Absolute motion's point of reference

[Dale]

My question is that it is impossible to happen ny internal forces

Do you mean the force between the buggy and the horse, or do you mean the internal forces holding the buggy together or the internal forces holding the horse together?

What is wrong with the internal forces in the case of a backwards moving horse and buggy? Can you draw a free body diagram or cite some force law that causes the internal forces to have a problem?

Let me be clear. You are suggesting that you are smarter than all of the most brilliant minds on the planet for the last century. You should at least be able to do the things we would expect of a freshman-level undergraduate student such as draw a free-body diagram, cite a force law, and derive an expression for the critical internal force as a function of the velocity. This is a very minimal requirement I am asking here considering the enormity of your claim.

 

[JesseM]

So you say now that objects are not being moved apart by a force internal to the object, but rather by an external force such as the road, water or wind (for ships), and the object itself might actually be moving in the opposite direction.

No, I said nothing about any force applied by the surface the objects are moving on. For example, a car or wagon moving along a road need not be receiving any sideways force from the road--this is the ideal case of rolling without slipping. And we could also just imagine some rockets directly above each horse-and-buggy, not in contact with the surface at all! In the case of the horse-and-buggy moving at constant speed relative to the road (with a forward speed relative to the road that's exactly equal to the backwards speed of the road in the frame of the ether, so this horse-and-buggy is at rest in the ether frame), the rocket above it has its rockets off, so it's not accelerating and is at rest relative to the ether too. Meanwhile, the other horse-and-buggy starts out at rest relative to the road (and is therefore moving backwards relative to the ether), then the horse starts accelerating relative to the road until this horse-and-buggy is moving forward in the ether frame; similarly, we can imagine the rocket above it initially has its engines off and is just coasting backwards at the same speed relative to the ether as the horse-and-buggy below it, then when this horse starts running forward relative to the road, the rocket turns on its engines and starts accelerating forward relative to the road too, thus moving in exactly the same way as the horse-and-buggy. In neither case is there any need for either of them to rotate in order to change their direction of motion in the ether frame.

(This is similar to what the Greek's thought about the stars and planets rotating every day around the world, that the universe carries them around the world, even though the planets have their own motion).

How is it similar? My example relies only on standard Newtonian physics, it doesn't require any non-Newtonian assumptions like the one that says forces can't act at a distance, or the one that says an object needs constant pushing to travel at constant velocity.

So now let's imagine this with a simple example, A and B are initially together, then A and B are being moved apart by an external force A<------------>B

The road in my example isn't responsible for "moving them apart"--they simply start out with different initial velocities, one initially at rest relative to the ether and one moving backwards relative to the ether. Do you understand that in Newtonian physics an object moving at constant velocity will continue to move at that velocity until some force is applied to it? So if an object is initially moving backwards in the ether frame it will continue to move that way unless some force pushes it forward (decreasing its speed in the backward direction), like the horse's legs pushing against a road or a rocket's engine firing.

this can be true even if A and B are both horse and buggies facing the opposite direction of the motion, (e.g. A faces the right, and B the left).

In my example I was assuming both horse and buggy were facing in the forward direction, it's just that one had an initial velocity in the direction opposite to the one it was facing.

The reason is because of an external force, that's what you explained.

No, there was nothing in my post about an external force.

Now imagine the external force (road, water, wind, or universe) changes its direction and instead of moving apart the objects it reunites them, (without any acceleration or rotation, actually in our example we don't rotation since the horse are anyway facing the direction of unity).
Now WHO of them is younger?

If two objects move apart and come back together symmetrically in any frame (i.e. each one has the same speed at any given time in that frame, though the direction of their motions will be opposite), then they will be the same age when they reunite.

 

[yoelhalb]

If two objects move apart and come back together symmetrically in any frame (i.e. each one has the same speed at any given time in that frame, though the direction of their motions will be opposite), then they will be the same age when they reunite.

Actually according to relativity evry one of them claims to be at rest and the other one moving, so according to A then B's clock is getting slower and according to B then A's clock is getting slower, then who of them will be younger when they reunit?.

 

[yoelhalb]

Do you mean the force between the buggy and the horse, or do you mean the internal forces holding the buggy together or the internal forces holding the horse together?

What is wrong with the internal forces in the case of a backwards moving horse and buggy? Can you draw a free body diagram or cite some force law that causes the internal forces to have a problem?

Let me be clear. You are suggesting that you are smarter than all of the most brilliant minds on the planet for the last century. You should at least be able to do the things we would expect of a freshman-level undergraduate student such as draw a free-body diagram, cite a force law, and derive an expression for the critical internal force as a function of the velocity. This is a very minimal requirement I am asking here considering the enormity of your claim.

All brilliant minds have believed in Aristotle's teachings for thousands of years, and it turned out to be wrong.
And Galileo has not disproved Aristotle with any diagrams or functions, just by putting it to test in real life, and with though experiments.
(Actually what it was found is, that all the brilliant minds never thought that Aristotle can be wrong, even though it was never proved.
Actually had you ever thought that the principle of relativity might be wrong, remember this is evidence based science, on the other hand the principle of relativity can never be proved).
Surely you are right that since there is an established way to present an argument I have to adhere to it, so can you please show me where I can see more on those diagrams.
Thanks.

What I am saying about internal force, I mean the usual force that a horse pulls a buggy with, which is the normal reason for a horse and buggy to be considered moving, and for this motion to change direction it has to rotate, and to speed up it has to accelerate.
Any other reason to the motion of an horse and buggy such as the road moving or the wind or the water (for ships) etc. I call here external, and for this type of motion you can get to speed without any acceleration and you can also move back without any rotation (for example two ships are being moved away by the water and they can also be reunited by the water without any rotation).
And I am asking, in this case who of them will be younger?.

 

[ghwellsjr]

The problem with your examples is that you don't say enough about what is going on.

So that's what this is all about--the Twin Paradox? This is the first time you have suggested that two of your objects come back together. Why didn't you say this in your first post where you mentioned an example?

When two objects (whether they be trains, boats, horses, buggies, clocks, people or anything else) start together and are at the same age (or have the same time on their clocks) and then one or both of them move in any direction at any speed for any distance with any rotations but they eventually come back together (even if it isn't their initial starting point) and they compare their ages (or clocks), there will be one and only one answer as to their ages (or the times on their clocks). This is reality. Now in order for you to tell what they will measure, it doesn't matter whether you analyze the problem using Special Relativity or any other consistent physical theory, you will get the same answer that they get. But you cannot ask us to tell what answer they get unless you tell us how they move. That is the reason why we are not getting anywhere in helping you.

You need to say which object is moving in which direction and for how long, etc, etc, etc. Now there is one special case where you don't have to give any details and that is when only one object accelerates while the other remains in the initial starting condition. In this case the one that accelerated will always be younger than the one that didn't accelerate. And, again, this has nothing to do with Special Relativity. You can analyze the problem the same way people analyzed the problem before Einstein came along and they and you will get the same answer. It's the way the world works.

 

[yoelhalb]

So that's what this is all about--the Twin Paradox? This is the first time you have suggested that two of your objects come back together. Why didn't you say this in your first post where you mentioned an example?

