Absolute motion's point of reference

[Dale]

So now my question is WHAT IS ACCELERATION?

JesseM already gave the definition of coordinate acceleration. There is also a coordinate-independent idea of acceleration called "proper acceleration", which is the acceleration measured by an accelerometer which is equal to the coordinate independent covariant derivative of the object's tangent vector.

1)let's assume that acccelration can claim resting, then we have the follwoing questions.
a) if acceleration can claim to be at rest then why does he feels those g-forces and why are the laws of phyiscs different for him?
for gravity we clearly know the answer, mass warps space, but for one in accelaration when there is no on the horizon then what happenes?

The components of the metric are different in a non-inertial coordinate system such as Rindler coordinates.

b)there is a stronger question, if accelaration and rotation can claim at rest then we oon the Earth can claim to have the correct point of view, so if we see that starts billions of light years far away are maikng their way every day around the world clearly more then the speed of light , then the speed of light would be violated.
(and there is no answer that because of accelaration the laws of physics are different [again why?] because speed of light can never be exceeded).

The coordinate speed of light can certainly exceed c in non-inertial frames. The second postulate only says that the coordinate speed of light is c in any inertial frame.

2) so let's assume that accelaration can not claim to be at rest.

This assumption is wrong, so let's skip the sub-questions. You can always make a coordinate system where any given observer is permanently at rest regardless of their acceleration. It will not generally be inertial, but that is OK.

AT EITHER WAY there is another question.
this is clear that his clock his slowing down absulotly,

This is not correct. Whether or not "his clock his slowing down" is a coordinate-dependent statement, not an absolute (coordinate independent) one.

So for anyone who thinks he have the answer, then he should explain wheeather accelaration can claim to be at rest or not, and then answer the questions on this claim, and also in either case he should answer the question about the timing
THANKS ALL OF YOU

Me. Done. Done. Done. You are welcome.

 

[yoelhalb]

Let me explain it again, and this time I will try to use more the notion of coordinate system so it will be easier to understand.

This is clear that although we can use many different coordinate systems, it sill does not have to be that all of them are true (in other words not all of them will reflect and explain the full reality).
Suppose that you want to use a flat geometry for the earth, you will able to do it to a certain extend, but this is not the true reality.
Or suppose a person looks on the world sun glasses and discovers that the world is darker, which is clearly because he is not seeing the world right while wearing the sun glasses.
The same can be here, although coordinate system is just a label that people use, still not all of them must describe correct the universe correctly, (just as flat geometry will explain the Earth but only to a certain extend, and just as Newtonian physics although correct does not describe the universe in full).
So let's analyze all coordinate systems to find which of them are not reflecting true reality.

First of all, we find that a non inertial coordinate system does not reflect reality, because according to this system objects will go faster then the velocity of light, and this is not true reality as the energy of the object will have to increase to infinity.
So the only coordinate system that can still be right are only inertial coordinate systems, and special relativity claims that you cannot differentiate between them.
However accelerating objects expirience g-force and the maginitude of the g-force increases while he increases acceleration.

Now if look at the accelerating object from different inertial frames of reference, the different frames of reference will give different magnitudes for the acceleration of the object, and clearly only one of them will match with the g-force that the accelerating object experience.
(For example while from one inertial coordinate system the accelerating object is increasing acceleration, from another inertial coordinate system the accelerating object will stay with the same acceleration, yet from a third inertial coordinate system it will decrease acceleration, yet only one of them will match the actual g-force felt by the object).

This is clearly showing that different inertial coordinate system can not be considered to be completely invariant, even though for most of the situations (when no acceleration is involved) they are.
And this can also prove which inertial coordinate system is the system that reflects true reality.
(I personally believe that extensive testing with acceleration will clearly give one coordinate system that will always reflect the g-force felt by any accelerating object).

Remember this is evidence based science, and if one coordinate system does not fit with observation then it has to be rejected.

 

[yoelhalb]

I hope one can answer the question I just asked.
I also liked the idea of expressing in terms of coordinate systems.
So I would like to ask if one of you can explain me the answer on the twin paradox in terms of coordinate systems, as I am finding it difficult to do it myself, (or at least provide me a link to a site or book that does that).
Thanks.

 

[Dale]

Let me explain it again, and this time I will try to use more the notion of coordinate system so it will be easier to understand.

