]http://upload.wikimedia.org/wikipedia/commons/6/6a/Twin_paradox_Minkowski_diagram.png[/qimg]

The t axis is the world line of the twin on Earth. The x axis is the set of events that are simultaneous with the event with coordinates (0,0), i.e. it's what the earthbound twin thinks of as "space, at time t=0". The other black lines are the world lines of the rocket moving away from Earth, and the rocket moving towards Earth.

In the Earth frame, all events on any straight line parallel to the x axis are simultaneous (with each other). In the frame of the rocket when it's moving away from Earth, all events on any of the blue lines (or other lines parallel to them) are simultaneous. I will call this frame R1 from now on. In the frame of the rocket when it's moving towards Earth, all events on any of the red lines (or other lines parallel to them) are simultaneous. I will call this frame R2 from now on.

What you need to see in this diagram, in order to understand the twin paradox, is which events on Earth are simultaneous with the astrounaut twin's experiences "the rocket will turn around in a second" (which happens when he's in frame R1) and "the rocket turned around a second ago" (which happens when he's in frame R2). Even though only two seconds passed on the astronaut twin's clock, his brother changed from being much younger than him to being much older than him (as can clearly be seen in the diagram by following the top blue line first, and then the bottom red line). This is because the planes of simultaneity got tilted the other way.

Here's a funny thing that's almost never mentioned in discussions about the twin paradox: If the rocket reverses its direction again, immediately after it did it the first time, so that it's now moving away from Earth again, then the astronaut twin is back in frame R1 where his brother is much younger than him again! This is not some sort of time travel. It's just relativity of simultaneity.

Edit: Actually, he wouldn't be back in frame R1. He would be in another frame, let's call it R1', that's the same as R1 in every way that matters (including its velocity in the Earth frame). The only difference between R1 and R1' is that they assign coordinates to events using different events as the origin.

How does this diagram indicate that the travelling twin will be younger when they eventually meet up? The 'age gap' seems to lessen as they approach each other - what am I missing?

 

[BillyJoe]

Good point! I can’t think of any state where there wouldn’t be some form of gravity, solar wind, etc that would case some amount of acceleration. But this only provides further proves that everything is constantly being accelerated, and therefore is constantly moving - Thanks.

Nobody has stated that there are objects that are stationary in an absolute sense, only that they can be taken to be stationaryfor the purposes of measuring the movement of other objects relative to them.

 

[Paulhoff]

Good point! I can’t think of any state where there wouldn’t be some form of gravity, solar wind, etc that would case some amount of acceleration. But this only provides further proves that everything is constantly being accelerated, and therefore is constantly moving - Thanks.

No, you missed the deceleration part, a planet (for one) in orbit does both. And acceleration in not needed for time to slow down, movement itself does that.

Paul

 

[robinson]

No, you missed the deceleration part, a planet (for one) in orbit does both. And acceleration in not needed for time to slow down, movement itself does that.

Does time slow down? Or is it considered less time passes, or what? Isn't it a space-time warp effect? I know from reading the GPS stuff that this is a real effect, not theoretical, so what is the theory behind the real change in time? Are the atoms moving slower in the atomic clock? Is the light frequency different? How do they offset the clocks?

Meh ... I feel a head exploding .... must ... stop ... thinking ...

 

[Paulhoff]

Does time slow down? Or is it considered less time passes, or what? Isn't it a space-time warp effect? I know from reading the GPS stuff that this is a real effect, not theoretical, so what is the theory behind the real change in time? Are the atoms moving slower in the atomic clock? Is the light frequency different? How do they offset the clocks?

Meh ... I feel a head exploding .... must ... stop ... thinking ...

Time is changed by speed. The speed of light is the fastest that any partial can move. Anything that has mass can’t go at the speed of light, only a mass-less partial can. Also when something goes in one direction, and/or on dimension, less speed is available in the other two dimensions and time slows down. So just like the light clock that slows down because the beam of light has to travel more distance between the mirrors so do atoms because the virtual photons that are exchanged between the electrons and the nucleus of the atom now have more distance to travel, and the gluons between the quarks etc this causes time to slow down. If an atom where to travel that the speed of light, virtual photons would not be able to travel between the electron and the nucleus because there was no more speed available and time would therefore stop for that atom, no change can then happen and without change there is no time.

Paul

 

[Fredrik]

How does this diagram indicate that the travelling twin will be younger when they eventually meet up? The 'age gap' seems to lessen as they approach each other - what am I missing?

That's a good question. Neither the diagram nor my post about it (#162) really explains it.

Here's what happens from the astronaut twin's point of view: When the rocket is moving away from Earth his twin is aging at a slower rate than him. When the rocket starts to turn around, the twin on Earth is slightly younger, but now the simultaneity planes get tilted the other way, so when the rocket has reached full speed again, the twin on Earth is much older, but will age at a slower rate until the rocket is back on Earth. So the age gap is decreasing during the return trip.