When two objects (whether they be trains, boats, horses, buggies, clocks, people or anything else) start together and are at the same age (or have the same time on their clocks) and then one or both of them move in any direction at any speed for any distance but they eventually come back together (even if it isn't their initial starting point) and they compare their ages (or clocks), there will be one and only one answer as to their ages (or the times on their clocks). This is reality.

Even if they move in uniform motion only?.
So we clearly know who was moving, and with claiming this you actually break the principle of relativity.

 

[JesseM]

If two objects move apart and come back together symmetrically in any frame (i.e. each one has the same speed at any given time in that frame, though the direction of their motions will be opposite), then they will be the same age when they reunite.

Actually according to relativity evry one of them claims to be at rest and the other one moving, so according to A then B's clock is getting slower and according to B then A's clock is getting slower, then who of them will be younger when they reunit?.

I should have written:

If two objects move apart and come back together symmetrically in any inertial frame (i.e. each one has the same speed at any given time in that frame, though the direction of their motions will be opposite), then they will be the same age when they reunite.

The SR law of time dilation, which says that clocks with a greater velocity in some frame run slower in that frame, only applies in inertial frames. In non-inertial frames, a clock with a greater coordinate velocity may sometimes run faster than a clock with a lesser coordinate velocity, you can't count on time dilation obeying the same rules in a non-inertial frame (but again, if you know the coordinate transformation from an inertial frame to the non-inertial frame, you can always deduce how laws of physics like time dilation work in the non-inertial frame by applying the coordinate transformation to the known equations expressing these laws in the inertial frame). Since A and B must accelerate in order to move apart and come back together, then although it is possible to define non-inertial rest frames for each one, there is no reason for each one of them to predict that the other one's clock must have elapsed less time.

Now that that's cleared up, are you going to address any of my other points in post #92? Do you finally see how it's true in classical Newtonian mechanics as well as relativity that objects can change their direction of motion without rotating or changing the direction that force is being applied to them, or are you still confused on this point?

 

[ghwellsjr]

What do you mean, "even if they move in uniform motion only?" Uniform motion means nonaccelerating. If they were both in uniform motion, say, two passengers on the same moving train, sitting next to each other, they would age at the same rate. But if one of them got up and went to the bathroom and came back and sat down while the other one remained seated, the one that went to the bathroom would be younger.

And like I say, this has nothing to do with Special Relativity. You can analyze this same problem using any theory of physics that works. They will all get the same answer. If you don't like the answer, you need to complain to Mother Nature, not to Einstein. He isn't making the results come true, he is only offering the simplest way to analyze Mother Nature.

If you don't like relativity, what other theory of physics would you like to propose to analyze your problems?

 

[JesseM]

What I am saying about internal force, I mean the usual force that a horse pulls a buggy with, which is the normal reason for a horse and buggy to be considered moving, and for this motion to change direction it has to rotate, and to speed up it has to accelerate.

But I already showed you this was wrong. You complained that in my example the road was itself applying a force, but this is always true of a horse and buggy, the horse can only move forward because of a sideways friction force applied to the horse's hooves by the road (a horse on a totally frictionless surface, like the smoothest ice imaginable, would be unable to change the motion of its center of mass--if its center of mass was originally at rest relative to the frictionless surface, then the horse would be unable to start moving forward relative to the frictionless surface by walking or running). No purely "internal" forces can cause a horse and buggy to change velocity. If you don't like examples where some "external" surface is applying a force, why not instead consider a buggy pulled along by a rocketship whose nose is pointing away from the buggy and whose exhaust nozzle is facing back towards the buggy? The rocket, unlike the horse, can provide a forward pull on the buggy without the need for any other object to apply a force on it, the rocket accelerates forward by accelerating its exhaust in the opposite direction. Clearly unless this rocket is rotated relative to the buggy, the rocket can only apply a forward force to the buggy, never a backward one, but nevertheless if the buggy starts out moving inertially backwards in the frame of the ether before the rocket is activated, then after the rocket starts thrusting it can change direction relative to the ether without any change in the orientation of the rocket.

 

[yoelhalb]

I should have written:

The SR law of time dilation, which says that clocks with a greater velocity in some frame run slower in that frame, only applies in inertial frames. In non-inertial frames, a clock with a greater coordinate velocity may sometimes run faster than a clock with a lesser coordinate velocity, you can't count on time dilation obeying the same rules in a non-inertial frame (but again, if you know the coordinate transformation from an inertial frame to the non-inertial frame, you can always deduce how laws of physics like time dilation work in the non-inertial frame by applying the coordinate transformation to the known equations expressing these laws in the inertial frame). Since A and B must accelerate in order to move apart and come back together, then although it is possible to define non-inertial rest frames for each one, there is no reason for each one of them to predict that the other one's clock must have elapsed less time.

Now that that's cleared up, are you going to address any of my other points in post #92? Do you finally see how it's true in classical Newtonian mechanics as well as relativity that objects can change their direction of motion without rotating or changing the direction that force is being applied to them, or are you still confused on this point?

Who says they must accelerate?.
Isn't it possible that a strong wind took one ship (for example) at a steady velocity?.
Imagine two ships in water, they meet and then they move apart, there needs to be no acceleration involved.
And what in case when both accelerated first?.
And even if only one of them accelerated for 10 minutes and then traveled for 100 years, who is then younger?.

 

[yoelhalb]

What do you mean, "even if they move in uniform motion only?" Uniform motion means nonaccelerating. If they were both in uniform motion, say, two passengers on the same moving train, sitting next to each other, they would age at the same rate. But if one of them got up and went to the bathroom and came back and sat down while the other one remained seated, the one that went to the bathroom would be younger.

And like I say, this has nothing to do with Special Relativity. You can analyze this same problem using any theory of physics that works. They will all get the same answer. If you don't like the answer, you need to complain to Mother Nature, not to Einstein. He isn't making the results come true, he is only offering the simplest way to analyze Mother Nature.

If you don't like relativity, what other theory of physics would you like to propose to analyze your problems?

Imagine two trains are moving in opposite directions coming from different locations, then they meet together, and continue their motion, this does not need any acceleration, and according to relativity every one might claim resting (but not according to regular physics in which you would find a reference to the some absolute point).
So every one claims to be at rest and the other trains clock to slow down.
Now the train who was moving backs up and they reunite, who of them is younger?.

 

[yoelhalb]

What do you mean, "even if they move in uniform motion only?" Uniform motion means nonaccelerating. If they were both in uniform motion, say, two passengers on the same moving train, sitting next to each other, they would age at the same rate. But if one of them got up and went to the bathroom and came back and sat down while the other one remained seated, the one that went to the bathroom would be younger.

And like I say, this has nothing to do with Special Relativity. You can analyze this same problem using any theory of physics that works. They will all get the same answer. If you don't like the answer, you need to complain to Mother Nature, not to Einstein. He isn't making the results come true, he is only offering the simplest way to anaylize Mother Nature.

If you don't like relativity, what other theory of physics would you like to propose to analyze your problems?

Let's put it different, is it possible for to have two people in linear motion without any acceleration or no?.
If no then we don't need relativity, since we always know who is moving.
If yes then in this situation when they reunite who is younger?.