This is clear that although we can use many different coordinate systems, it sill does not have to be that all of them are true (in other words not all of them will reflect and explain the full reality).
Suppose that you want to use a flat geometry for the earth, you will able to do it to a certain extend, but this is not the true reality.
Or suppose a person looks on the world sun glasses and discovers that the world is darker, which is clearly because he is not seeing the world right while wearing the sun glasses.
The same can be here, although coordinate system is just a label that people use, still not all of them must describe correct the universe correctly, (just as flat geometry will explain the Earth but only to a certain extend, and just as Newtonian physics although correct does not describe the universe in full).
So let's analyze all coordinate systems to find which of them are not reflecting true reality.

None of the above is correct. I really suggest that you learn about tensors. All coordinate systems are equally valid for physics.

You specifically mention the mistake of using flat geometry on a sphere, and this is obvious, for any given coordinate system you need to use the correct expression for the metric. If you use the wrong metric then you will obviously get wrong answers. This is not because the coordinate system is inherently faulty, but rather because your expression for the metric was wrong.

First of all, we find that a non inertial coordinate system does not reflect reality, because according to this system objects will go faster then the velocity of light,

No, in a non inertial coordinate system objects may have a coordinate speed faster than c, but light also may have a coordinate speed different from c, so going faster than c does not imply going faster than light in non-inertial frames.

The coordinate independent statement is that light always travels on null geodesics and massive objects always have timelike worldlines. This is the coordinate-independent statement that nothing goes faster than light, and it holds in non-inertial coordinate systems.

However accelerating objects expirience g-force and the maginitude of the g-force increases while he increases acceleration.

Now if look at the accelerating object from different inertial frames of reference, the different frames of reference will give different magnitudes for the acceleration of the object, and clearly only one of them will match with the g-force that the accelerating object experience.
(For example while from one inertial coordinate system the accelerating object is increasing acceleration, from another inertial coordinate system the accelerating object will stay with the same acceleration, yet from a third inertial coordinate system it will decrease acceleration, yet only one of them will match the actual g-force felt by the object).

This is clearly showing that different inertial coordinate system can not be considered to be completely invariant, even though for most of the situations (when no acceleration is involved) they are.
And this can also prove which inertial coordinate system is the system that reflects true reality.
(I personally believe that extensive testing with acceleration will clearly give one coordinate system that will always reflect the g-force felt by any accelerating object).

What you are describing here, the g-force felt by an accelerating object, is called proper acceleration. I already mentioned this above. Proper acceleration is given by the covariant derivative of the tangent, so it is a coordinate-independent tensor. All coordinate systems, inertial or non-inertial, will agree on it.

You really should learn about tensors. It will help you a lot in understanding non-inertial coordinate systems.

 

[yoelhalb]

No, in a non inertial coordinate system objects may have a coordinate speed faster than c, but light also may have a coordinate speed different from c, so going faster than c does not imply going faster than light in non-inertial frames.

Thanks for your reply.
But the speed of light c was measured here on earth, and it is certainly much far less then the speed of objects from our coordinate.
Again from our perspective all the objects in the entire universe are making there way every day around the world, in other words traveling billions of light years, far more then the measured speed of light.

 

[Dale]

Again from our perspective all the objects in the entire universe are making there way every day around the world, in other words traveling billions of light years, far more then the measured speed of light.

No, please be careful with your wording. Their coordinate speed is far greater than c, but light's coordinate speed is even greater than that. So they are still not going faster than light.

Again, try to use the coordinate-independent language. The objects traveling billions of light years every day in our non-inertial frame still have timelike worldlines, and light still has a lightlike or null worldline, so they are all going slower than light in a coordinate-independent sense that is true in all reference frames.

 

[yoelhalb]

Thanks for your reply.
Do you have a light and easy source on that concept?
If yes then I would appreciated.

 

[JesseM]

This is clear that although we can use many different coordinate systems, it sill does not have to be that all of them are true (in other words not all of them will reflect and explain the full reality).

Wrong, they all make exactly the same predictions about coordinate-independent facts, as long as you express the equations for the laws of physics correctly in each coordinate system (and again, if you have two coordinate systems A and B with a coordinate transformation between them, and you know the correct equations for the laws of physics in A, you can just apply the coordinate transformation to the equations themselves to get the correct equations in B)

Suppose that you want to use a flat geometry for the earth, you will able to do it to a certain extend, but this is not the true reality.

Coordinate systems don't describe geometry, for that you need a metric tensor (also see metric), which will be expressed using different equations in different coordinate systems, but which will always describe a spherical geometry (see differential geometry and differential geometry of surfaces)

First of all, we find that a non inertial coordinate system does not reflect reality, because according to this system objects will go faster then the velocity of light, and this is not true reality as the energy of the object will have to increase to infinity.

