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Relativity - Oh dear, here we go again!

Paulhoff said:
This may help you.

http://nobelprize.org/educational_games/physics/relativity/paradox-1.html

Paul

:) :) :)
Click to expand...
Thanks Paul, but it doesn’t help unfortunately.

From the linked page . . .

“However, can you not turn the discussion around and say that Eve has been at rest in her space-ship while Adam has been on a "space journey" with planet Earth? In that case, Adam must be younger than Eve at the reunion! If these discussions were both correct, then Adam should be both older and younger than Eve at the same time. But both these discussions are not correct. Adam is at rest all the time on Earth, i.e., he is in the same inertial frame all the time, but Eve is not (as was stated above). Eve will feel forces when her space-ship accelerates and retards, and Adam will not feel such forces.”

The only time I can see that time dilation could take place between the twins is during the period of accelerating of one of the twins from one frame to another. During this period the twins are experiencing different conditions. During the period that the twins are merely moving in relation to each other (neither is accelerating) they are essentially experiencing the same conditions. I guess this saying that a single object can’t have velocity and that velocity is the "common" speed at which two objects move toward or away from each other. To attribute velocity to a single object is to say that another is stationary. No object is truly stationary

This is all said with reference to my signature below.
 
ynot said:
It seems you are saying that both twins would say to each other “You have aged less than me”.
Click to expand...
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):

Twin_paradox_Minkowski_diagram.png


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.
 
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ynot said:
Yes, I can understand it from just one frame, but two frames always exist. In the twins paradox we start with one frame (twins together) that changes to two frames (twins moving apart then together), then back to one frame (twins back together).
Click to expand...

No. There are at least 3 frames involved: the earthbound twin's frame, the traveling twin's outbound frame, and the traveling twin's inbound frame. You cannot treat the outbound and inbound frames as being the same. They are not.

The comparison of ages is made by both twins when they are back together in a single frame. If we just consider velocity and not acceleration, I still can’t see why the velocity is not equal and opposite for both twins.
Click to expand...

Well, let's think about that. What happens if we pick a frame moving away from earth such that the earthbound twin and the traveling twin are both moving away in opposite directions at the same speed? Well, it looks symetric then, right? Yes, but ONLY for the first part of the traveling twin's journey. For the second part of the traveling twin's journey, the traveling twin must go FASTER than the earth-bound twin to catch up with him. So his velocity for the second half is greater, his time dilation is greater, and the total journey is not symmetric.

If the ”travelling” twin ages less than the “stationary” twin, they should both age less as they are equally “stationary” and “travelling”.
Click to expand...

No. There is no single reference frame in which the traveling twin does not, at some point, go faster than the earthbound twin. No single frame. Please try to understand that statement, because so far you clearly do not, and it's at the heart of the problem. Diagrams may help, but you'll need to wait a while longer (probably till Sunday) for them.

It seems you are saying that both twins would say to each other “You have aged less than me”.
Click to expand...

That is precisely not what I am saying.
 
ynot said:
The only time I can see that time dilation could take place between the twins is during the period of accelerating of one of the twins from one frame to another.
Click to expand...
Actually there is a lot less time dilation going on during the acceleration phase, because the rocket is slowing down to zero velocity and then speeding up again. When the velocity is zero there's no time dilation at all going on, even though the acceleration may be at it's maximum. The only relevant thing that happens during the acceleration phase is that the meaning of "simultaneous" (from the astronaut twin's point of view) changes from "one of the blue lines" to "one of the red lines". That is, however, extremely relevant.
 
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ynot,

I don't know if this will help:


Code: 
[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.



NOTE:
The reason there is such as thing as time dilation (and length contraction) is that the speed of light is absolute. It was a surprising result that the speed of light is absolute, but, having established that fact, time dilation and length contraction followed logically.
 
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An old Zen master and his student decided to board a colony ship to Sirius. The pamphlet said that the colony ship would travel at about 0.866c, and so the travellers would experience time dilation - there would only be one year of colony ship time for every two years of Earth time.

The colony ship departed. After a year, the student asked a question: "Master, they told us that because of our high velocity, we only experience one year for every two years of Earth time. Is that true?"
"Yes," the master said.
"But, for all I know, we are just standing still in the universe and the Earth is speeding away from us. As I see it, it's the Earth that's moving fast and its time slows down by a factor of two. I say that during the one year since we left, the Earth aged only six months, not two years."
"Correct," the master said.
"I can't understand that. I'm tired of the Zen way, it's full of contradictions. I want to go back to Earth. My girlfriend said she would wait three years for me before she marries someone else. If only six months passed on Earth, I can still make it. I'll just travel back at the same speed, so she'll only have waited for a year by the time I get back."
"Travel back?" the master said with surprise. "We don't travel anywhere. We are just standing still in the universe and the Earth is speeding away from us."
"But that was just a way of looking at it. We're really travelling, aren't we?"
"If we're really travelling, then two years have really passed on Earth, not six months. - If six months have passed on Earth, then we're standing still and the Earth is speeding away from us."
"Oh, have it your way. We're standing still and the Earth is moving away. I'll just take a personal shuttle and catch up with it."
"The Earth is moving away at 0.866c," the Zen master said. "It will be difficult to catch up with something moving away so fast. You cannot travel faster than light."
"I'll go as fast as I can. I'll travel at 0.99c."
"Even if you travel that fast, it will take you seven years to catch up with Earth."
"But travelling that fast, I'll be so time dilated, that it will only be a year to me."
"Correct," the master said. "And how much will the Earth, travelling at 0.866c, age during those seven years?"