 

[JesseM]

Who says they must accelerate?.
Isn't it possible that a strong wind took one ship (for example) at a steady velocity?.
Imagine two ships in water, they meet and then they move apart, there needs to be no acceleration involved.

Now you're changing the scenario! Before you said they moved apart and then reunited again:

So now let's imagine this with a simple example, A and B are initially together, then A and B are being moved apart by an external force A<------------>B
this can be true even if A and B are both horse and buggies facing the opposite direction of the motion, (e.g. A faces the right, and B the left).
The reason is because of an external force, that's what you explained.
Now imagine the external force (road, water, wind, or universe) changes its direction and instead of moving apart the objects it reunites them, (without any acceleration or rotation, actually in our example we don't rotation since the horse are anyway facing the direction of unity).
Now WHO of them is younger?

If two objects just move apart at constant speed, they can never meet at the same location to compare clocks, so there is no frame-independent truth about which one is older, because of the relativity of simultaneity. If you and I are both 20 when we meet and then we move apart inertially at 0.6c, then in my rest frame the event of my turning 40 is simultaneous with the event of your turning 36, but in your rest frame the event of my turning 40 is simultaneous with the event of you turning 45, so our two frames disagree on which of us has aged more at the moment I turn 40.

 

[yoelhalb]

Now you're changing the scenario! Before you said they moved apart and then reunited again:

If two objects just move apart at constant speed, they can never meet at the same location to compare clocks, so there is no frame-independent truth about which one is older, because of the relativity of simultaneity. If you and I are both 20 when we meet and then we move apart inertially at 0.6c, then in my rest frame the event of my turning 40 is simultaneous with the event of your turning 36, but in your rest frame the event of my turning 40 is simultaneous with the event of you turning 45, so our two frames disagree on which of us has aged more at the moment I turn 40.

I have not changed the story, the ships can be brought back together without acceleration or rotation, just be the wind or the water.
Anyway if the universe is round as Einstein proposed and we can come back to where we started, then who will be younger.
Anyway only one of them can be younger at a given time, and even if we don't have to know which one of them is younger there is only one who is younger.

 

[JesseM]

I have not changed the story, the ships can be brought back together without acceleration or rotation, just be the wind or the water.

Once again you seem not to understand the basic meaning of "acceleration"! Any change in speed or direction is acceleration, it doesn't matter whether the reason for this change in direction is something "internal" like firing a rocket or "external" like the wind or water applying a force on the object.

Anyway if the universe is round as Einstein proposed and we can come back to where we started, then who will be younger.

In this case spacetime is curved so no coordinate system covering each object's entire path can qualify as "inertial", and again there is no requirement that time dilation work the same way in a non-inertial frame. So even if you define a non-inertial coordinate system where object A is at rest throughout the journey while object B moves away and then returns, there's no reason to predict that B ages more slowly throughout the journey in this non-inertial coordinate system, it's only in inertial coordinate systems that objects in motion always age more slowly than objects at rest.

Anyway only one of them can be younger at a given time, and even if we don't have to know which one of them is younger there is only one who is younger.

If they're far apart there doesn't have to be any frame-independent truth about which is younger. Again, in relativity there is no frame-independent notion of a "given time", different frames have different definitions of which sets of events occur at the "same time" and which occur at "different times" (i.e. whether a given pair of events are assigned the same time-coordinate or different time-coordinates), so two events that happened at the same time in one frame can have happened at different times in another frame (unless both events happened at both the same place and the same time in one frame, in which case all frames agree the events happened at the same place and time). Did you look at the link I gave you on the "relativity of simultaneity"? Here is another one: http://www.pitt.edu/~jdnorton/Goodies/rel_of_sim/index.html

 

[yoelhalb]

Once again you seem not to understand the basic meaning of "acceleration"! Any change in speed or direction is acceleration, it doesn't matter whether the reason for this change in direction is something "internal" like firing a rocket or "external" like the wind or water applying a force on the object.

What I called here acceleration I mean experiencing g-force.
Here nobody will encounter any g-force and both of them will claim rest, so again when they are reunited who is younger?.

In this case spacetime is curved so no coordinate system covering each object's entire path can qualify as "inertial", and again there is no requirement that time dilation work the same way in a non-inertial frame. So even if you define a non-inertial coordinate system where object A is at rest throughout the journey while object B moves away and then returns, there's no reason to predict that B ages more slowly throughout the journey in this non-inertial coordinate system, it's only in inertial coordinate systems that objects in motion always age more slowly than objects at rest.

So you actually claim that when Einstein proposed that the universe is round then he disregarded special relativity entirely.
Actually even if we will claim the universe to be flat, still there can never be a true inertial frame of reference, since any two objects always exert some gravity on each other.
What do you say to that?.
So all the brilliant minds on the planet for the last 100 years had dealt with something that can't exist.

If they're far apart there doesn't have to be any frame-independent truth about which is younger. Again, in relativity there is no frame-independent notion of a "given time", different frames have different definitions of which sets of events occur at the "same time" and which occur at "different times" (i.e. whether a given pair of events are assigned the same time-coordinate or different time-coordinates), so two events that happened at the same time in one frame can have happened at different times in another frame (unless both events happened at both the same place and the same time in one frame, in which case all frames agree the events happened at the same place and time). Did you look at the link I gave you on the "relativity of simultaneity"? Here is another one: http://www.pitt.edu/~jdnorton/Goodies/rel_of_sim/index.html

It is clear to all of us that if the twin are meeting together then there is only one who is younger, even though they may use different space time coordinates.
Now let's imagine we are putting a sheet of paper between the twin, still only one of them is younger.
Now let us make tichker the paper till it is getting a wall, still only one of them is younger.
So let us make it thicker and thicker till it spans many light years, is there any point when we can start claiming that it can be possible that both are younger?
To illustrate that even further, let's instead of paper and a wall fill the gap with people, on which two persons can we claim that he and his immediate neighbor are both younger?.
Since there is no such thing, we can't claim it on any persons in the universe.

 

[JesseM]

What I called here acceleration I mean experiencing g-force.
Here nobody will encounter any g-force and both of them will claim rest, so again when they are reunited who is younger?.

Yes, anytime you change speed or direction you experience a G-force, regardless of the cause. You really should try to learn basic Newtonian physics before you try to challenge relativity!

So you actually claim that when Einstein proposed that the universe is round then he disregarded special relativity entirely.

This proposal was made in the context of his theory of "general relativity" in which spacetime is curved, not special relativity where spacetime is flat. However, according to the equivalence principle we can still say that the laws of special relativity still work "locally" in an arbitrarily small region of curved spacetime, you can define a "locally inertial frame" in such a small region.

Actually even if we will claim the universe to be flat there can never be a true inertial frame of reference, since any teo objects always exert some gravity on each other.
What do you say to that?.
So all the brilliant minds on the planet for the last 100 years had dealt with something that can't exist.

In physics successful theories are rarely shown to be completely wrong, instead they are usually shown to be a limiting case of some more accurate theory (do you understand the calculus notion of a limit?) For example, Newtonian physics is still very useful in many scenarios, and it's possible to show that it is a very accurate approximation to both special relativity and general relativity in the appropriate limits (for example, the relative velocities being very small compared to c). Likewise, as I mentioned above SR can be understood as the limit case of GR as the size of the region of spacetime being considered becomes very small (so 'tidal effects' which depend on curvature become very small as well).