The reason the astronaut twin is younger when the rocket gets back to Earth is that the sudden jump in age difference (from the astronaut twin's point of view) when the rocket turns around is more than twice as big as the decrease during the return trip.

The diagram doesn't prove that. What's missing is the scale on the time axes of the three inertial frames. I'm too lazy to make a diagram that shows the correct scales, but I will describe how we can figure out what they are. We could plot curves of the form t=sqrt(x^2+A^2) in the diagram. A is a constant that we choose to be 1 year, 2 years, 3 years, etc. Note that these curves intersect the t axis at t=A. When you follow such a curve to the right, it will bend upwards but approach the line t=x as x goes to infinity. The points where these curves intersect the world line of the outbound twin are the events where he has aged A years. Note that the distance (in the diagram) between such points is greater on the rocket's world line than on the Earth's world line.

We could plot a similar set of curves for the return trip. It would be a bit more complicated, but we would again find that the distance in the diagram between events on the rocket's world line that are 1 year apart in the rocket's frame, is greater then the distance in the diagram between events on the Earth's world line that are 1 year apart in the Earth's frame.

We could use these curves to make markings on the world lines that are 1 year apart in the respective frames. These markings would enable us to see how old the twins are at any point on their world lines. In particular we would see how much the age difference changes during the inbound and outbound trips, and by following the simultaneity lines in the two rocket frames immediately before and after the turnaround, we could compare the result to the sudden jump in age difference (from the astronaut twin's point of view) that occurs when the rocket turns around.

 

[BillyJoe]

Hey, I think we need to keep this simple.
We're in danger of killing the thread.

 

[robinson]

Don't worry, it will pop up again, in a different form.

 

[ynot]

That's not what I said is correct, but I agree with this too. (What I said you were right about was that everything in the real world is accelerating).

Let’s just agree on these two points and move on. I take it that you mean “world” in the universal sense.

Just about every time you quote me, you answer as if the text you quoted was about something different than it actually was. It's a little frustrating. What I said was that the fact that everything is accelerating in the real world has nothing to do with relativity.

“No . . . Please don‘t . . . Stop” and “No . . . Please don’t stop.” use the same words but have exact opposite meanings. Did I say it wrongly, or did you hear it wrongly? I’m not overly fluent in Relativity/physics speak so apologise if I get the terminology wrong some times. (Never mind the quality, feel the width

What exactly has everything to do with what we're discussing, and why? (It's hard to know since you're constantly changing the subject and acting as if you don't).

“It” the same “It’'s” you were talking about in the piece I answered.

I would have to say that it's an abstract concept, but I would say the same about an electron and the number 3, so I don't see the point of the question. We can only define these things exactly within the framework of a theory, so if we are talking about well-defined things we are always talking about abstract concepts. If the theory is a good approximate description of the universe, there might however be something in the real universe that's approximately described by the abstract concept. So I would also say that since SR is a good theory, it's a fact that something very much like a stationary object can exist in the real universe. The question of whether something that's very much like a stationary object in SR does exist in our universe is completely irrelevant, but if you really want an answer to that, the answer is "no".

I think we all agree that nothing is universally stationary, but a thing can be stationary relative to another.

Do you feel that we've made any progress at all in this discussion? Is there anything that you feel that you understand now that you didn't from the start?

Thanks for asking. Not sure. Answers tend to bring up more questions. I think the quality of the responses have been very good and I thank everyone for them. Not sure that I’m clearly presenting my concerns with Relativity. Even though you don’t agree, do you understand in any way what my concerns are?

 

[ynot]

No, you missed the deceleration part, a planet (for one) in orbit does both. And acceleration in not needed for time to slow down, movement itself does that.

Paul

Acceleration and deceleration are essentially the same. When I use the word acceleration it includes deceleration. Bit like Manager and Actor including both sexes these days. I also wasn’t talking about time dilation, just movement. A thing that is accelerating from one frame to another has to be moving to do so. That everything is accelerating proves that everything is moving.

 

[ynot]

Time is changed by speed. The speed of light is the fastest that any partial can move. Anything that has mass can’t go at the speed of light, only a mass-less partial can. Also when something goes in one direction, and/or on dimension, less speed is available in the other two dimensions and time slows down. So just like the light clock that slows down because the beam of light has to travel more distance between the mirrors so do atoms because the virtual photons that are exchanged between the electrons and the nucleus of the atom now have more distance to travel, and the gluons between the quarks etc this causes time to slow down. If an atom where to travel that the speed of light, virtual photons would not be able to travel between the electron and the nucleus because there was no more speed available and time would therefore stop for that atom, no change can then happen and without change there is no time.