At that moment, the student attained enlightement.
 
ynot said:
The only time I can see that time dilation could take place between the twins is during the period of accelerating of one of the twins from one frame to another. During this period the twins are experiencing different conditions. During the period that the twins are merely moving in relation to each other (neither is accelerating) they are essentially experiencing the same conditions.
Click to expand...


You seem to think that there really is some sort of global, absolute time, except that some clocks, under certain conditions, might run slowly relative to it, in much the same way as a clock will run slowly if you lengthen its pendulum or weaken its spring.

That's not how relativity works.

The whole idea of time is much less "real" in relativity.

When the twins meet again, one is older than the other. That much is real. But you can't point to a particular time and say, "this is absolutely when time dilation happened". In relativity, different observers generally disagree about when things happen. Which means that none of them should be taken too seriously.

Different observers, here, can disagree about whether a thing has happened yet, there, because it doesn't matter anyway: even if the distant happening has "already happened", it can't affect anyone here until later, after light from there has had a chance to reach here.

When the twins meet, one is older. What difference does it make "when" he got older? What would that even mean? Neither twin ever felt themselves aging oddly. On what basis could either say, "now I'm aging normally" or "now I'm aging quickly" or "now I'm aging slowly"?
 
Thabiguy,

That's actually quite good.
I think ynot can't help but be enlightened.
We'll see.

BJ
 
BillyJoe said:
ynot,

I don't know if this will help:


Code: 
[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.



NOTE:
The reason there is such as thing as time dilation (and length contraction) is that the speed of light is absolute. It was a surprising result that the speed of light is absolute, but, having established that fact, time dilation and length contraction followed logically.
Click to expand...
A universal rest frame doesn’t exist so one shouldn’t be applied. c is only travelling faster than b toward an imaginary rest frame that doesn‘t exist. Remove the rest frame (it didn’t exist anyway) and what you have is three objects that are moving relative to each other. The only speed that can be attributed is the speed at which the objects are moving relative to each other (relative speed). Speed cannot be attributed to a single object. The relative speed of a and b is slower than the relative speed of a and c. In other words, c is travelling faster relative to a than b is. This doesn’t mean however that c is universally travelling faster than b. The relative speed of b and c is not the speed of either b or c.

There is of course an infinitely small period when objects are passing and have no relative speed.

Not sure if the terminology I have used is correct. Rather than say “relative speed“ I would prefer to say some thing like “differential speed“.
 
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BillyJoe said:
Thabiguy,

That's actually quite good.
I think ynot can't help but be enlightened.
We'll see.

BJ
Click to expand...
I SEE THE LIGHT!!! . . . But what’s light got to do with it?

And God said “Let there be light. Let the light travel only at c, and let nothing travel faster.“ (or was that Einstein :-).

Time seems to have something to do with the speed/pace/rate of change, and change occurs due to movement. I guess I can see that light might have something to do with time. Unfortunately time is my enemy right now. I think it might help to have a definition of what time is.
 
polaristutoring@tisc said:
If we 'observe' a star in a far-off galaxy.....14,000 lya, moving at say 0.6c relative to us, then shouldn't its stars be younger?:confused:

If it all started from a single point, the BB, then after so long of being accelerated + high vel., shouldn't we look at far off galaxies and see all young stars?
Click to expand...
I believe several people have already explained that is exactly what we see. Distant galaxies have younger stars.

What does "Lya" stand for? I would point out that 14,000 light years is not all the far. Our galaxy is 100,000 light years across. Nothing in our own galaxy is moving at .6c (other than cosmic rays). You've got to go a long way away to find galaxies receding from us at .6c.
 
ynot,

I think you are determined not to understand this. :mad:


:D


But seriously, where did I call o the universal rest frame?
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.


The only speed that can be attributed is the speed at which the objects are moving relative to each other. Speed cannot be attributed to a single object.
Click to expand...


No problem. Lets just call o an object. The other three objects in the illustration are moving relative to that object.