But yes, everyone understands that SR is not the most accurate known theory for calculating elapsed time on various clocks, GR is.

It is clear to all of us that if the twin are meeting together then there is only one who is younger, even though they may use different space time coordinates.

Yes, if we idealize the twins as point particles and suppose they meet at the same precise point of spacetime, then all frames agree on their ages when they meet.

Now let's imagine we are putting a sheet of paper between the twin, still only one of them is younger.

If there is any finite distance between them, then different frames can disagree on the precise difference in their ages, although it may still be the case that all frames agree one is younger (but perhaps one frame will say the younger twin is younger by 457902910335298.3 nanoseconds while another will say the younger twin is younger by 457902910335298.2 nanoseconds)

A geometric analogy may help. Suppose we have two curves on a flat 2D wall which meet at one point P1, move apart, and then meet again at another point P2. If different observers have different definitions of which direction along the wall is "vertical" and which is "horizontal", they may disagree on the vertical and horizontal distances between P1 and P2, but they will all agree on the length of each curve between P1 and P2 (i.e. the distance an ant would measure if he walked along each curve from P1 to P2.

On the other hand, suppose both curves travel through P1 on the wall, but while the first curve also travels through P2, the second curve gets very close to P2 but never actually touches the first curve, after P2 it just remains parallel to the first curve but never quite touches it. And suppose we again imagine different observers with different definitions of which direction on the wall is "vertical" and which is "horizontal" (or what direction the y-axis and x-axis of their cartesian coordinate systems lie, if you prefer), then they will have different answers to the question "what point P3 on the second curve is at exactly the same vertical height as P2 on the first curve"? And so they will also disagree on the question "exactly what is the difference between the distance an ant must travel from P1 to P2 on the first curve and the distance an ant must travel from P1 to P3 (the point at the same vertical height as P2) on the second curve?" If the second curve gets very close to P2 and the different observer' vertical axes are not at too great an angle relative to one another (not more than 90 degrees, say) then the disagreement about ant-travel-distance to get to the same vertical height as P2 may not be too great, but there will still be some small difference.

It's almost exactly the same story in relativity. If you have one pointlike twin whose worldline goes between events E1 and E2, and another twin whose worldline goes through E1 and gets very very close to E2 but never actually crosses the worldline of the first twin again, then different frames disagree about what event E3 on the worldline of the second twin happens "at the same time" as E2 on the worldline of the first twin (i.e. they disagree about what E3 is at the 'same height on the time axis' as E2). And just as all frames in the geometric example agree about the distance along a curve (as traveled by an ant) between any two specific points on that curve, so all frames in relativity agree about the elapsed time on any worldline between any two events on that worldline. So all frames agree how much the first twin ages between E1 and E2, but since "E3" is defined to be the event that occurred at the same time as E2 and different frames disagree about which event this is, they will get different answers to the question "how much does the second twin age between event E1 and E3"? The difference may be slight if the second twin is very close to E2 (say, only a paper-thin separation between them) but it's not zero.

 

[Dale]

Surely you are right that since there is an established way to present an argument I have to adhere to it, so can you please show me where I can see more on those diagrams.

Here is a good place to learn about free-body diagrams:
http://www.physicsclassroom.com/class/newtlaws/u2l2c.cfm#1

If you are not already familiar with them then I would recommend learning Newtonian mechanics before tackling relativity. You need to understand basic concepts like force, energy, acceleration, and velocity before relativity.

What I am saying about internal force, I mean the usual force that a horse pulls a buggy with,

So your concern is indeed the one I identified way back in https://www.physicsforums.com/showpost.php?p=2927641&postcount=73". It would help if you would clarify such things right away; in this case it would have saved more than 30 posts.

Usually a horse pulls a buggy using a rigid rod which is called a tongue, this enables the horse to push the buggy backwards as well as pull it forwards, it also allows the horse to stop which is usually convenient feature once the buggy has reached its destination. However, for the sake of argument, let's suppose that we had a bad buggy designer who replaced the usual rigid tongue with a rope. In such a case the buggy would only function correctly when the tension in the rope is positive. So let's analyze the tension:

In an inertial frame there are three forces acting on the buggy, the normal force, N, the weight, mg, and the tension, T. Assuming that the ground is level N=-mg and therefore the sum of the forces on the buggy is equal to the tension (f=N+mg+T=T). So, by Newton's second law (f=ma) we easily derive T=ma. Note, the tension is NOT a function of the velocity, v, but only of the acceleration, a. Therefore, even with a poorly-designed buggy, as long as the buggy is accelerating in the positive direction there will be positive tension, and it does not matter if the velocity is positive or negative.

Your key point does not hold up to scrutiny. This has nothing to do with relativity, it is basic, first-semester Newtonian mechanics.

 

[ghwellsjr]

Imagine two trains are moving in opposite directions coming from different locations, then they meet together, and continue their motion, this does not need any acceleration, and according to relativity every one might claim resting (but not according to regular physics in which you would find a reference to the some absolute point).
So every one claims to be at rest and the other trains clock to slow down.
Now the train who was moving backs up and they reunite, who of them is younger?.

OK, we have two trains moving towards each other and when they meet, (without stopping or slowing down) an observer in each train starts a stopwatch. Now they "continue their motion" but now they will be moving apart. After some time, one of the trains "backs up and they reunite". At this point, the two observers stop their stopwatches and now the one in the train that backed up is the one with less elapsed time. If the two observers were the same age when they first met, the one in the train that backed up is the one that will be younger when they meet the second time.

This is what actually happens. You can analyze this "according to relativity" or you can analyze it "according to regular physics in which you would find a reference to the some absolute point" or you can actually perform the experiment, you will get the same answer in all three cases, correct?

Now, I want to point out an example of something that is extremely irritating and confusing in all your posts. Look at this phrase:

"according to regular physics in which you would find a reference to the some absolute point"

I don't know what you mean by this because it isn't correct English. I will fix it three possible ways:

1) "according to regular physics in which you would find a reference to some absolute point"

2) "according to regular physics in which you would find a reference to the absolute point"

3) "according to regular physics in which you would find a reference to the same absolute point"

When somebody reads this, it is impossible to know which way you meant it to be or even if you meant it a fourth way. You may be saving a little bit of time by not proof-reading your posts before you post them and by not rereading them and editing them after you post them, but you are wasting everyone else's time when you do this. We're trying to help you understand something that you need help on. Please help us help you by proof-reading and editing your posts to get rid of the incorrect English.

Now I would like to ask you which of the three corrections did you mean or are they all incorrect?

 

[ghwellsjr]

Let's put it different, is it possible for to have two people in linear motion without any acceleration or no?.
If no then we don't need relativity, since we always know who is moving.
If yes then in this situation when they reunite who is younger?.

OK, let's work on the first sentence (correcting the typo):

I think you mean: "Let's put it differently, is it possible to have two people in linear motion without any acceleration?"