Paul

I like "real world" explanations - Thanks

 

[BillyJoe]

I like "real world" explanations - Thanks

Don't worry. If you understood that explanation, I'd be worried for you.
(sorry, Paul.)

 

[Paulhoff]

Don't worry. If you understood that explanation, I'd be worried for you.
(sorry, Paul.)

Sorry if I didn't use five thousand words for you.

Paul



I can do a lot more with that avatar...........

 

[ynot]

Don't worry. If you understood that explanation, I'd be worried for you.
(sorry, Paul.)

Was thanking him for the method, not necessarily the content.

 

[BillyJoe]

I think we all agree that nothing is universally stationary, but a thing can be stationary relative to another.

Yes.
But can you also agree that it is legitimate to take any object as being stationary for the practical purpose of measuring the movement of other objects relative to it?

 

[BillyJoe]

If so, what do you now think of the following....

[B]o[/B]                      [B]a[/B]                        [B]b[/B]                                         
                       >                        <                                         
 
 
[B]o[/B]                               [B]ab[/B]                                            [B]c[/B]
                                ><                                            <
 
 
[B]o[/B]                  [B]b[/B]                    [B]ac[/B]
                   <                    ><
 
 
[B]o[/B]     [B]bc[/B]                                         [B]a[/B]
      <<                                         >

o is the rest frame.
a, b, and c are spaceships travelling at constant speed in a straight line.
> and < indicate the direction of travel.

When a meets b, they synchronise their clocks.
When a meets c, c matches his clock to a's.
When b and c meet, they compare times.

The time on c's clock will be less than that on b's clock
There has been relative time dilation because of the greater speed of c relative to b.
Acceleration cannot be the cause because no one has accelerated.
In other words, relative time dilation is a function of relative speed, not acceleration.

This was an attempt to show that time dilation is real and that it is not caused by acceleration.

 

[Fredrik]

Even though you don’t agree, do you understand in any way what my concerns are?

I think I understand what your post #1 was about, and I feel that I have answered that thoroughly in #13 and #48 (especially #48).

I don't understand your concerns about the "the basis on which math is founded".

I don't think the twin paradox should have been brough into this, since it's a much more difficult problem than the original issue, but I feel that I have explained that pretty thoroughly too, in #59, #142, #162, #164 and #227 (especially #162). I have also made a space-time diagram that I will post in a few minutes.

I'm not sure I understand your concerns about rest frames and stationary/non-accelerating objects. The fact that you made a big deal of the question of whether an actual physical object can be truly stationary seems (to me) to indicate that you don't fully understand the concept of mathematical idealizations. What you did isn't very different from rejecting the geometry you learned in high school because there are no physical objects that are exactly spherical, or have exactly straight lines as edges.

I consider a request for an example of a truly stationary object in the real world not only irrelevant, but illogical. The word "stationary" is only rigorously defined within the framework of a theory, so it doesn't exactly apply to anything in the real world.

Anyway, I defined the word "stationary" in #203.

 

[Fredrik]

This is not the first time and probably not the last time that I've been involved in a discussion about the twin "paradox". So I decided to draw a space-time diagram that shows a lot of details, including the ages of the twins at several different events on their respective world lines.

I have explained a lot of this already, in the posts I listed in #238. In this diagram, I'm calling the twin on Earth "A" and the twin in the rocket "B".

Blue lines: Events that are simultaneous in the rocket's frame when it's moving away from Earth.

Red lines: Events that are simultaneous in the rocket's frame when it's moving away from Earth.

Cyan (light blue) lines: Events that are simultaneous in Earth's frame.

Dotted lines: World lines of light rays.

Vertical line in the upper half: The world line of the position (in Earth's frame) where the rocket turns around.

Green curves in the lower half: Curves of constant -t^2+x^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket left Earth.

Green curves in the upper half: Curves of constant -(t-20)^2+(x-16)^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket left the position (in the Earth's frame) where it turned around.

Any questions?

 

[ynot]

I was hoping to keep this thread simple, so I guess bringing the “terrible twins” in to it was a bit of a mistake. I want to summarise what I think I know, so please let me know if you don’t agree with anything.

All objects in the universe are constantly moving, and there is no actual reference point that can be acurately called stationary.

Some objects are not moving in relation to others (but they are still moving). Essentially they are moving in the same direction at the same speed (they share the same frame).

An object can accelerate from one frame to another. It can’t be said that an object is either speeding up or slowing down to do this (I think this is important).

Speed cannot be attributed to a single object (not sure about spin/rotation). Speed is the rate that objects move relative to others. In other words, the speed at which they are coming together or moving apart (which is not the speed of either object).

I’ll leave it there for now.