The relative speed of a and b is slower than the relative speed of a and c. In other words, c is travelling faster relative to a than b is. This doesn’t mean however that c is universally travelling faster than b. The relative speed of b and c is not the speed of either b or c.
Click to expand...


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?

There is of course an infinitely small period when objects are passing and have no relative speed.
Click to expand...


Think about it bit and see if you can understand that your above statement is incorrect. The relative motion does not stop even for a vanishingly, infinitesimally small nanosecond as the objects are passing.
 
ynot said:
I SEE THE LIGHT!!! . . . But what’s light got to do with it?
Click to expand...


I suppose you have grasped what physicists mean when they say that the speed of light is absolute:

Code: 
-> -> -> -> -> light -> -> -> -> -> -> -> -> -> -> -> -> ->                   
  A                        B                         C

A beam of light is travelling past A, B, and C.
A, B, and C are at rest relative to each other.

The speed of light in A's frame of reference is c.
The speed of light in B's frame of reference is c.
The speed of light in c's frame of reference is c.

That's pretty straight forward.

Code: 
-> -> -> -> -> light -> -> -> -> -> -> -> -> -> -> -> -> ->                   
  A                       B                         C
  >                                                 <

In the frame of reference of B, A and C are moving according to the arrows.
Let's have them moving at the speed of .8c

The speed of light in A's frame of reference is c.
The speed of light in B's frame of reference is c.
The speed of light in C's frame of reference is c.

As I said before, this is a surprising result but it has been experimentally confirmed and there is no room for doubt: the speed of light is absolute, meaning it's the same value (c) in all frames of reference, no matter how they are moving relative to each other. Time dilation and space contraction are a consequence of the fact that the speed of light is absolute. And to repeat what has been said before, time dilation has also been confirmed experimentally.
 
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BillyJoe said:
ynot,

I think you are determined not to understand this. :mad:


:D
Click to expand...

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

BillyJoe said:
But seriously, where did I call o the universal rest frame?
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.
No problem. Lets just call o an object. The other three objects in the illustration are moving relative to that object.
Click to expand...

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.

BillyJoe said:
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?
Click to expand...
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?



BillyJoe said:
Think about it bit and see if you can understand that your above statement is incorrect. The relative motion does not stop even for a vanishingly, infinitesimally small nanosecond as the objects are passing.
Click to expand...
That‘s why I said “infinitely small“. I’ve often wondered whether existence can ever be defined as an “actual instance” in which there is no movement. But you‘re right, I shouldn‘t have added it in to the mix.
 
BillyJoe said:
ynot,

I don't know if this will help:


Code: 
[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.



NOTE:
The reason there is such as thing as time dilation (and length contraction) is that the speed of light is absolute. It was a surprising result that the speed of light is absolute, but, having established that fact, time dilation and length contraction followed logically.
Click to expand...

Actually, ynot has a point here. You can't just say that the reason c's clock shows less time elapsed when b and c meet is because c's velocity is greater than b's. In a different inertial reference frame, b could be faster. For instance, here's the scenario from c's reference frame:

Code: 
        a               b                            c                                         
        >               >                            |                                         
 

                                ab                   c
                                >>                   |
 
 
                                          b         ac
                                          >         >|
 
 
                                                    bc
                                                    >|

It's not that b's clock is moving faster than c's, it's that the total distance traveled by a's clock from ab to ac, plus c's clock's from ac to bc, is greater than b's clock going directly from ab to bc. So the ab to ac and ac to bc legs of the trip must, taken together, be faster.

In the reference frame in which c is stationary, b is moving faster than c, but there will still be less time on c's clock when b and c meet because a is faster still. A's clock will therefore count less time during the ab to ac segment.

In any reference frame, ab, ac, and bc form a triangle, and b's clock goes directly from ab to bc along one side of the triangle, while the other clocks go from ab to ac to bc along the other two sides of the triangle. Regardless of the reference frame, two sides of a triangle will be a greater distance travelled than the third side, between the same two events ab to bc. Therefore c's clock will be behind b's when they meet, and that prediction is consistent in whatever intertial reference frame you choose to examine it in.

Respectfully,
Myriad
 
ynot said:
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.
Click to expand...
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.

ynot said:
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.
Click to expand...
So? You can think of that "o" as a feather in space if you'd like.
 
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And guys...how about using mspaint or something like that to draw space-time diagrams instead of doing them in ASCII? It's not like it's difficult.
 
Fredrik said:
And guys...how about using mspaint or something like that to draw space-time diagrams instead of doing them in ASCII? It's not like it's difficult.
Click to expand...


Humbug. You don't appreciate how much of a luxury it is even to have ASCII diagrams. When I was in school we had to tap out our space-time diagrams in Morse code on the walls of our dormitory cells.

Respectfully,
Myriad
 
ynot said:
... 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. ...
Click to expand...

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.

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.
 
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