To me, when someone says that a person is in linear motion, I think that means the person is traveling in a straight line at a constant speed. This means no acceleration. But, I don't know, maybe you mean this person is traveling in a straight line at a varying speed. That would mean there was acceleration. But now you want to ask about two people in linear motion. I'm wondering, what does he mean? Does he mean they are traveling together in a straight line, with or without acceleration? Or does he mean they are traveling in the same straight line but one is in front of the other one and maybe he means they are traveling at the same constant speed or maybe he means one of them is changing his speed while the other is at a constant speed or maybe they're both changing their speeds? Or does he mean they are traveling in the same straight line but they are going in opposite directions coming towards each other or maybe they are traveling in the same straight line but going away from each other, and again, maybe one of them maintains a constant speed or maybe both of them are maintaining a constant speed? Maybe one of them reverses direction. Maybe both of them reverse direction. Or does he mean that they are both on different straight lines going at an angle to each other, etc, etc, etc, etc? It never ends, I don't know what you are asking but I think the answer could be either yes or no.

OK, now let's work on the second sentence:

"If no then we don't need relativity, since we always know who is moving."

I'm trying really hard to understand why you would make this statement in response to a "no" answer to the first question. Why would no acceleration mean that you know which of the two people is moving? This could only make sense if one of the people was not moving, but you said that we had two people in motion. I have absolutely no idea what you are thinking of here. Beyond that, I don't understand why you think that knowing who is moving draws you to the conclusion that you don't need relativity. You don't need relativity in any situation. You can analyze any problem with the concept of an absolute reference frame if you want to. I just don't follow your thought process here.

Now for the last sentence:

"If yes then in this situation when they reunite who is younger?"

Now this question has a lot of assumptions that should have been stated earlier before anyone can possibly answer this question. The word "reunite" means that they were at one time united and then they separated by some undefined process and then they came back together by another undefined process. And no one can answer the question about who is younger until and unless you specify their ages at the time they were first united. Maybe you think it is obvious that they were the same age but unless you specifically say so, there is no way to answer this question. There is also no way to answer this question until you specify how the two people move from the first time they are united until they reunite.

The fact that you persist in asking these ill-formed questions over and over again means either that you are too lazy to ask a coherent question or your present understanding of physics is so limited that you don't know that your questions don't make any sense. So which is it: are you lazy or are you ignorant or is there another explanation I haven't considered?

 

[Passionflower]

Imagine two trains are moving in opposite directions coming from different locations, then they meet together, and continue their motion, this does not need any acceleration, and according to relativity every one might claim resting (but not according to regular physics in which you would find a reference to the some absolute point).

Regular physics? So you think relativity is not regular physics?

I wonder what your point is yoelhalb? Are you questioning the validity of relativity or do you try to understand it? If it is the former you are wasting everybody's time.

 

[yoelhalb]

Yes, anytime you change speed or direction you experience a G-force, regardless of the cause. You really should try to learn basic Newtonian physics before you try to challenge relativity!

Again my story is when there is sudden change such as the wind carries along the ship in which case the slope of the velocity will always be 0 and accordingly the g-force formula gives that the g-force will be 0.
(Yet I have no way of writing such velocity as a function, the only thing I would see on a graph is, that the slope will always be 0, but maybe you have a way to get the acceleration, if so then please let me know)

But anyway isn't it possible that both are encountering g-force?.
Let's take an example, two twins A and B, A takes of with a rocket while in the same time B accelerates in its car on a road to his house, later the rocket turns around but in the same time his brother on Earth also made a u-turn, now when they reunite who is younger?.
(here both are claiming that the other one has moved and that he did only local acceleration or rotation, if you are for example now rotating on your axis do you start traveling?).

Want another example for the twin paradox (without any acceleration or rotation), here it is.
Suppose A and B and C are already in uniform motion, A is traveling to the left direction according to B's perspective on a rate of 100 m/s, and A claims that B moves to the right with a rate of 100 m/s.
Yet initially B sees A coming from the right, and when A passes B they both see that they are exactly the same age.
Then when A is already to the left of B, then we see that C is coming from the left with a linear motion of 200 m/s, (again C claims to be at rest).
Now when C passes A they both see that they are also the same age, C proceeds now to B.
So when C will meet B who will be younger?.

This proposal was made in the context of his theory of "general relativity" in which spacetime is curved, not special relativity where spacetime is flat. However, according to the http://www.einstein-online.info/spotlights/equivalence_principle we can still say that the laws of special relativity still work "locally" in an arbitrarily small region of curved spacetime, you can define a "locally inertial frame" in such a small region.

In physics successful theories are rarely shown to be completely wrong, instead they are usually shown to be a limiting case of some more accurate theory (do you understand the calculus notion of a limit?) For example, Newtonian physics is still very useful in many scenarios, and it's possible to show that it is a very accurate approximation to both special relativity and general relativity in the appropriate limits (for example, the relative velocities being very small compared to c). Likewise, as I mentioned above SR can be understood as the limit case of GR as the size of the region of spacetime being considered becomes very small (so 'tidal effects' which depend on curvature become very small as well).

But yes, everyone understands that SR is not the most accurate known theory for calculating elapsed time on various clocks, GR is.

So if it is possible to make an inertial frame on a small scale when the affects of the curve will be small, don't you think that the same can be said on a curve as big as the entire universe?.
And what if the universe expands to trillion times larger?, would not be the curve and the g-force getting even smaller?.
So there must be some size that when the universe will become that size, then we should be able to claim that both of them are in inertial frame of reference, now in this case when they will reunite who of them will be younger?.
(Actually according to Galileo and his ship, even the curve of Earth is small enough that a moving object should be able to claim rest).

Yes, if we idealize the twins as point particles and suppose they meet at the same precise point of spacetime, then all frames agree on their ages when they meet.

If there is any finite distance between them, then different frames can disagree on the precise difference in their ages, although it may still be the case that all frames agree one is younger (but perhaps one frame will say the younger twin is younger by 457902910335298.3 nanoseconds while another will say the younger twin is younger by 457902910335298.2 nanoseconds)

A geometric analogy may help. Suppose we have two curves on a flat 2D wall which meet at one point P1, move apart, and then meet again at another point P2. If different observers have different definitions of which direction along the wall is "vertical" and which is "horizontal", they may disagree on the vertical and horizontal distances between P1 and P2, but they will all agree on the length of each curve between P1 and P2 (i.e. the distance an ant would measure if he walked along each curve from P1 to P2.

On the other hand, suppose both curves travel through P1 on the wall, but while the first curve also travels through P2, the second curve gets very close to P2 but never actually touches the first curve, after P2 it just remains parallel to the first curve but never quite touches it. And suppose we again imagine different observers with different definitions of which direction on the wall is "vertical" and which is "horizontal" (or what direction the y-axis and x-axis of their cartesian coordinate systems lie, if you prefer), then they will have different answers to the question "what point P3 on the second curve is at exactly the same vertical height as P2 on the first curve"? And so they will also disagree on the question "exactly what is the difference between the distance an ant must travel from P1 to P2 on the first curve and the distance an ant must travel from P1 to P3 (the point at the same vertical height as P2) on the second curve?" If the second curve gets very close to P2 and the different observer' vertical axes are not at too great an angle relative to one another (not more than 90 degrees, say) then the disagreement about ant-travel-distance to get to the same vertical height as P2 may not be too great, but there will still be some small difference.

It's almost exactly the same story in relativity. If you have one pointlike twin whose worldline goes between events E1 and E2, and another twin whose worldline goes through E1 and gets very very close to E2 but never actually crosses the worldline of the first twin again, then different frames disagree about what event E3 on the worldline of the second twin happens "at the same time" as E2 on the worldline of the first twin (i.e. they disagree about what E3 is at the 'same height on the time axis' as E2). And just as all frames in the geometric example agree about the distance along a curve (as traveled by an ant) between any two specific points on that curve, so all frames in relativity agree about the elapsed time on any worldline between any two events on that worldline. So all frames agree how much the first twin ages between E1 and E2, but since "E3" is defined to be the event that occurred at the same time as E2 and different frames disagree about which event this is, they will get different answers to the question "how much does the second twin age between event E1 and E3"? The difference may be slight if the second twin is very close to E2 (say, only a paper-thin separation between them) but it's not zero.

Again how can you say that both can be younger, if A < B then it cannot be that B < A.
and you can also not claim that since their clocks are differenet they can both claim younger, as this is like two people on different timezones claiming that both can be younger, or like saying that twin here in our example can both claim each other to be dead, or to say that we can claim that both are on the left side of each other.
And you can also not claim anyone of them to be in the past since "past" means what is no longer there.

But if you want proof, I will do the proof again (and show that thiw is not answered by your claim).
Imagine we fill the gap with people, since all the people claim each other resting there clocks must be synchronized.
To prove this even farther we can have someone accelrating over the entire length of the row of people, since all people will claim to accelrate with the same rate so they know exactly how muce his clock got slower, so they now have proof that their clcoks are synchronized.
since this can be extanded to any length, there is clearly no such claim that two people can be younger at the same time.

And this is actually my answer to the relativity of simultaneous.
Einstein had never prooved that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
What he had proved is, That what it APPEARS to be simultaneous in one frame, does not have to APPEAR simultaneous in another frame, and this we know without him.
But Einstein's claim that since both frames are equely valid according to relativity, then it follows that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
However I am just wondering on that, even if there would be no proof against relativity, it is still just a logical hypotesis, so why had Einstein choosen the more paradoxial relativity over the more straightforward hypotesis that simultaneous event are simultaneous every where?.

 

[Dale]

Again how can you say that both can be younger, if A < B then it cannot be that B < A.

That is not what we are saying. We are saying that if A<B then it is still possible that B'<A'. A is not the same as A' and B is not the same as B'

Einstein had never prooved that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
What he had proved is, That what it APPEARS to be simultaneous in one frame, does not have to APPEAR simultaneous in another frame, and this we know without him.

No, this is a basic misunderstanding of SR that is, unfortunately, fostered by the whole "thought experiment" approach to teaching SR. The SR effects of time dilation, length contraction, and relativity of simultaneity are NOT "appearances" or "optical illusions" due to the finite speed of light. They are what remains after correctly accounting for the finite speed of light and removing that confounding effect.

 

[yoelhalb]

That is not what we are saying. We are saying that if A<B then it is still possible that B'<A'. A is not the same as A' and B is not the same as B', so the .

Again so two people in different timezones on Earth can claim to be younger?.
Had you seen my proof?, (actually the post you are referring to has more proof in the beginning of it).

No, this is a basic misunderstanding of SR that is, unfortunately, fostered by the whole "thought experiment" approach to teaching SR. The SR effects of time dilation, length contraction, and relativity of simultaneity are NOT "appearances" or "optical illusions" due to the finite speed of light. They are what remains after correctly accounting for the finite speed of light and removing that confounding effect.

Again what I say is that it is based on the claim that the principle of relativity must be true.
(Now read again my question at the end of the post).

 

[LBrandt]

I have been following this thread, and I'm totally lost. Can someone (other than Yoelhalb) state briefly what Yoelhalb contends or what he is asking?

 

[Dale]

Again so two people in different timezones on Earth can claim to be younger?.

Yes, if they are also going at different velocities.

Again what I say is that it is based on the claim that the principle of relativity must be true.

Which is thus far supported by the evidence: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

Btw, I am curious to read your reply to the horse and buggy analysis and see what new folly you will introduce.

 

[ghwellsjr]

Let's take an example, two twins A and B, A takes of with a rocket while in the same time B accelerates in its car on a road to his house, later the rocket turns around but in the same time his brother on Earth also made a u-turn, now when they reunite who is younger?.
(here both are claiming that the other one has moved and that he did only local acceleration or rotation, if you are for example now rotating on your axis do you start traveling?).

Want another example for the twin paradox (without any acceleration or rotation), here it is.
Suppose A and B and C are already in uniform motion, A is traveling to the left direction according to B's perspective on a rate of 100 m/s, and A claims that B moves to the right with a rate of 100 m/s.
Yet initially B sees A coming from the right, and when A passes B they both see that they are exactly the same age.
Then when A is already to the left of B, then we see that C is coming from the left with a linear motion of 200 m/s, (again C claims to be at rest).
Now when C passes A they both see that they are also the same age, C proceeds now to B.
So when C will meet B who will be younger?.

Here you have provided two more ill-formed examples.

I'm going to interpret the first one as I think you mean: Two twins start together in the same place and are the same age. Twin A takes off in a rocket at 1000 kilometers per hour while his brother, Twin B, takes off in his car at 100 kilometers per hour. After a while, they both turn around and travel back toward their starting point at the same speeds. When they meet, Twin A will be younger because he was traveling at a higher speed than his twin during the same intervals of time.

Now the second one is even more ill-formed because you haven't specified the frame in which C is traveling. But it doesn't matter as long as we assume that C is traveling to the right at 200 m/s with respect to either A or B. In either case, C will be younger than B when they meet.

One of your problems is that you keep thinking that it is permissible to analyze part of the situation from the perspective of one observer and another part from the perspective of another observer. You need to specify the situation from one frame of reference, it doesn't matter which one and then analyze the problem from one frame of reference (either the same one or a different one, you will get the same answer, but I always like to take the simplest frame of reference).

For example, in your second example, if we use the frame of reference in which B is at rest, A will be traveling to the left at 100 m/s and we assume that C will be traveling to the right at 200 m/s. So, because B is at rest during the entire time and A and C are traveling, they are the ones that age more slowly and so C ends up younger than B.

If you meant that C was traveling to the right at 200 m/s with respect to A instead of B, we will have to do some calculation to determine C's speed in B's frame of reference but we will still come to the conclusion that C is younger than B because B has been at rest the whole time.

If on the other hand, we use the frame of reference in which A is at rest and B is traveling to the right at 100 m/s and assume now that C is traveling to the right at 200 m/s with respect to A, it will not be as obvious whether C or B is younger when they meet because both of them are traveling. So that is why I prefer to analyze the problem in the frame of reference that is easiest to do the calculations.

By the way, thanks very much for improving you spelling and grammar.

 

[ghwellsjr]

I have been following this thread, and I'm totally lost. Can someone (other than Yoelhalb) state briefly what Yoelhalb contends or what he is asking?

Yoelhalb has a misunderstanding of the theory of Special Relativity. He thinks that it is permissible to look at different parts (observers) of a scenario from different frames of reference at the same time and see contradictions. He thinks that if we assume an absolute reference frame, then all the contradictions will vanish, which is true, but that is exactly the same as using just one frame of reference within Special Relativity. He hasn't yet come to terms with the problem of knowing which absolute reference frame to use. If he will propose one, then I will ask him what happens if we propose a different absolute reference frame that is traveling at some speed with respect to the one he is proposing. Maybe then, the light will come on and he will see that there is no difference between believing that there exists one absolute reference frame and believing in Special Relativity, because we can't know which is the correct absolute reference frame and assuming a different one is exactly the same as using a different reference frame in Special Relativity.

 

[JesseM]

Again my story is when there is sudden change such as the wind carries along the ship in which case the slope of the velocity will always be 0 and accordingly the g-force formula gives that the g-force will be 0.

No, velocity is a vector which has components on all three spatial axes x-y-z, like v = [v_x, v_y, v_z], therefore even if the magnitude of the velocity vector (i.e. the speed, given by \sqrt{v_x^2 + v_y^2 + v_z^2}) stays constant, if there is any change in the direction of the velocity vector (i.e. individual components like v_x are changing even though the total magnitude of \sqrt{v_x^2 + v_y^2 + v_z^2} is constant) that means the acceleration vector (given by a = [dv_x/dt, dv_y/dt, dv_z/dt]) will be nonzero and you will experience G-forces. For example, if you are sitting on the edge of a spinning disc, then even if the disc is spinning at a constant rate so you are traveling in a circle at constant speed, you will still experience a G-force that seems to push in the outward direction, this "fictitious force" (i.e. apparent force experienced by an accelerating observer which is really just due to his own inertia) is known as the centrifugal force. The only way to avoid experiencing G-forces is to travel at constant speed and in a constant direction, i.e. traveling in a straight line forever.

But anyway isn't it possible that both are encountering g-force?.
Let's take an example, two twins A and B, A takes of with a rocket while in the same time B accelerates in its car on a road to his house, later the rocket turns around but in the same time his brother on Earth also made a u-turn, now when they reunite who is younger?.
(here both are claiming that the other one has moved and that he did only local acceleration or rotation, if you are for example now rotating on your axis do you start traveling?).

If both have changing velocity, then if you know each one's speed as a function of time v(t) in some inertial frame, and you know the times t₀ and t₁ when they departed from one another and then reunited, you can calculate how much each one ages between meetings using the integral:

\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt

SR says that if an object is traveling at constant speed v for a time interval of \Delta t, then the object will age by \Delta t \sqrt{1 - v^2/c^2} during that time interval (the time dilation formula), so if you're familiar with the basic idea of integrals in calculus you can see this one is essentially breaking up the path into a bunch of "infinitesimal" time intervals with length dt and calculating the sum of the aging on each one.

Want another example for the twin paradox (without any acceleration or rotation), here it is.
Suppose A and B and C are already in uniform motion, A is traveling to the left direction according to B's perspective on a rate of 100 m/s, and A claims that B moves to the right with a rate of 100 m/s.
Yet initially B sees A coming from the right, and when A passes B they both see that they are exactly the same age.
Then when A is already to the left of B, then we see that C is coming from the left with a linear motion of 200 m/s, (again C claims to be at rest).
Now when C passes A they both see that they are also the same age, C proceeds now to B.
So when C will meet B who will be younger?.

C will be younger. You can derive this in any frame you like (A's frame, B's frame, or C's frame) by taking into account the way the moving clocks are running slower in that frame, and also taking into account the definition of simultaneity in that frame. For example, say that in B's frame, A is moving at 0.6c to the left and C is moving at 0.6c to the right, and A and B's clocks both read 0 when A passes B, and the event of C passing A happens at t=10 years in B's frame (simultaneous with B's own clock reading 10 years), while the event of C passing B happens at t=20 years (simultaneous with B's clock reading 20 years). In this case since A is traveling at 0.6c, in B's frame A's clock is slowed down by a factor of \sqrt{1 - 0.6^2} = 0.8, so at t=10 years A's clock only reads a time of 8 years, and by assumption C's clock also reads 8 years when he passes A at this moment. In B's frame C is moving at the same speed and so his clock is running slow by the same factor of 0.8, so 10 years later when he passes B his clock has only ticked forward by 8 more years, so it reads 8 + 8 = 16 years at that moment. And 10 years before C passed A (at t=0 when A was passing B), C's clock only read 8 years less, i.e. 8 - 8 =0 years, so in this frame the event of A passing B when both their clocks read 0 seconds was simultaneous with C's own clock reading 0 years.

But now if we switch to C's own rest frame, he has a different definition of simultaneity, it's no longer true that C's clock read 0 years simultaneously with A passing B. Instead, in this frame the event of A passing B is simultaneous with C's clock reading -9 years. At this moment in C's frame, A and B are at a distance of 15 light-years from C (I can show how I got these numbers using the Lorentz transformation if you like). And if A is moving at 0.6c to the left in B's frame, and B is moving at 0.6c to the left in C's frame, then using the velocity addition formula A must have a speed of (0.6c + 0.6c)/(1 + 0.6*0.6) = 0.88235c in C's frame. So, starting from 15 light-years away A will take a time of 15/0.88235 = 17 years to reach C in this frame, when C's clock will read -9 + 17 = 8 years. And A's clock started from 0 when A was 15 light-years away, then over the course of those 17 years A's clock was running slow by a factor of \sqrt{1 - 0.88235^2} = 0.4706 in C's frame, so A's clock should read 17*0.4706 = 8 years when A meets C. So you can see that in C's frame we predict that when C passes A, both their clocks read 8 years, same as what we predicted when we used B's frame before. Likewise, in C's frame B's clock started from 0 when B was at a distance of 15 light-years (when C's clock read -9 years), and B is traveling towards C at 0.6c, so B should take a time of 15/0.6 = 25 years to reach C in this frame, meaning C's own clock reads -9 + 25 = 16 years when they meet, and B's clock is running slow by a factor of 0.8 so in these 25 years his clock ticks forward by 25*0.8 = 20 years. So in C's frame we get the prediction that C's clock reads 16 years and B's clock reads 20 years when they meet, exactly the same prediction we got in B's frame.

So if it is possible to make an inertial frame on a small scale when the affects of the curve will be small, don't you think that the same can be said on a curve as big as the entire universe?.

No. Think about an analogy with spatial coordinate systems--just as it's true that a small region of spacetime is approximately like SR, it's true that a small region of the surface of a big sphere looks approximately like a flat 2D plane, so to a good approximation the laws of Euclidean geometry can be expected to hold for shapes and lines drawn on a small patch of a giant sphere. For example, the sum of the angles of a triangle drawn on such a small patch will add up to about 180 degrees. But does that mean that if the sphere is huge enough, then shapes which cover significant regions of the entire sphere will obey the laws of Euclidean geometry? No, for example on any sphere we can draw an equilateral triangle covering up 1/8 of the sphere's surface (1/4 of a hemisphere) such that all three angles are right angles (as seen in a small patch centered on each corner), so the sum of the angles is 90 + 90 + 90 = 270, which is impossible in Euclidean geometry. This page has a diagram:

Other laws of Euclidean geometry break down when you look at shapes and lines covering large proportions of the surface, for example the closest analogue to a "straight line" on a sphere is a great circle (like the equator or a line of longitude on a globe), and you can draw two great circles which are at one point "parallel" to one another in the sense that you can draw another great circle which is "orthogonal" to both, i.e. it meets both at a right angle (like two lines of longitude which are orthogonal to the equator), yet these great circles will later cross (like two lines of longitude crossing at the pole). In Euclidean geometry, if two straight lines are "parallel" in the sense that you can find a third line that's orthogonal to them both, then they can never cross.

And what if the universe expands to trillion times larger?, would not be the curve and the g-force getting even smaller?.

The condition needed for SR to work approximately is not that "g-force" becomes small (even in SR an accelerating observer experiences G-force, and in GR an observer in freefall experiences no G-force), it's that tidal forces become small (the article on the equivalence principle I gave you has an animated diagram at the bottom showing one example of tidal force: the fact that two objects dropped straight 'down' on what seem to be parallel paths will nevertheless get closer together over time). The extent to which tidal forces are measurable depends both on the spatial size of the region you're looking at, and the window of time in which you make your measurements (i.e. the total 'size' of the region of spacetime on which the measurements are made), even with weak curvature the effects are more easily measurable if you expand the spatial or temporal extent of your measurements. As for "what if the universe expands to trillion times larger", that would just mean that if you want to talk about a situation where one twin circumnavigates the entire universe, the size of the spacetime region covering his entire path would have to become about a trillion times larger too. Again think of the analogy with geometry on a sphere--to see departures from Euclidean rules on a patch of the sphere, what matters is not the absolute size of the patch, but rather the proportion of the sphere's entire surface taken up by the patch.

Again how can you say that both can be younger, if A < B then it cannot be that B < A.

But in relativity there is no way to say "A < B" or "B < A" in an absolute way unless you are comparing ages at a single point in spacetime--if you're not, then you can only compare their ages in a frame-dependent way. There is no contradiction between the statement "in B's rest frame, A < B" and the statement "in A's rest frame, B < A", the two frames just define simultaneity differently. Again think of geometry--if we have a wall with two dots A and B on it, and you and I both use chalk to draw a different set of x-y coordinate axes on the wall, with your x-y axes rotated relative to mine, then there is no contradiction in the statement "in my coordinate system, A has a smaller y-coordinate than B" and "in your coordinate system, B has a smaller y-coordinate than A". Well, in relativity time is treated a lot like another spatial direction, one frame can have a time axis rotated relative to the other, so we can say "in frame #1, event A has a smaller t-coordinate than B" and "in frame #2, event B has a smaller t-coordinate than A".

And you can also not claim anyone of them to be in the past since "past" means what is no longer there.

Now you're getting metaphysical! Like I said, relativity treats time much like a spatial dimension, "past" just means "at an earlier time-coordinate", so different frames can disagree about whether an event B lies in the "past" of event A or not. Of course, because of the finite speed of light, judgments about time-coordinates of events off my own worldline can only be made in retrospect anyway--for example, if in 2010 I see the light from an event A at a position 8 light-years away in my frame, and in 2012 I see the light from an event B at a position 10 light-years away in my frame, I can say that in my frame they both happened "simultaneously" in 2002 even though I wasn't aware of them until later. Someone in a different frame who also subtracts the distance in light-years from the time in years when he saw them may conclude that A happened in the past of B, and someone in a third frame may conclude B happened in the past of A, but none of us were aware of them until they were both in our own past (i.e. our own past light cone...and if an event X lies in the past light cone of another event Y, then in that case all inertial frames do agree that X happened in the past of Y).

Imagine we fill the gap with people, since all the people claim each other resting there clocks must be synchronized.

"synchronized" has no frame-independent meaning in SR. If you have two rows of clocks, with all the clocks in row A at rest and synchronized relative to one another and all the clocks in row B at rest and synchronized relative to one another, then if row A is in motion relative to row B, row A will judge that all the clocks in row B are out-of-sync and row B will judge that all the clocks in row A are out-of-sync. I drew up some detailed illustrations of this in this thread, you might want to check those out.

To prove this even farther we can have someone accelrating over the entire length of the row of people, since all people will claim to accelrate with the same rate so they know exactly how muce his clock got slower, so they now have proof that their clcoks are synchronized.

I don't understand what you mean here. If the guy is accelerating, then the rate at which his clock is running will be constantly changing, since the rate a clock ticks is a function of the clock's speed and acceleration means his speed is changing. My diagrams on the other thread show how, since the two rows of clocks A and B are moving at constant speed relative to one another, each individual clock in A (like the one with the red hand) is running slow as measured by the clocks in B, and each individual clock in B is running slow as measured by the clocks in A. There's no paradox there once you take into account the relativity of simultaneity.

And this is actually my answer to the relativity of simultaneous.
Einstein had never prooved that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
What he had proved is, That what it APPEARS to be simultaneous in one frame, does not have to APPEAR simultaneous in another frame, and this we know without him.
But Einstein's claim that since both frames are equely valid according to relativity, then it follows that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.

As a metaphysical hypothesis you are free to believe that one frame's definition of simultaneity is "correct" in a metaphysical sense and the other frames' definitions are "incorrect". However, as long as all the fundamental laws of physics obey Lorentz-symmetric equations, so the equations in one inertial frame are the same as in any other, then any experiment you do that's confined to a windowless chamber (so you don't have any external landmarks to look at) will give the same results regardless of whether you are at rest in inertial frame #1 or inertial frame #2, so there's no experimental reason to pick out anyone frame as "preferred" by the laws of nature, and thus it must forever remain a mystery to you which frame is "metaphysically preferred" in the sense that its definition of simultaneity is metaphysically correct. Philosophically I think it's lot simpler to apply razor[/url] and eliminate the notion of a "true" definition of simultaneity, instead adopting an eternalist philosophy of time where events at all points in time are equally "real", but if you prefer the presentist philosophy of time where there is an absolute present and events not in the present have objectively "ceased to exist", nothing in relativity will contradict you as long as it's a purely metaphysical hypothesis without any physical implications about the results of actual experiments.

However I am just wondering on that, even if there would be no proof against relativity, it is still just a logical hypotesis, so why had Einstein choosen the more paradoxial relativity over the more straightforward hypotesis that simultaneous event are simultaneous every where?.

Basically, he picked it so that the laws of electromagnetism could work in every inertial frame as opposed to just a preferred "ether" frame (since Maxwell's laws say that electromagnetic waves always move at c, but the only way for different frames to agree that all electromagnetic waves move at the same speed is for them to have different definitions of simultaneity, as shown for example by the train thought-experiment). In part he may have been inspired by the failure of various experiments (like the Michelson-Morley experiment) to find a preferred ether frame, and subsequent experiments have consistently supported the idea that the fundamental laws of physics obey Lorentz-invariant equations.

 

[Dale]

Yoelhalb has a misunderstanding of the theory of Special Relativity.

He also has a misunderstanding of Newtonian mechanics.