"Energy" is itself a coordinate-dependent quantity, and if it makes sense to define a conserved quantity called "energy" in non-inertial coordinate systems (I'm not entirely sure about this), then the equation relating energy in that coordinate system to coordinate velocity will presumably work differently than in an inertial frame, so that energy needn't approach infinity as v approaches c. And whether or not it makes sense to talk about "energy" in a non-inertial frame, you can be sure that this frame will make correct predictions about all local physical facts such as the readings on any physical instruments in any experiment (including one where we are using the instrument readings to calculate the 'energy' in some frame).

So the only coordinate system that can still be right are only inertial coordinate systems, and special relativity claims that you cannot differentiate between them.
However accelerating objects expirience g-force and the maginitude of the g-force increases while he increases acceleration.

Now if look at the accelerating object from different inertial frames of reference, the different frames of reference will give different magnitudes for the acceleration of the object, and clearly only one of them will match with the g-force that the accelerating object experience.

No, each frame would predict the same thing about the readings on any physical device to measure G-force (i.e. any accelerometer). It just happens to be true that the reading of G-force does not correspond to the coordinate acceleration at a point on the object's worldline where the object is not instantaneously at rest in that inertial frame. However, the laws of physics are still the same in each frame because the way G-force relates to coordinate acceleration as a function of velocity is still the same in each frame. In every frame, if you know the coordinate velocity v and the coordinate acceleration dv/dt at some point on the object's worldline, the formula for calculating the measured G-force a at that point would be:

a = \frac{1}{(1 - v^2/c^2)^{3/2}} dv/dt

So, this shows how the general laws of physics do work the same in every frame, despite the fact that for any particular point on an accelerating object's worldline, there will be only one particular inertial frame where the coordinate acceleration is equal to the measured G-force (the frame where v=0, as you can see from the above equation).

 

[Dale]

Thanks for your reply.
Do you have a light and easy source on that concept?
If yes then I would appreciated.

My first suggestion would be the Leonard Susskind lecture series on GR which is available on YouTube. That is probably a little too light and easy, but still very valuable as far as an introduction to tensors, coordinate systems, and gravity.

One step up from that I would suggest Sean Carrol's lecture notes on GR
http://arxiv.org/abs/gr-qc/9712019

You can also learn about interesting features of Rindler coordinates (accelerating in flat spacetime) at these two sites:
http://en.wikipedia.org/wiki/Rindler_coordinates
http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

 

[yoelhalb]

And whether or not it makes sense to talk about "energy" in a non-inertial frame, you can be sure that this frame will make correct predictions about all local physical facts such as the readings on any physical instruments in any experiment (including one where we are using the instrument readings to calculate the 'energy' in some frame).

Actually Energy was defined and used here on earth, which is clearly a non-inertial frame

 

[JesseM]

Actually Energy was defined and used here on earth, which is clearly a non-inertial frame

A small region of curved spacetime (like the region of a lab on Earth where physics experiments are typically done) is pretty much indistinguishable from flat spacetime--are you familiar with the http://www.einstein-online.info/spotlights/equivalence_principle to represent the G-force felt due to acceleration). For example, the path of light rays would be slightly curved in such a frame, and the coordinate speed of light would be slightly different from c, but the effect would be very tiny, so it's not too surprising that observers on Earth didn't notice these small corrections and just came up with the simpler equations that would apply in an inertial frame.

 

[yoelhalb]

No, each frame would predict the same thing about the readings on any physical device to measure G-force (i.e. any accelerometer). It just happens to be true that the reading of G-force does not correspond to the coordinate acceleration at a point on the object's worldline where the object is not instantaneously at rest in that inertial frame. However, the laws of physics are still the same in each frame because the way G-force relates to coordinate acceleration as a function of velocity is still the same in each frame. In every frame, if you know the coordinate velocity v and the coordinate acceleration dv/dt at some point on the object's worldline, the formula for calculating the measured G-force a at that point would be:

a = \frac{1}{(1 - v^2/c^2)^{3/2}} dv/dt

I don't understand that correctly, (maybe you would like to supply me with a source for that, if so then thanks in advance).
From where does the velocity v coming if this is coordinate system to use?
What I understand from your words that you need the to use the velocity of the uniform motion.
And if that is then he cannot claim resting and we must say that his time is the one that is getting slower.

 

[JesseM]

I don't understand that correctly, (maybe you would like to supply me with a source for that, if so then thanks in advance).

Sure, check out this textbook for example.

From where does the velocity v coming if this is coordinate system to use?
What I understand from your words that you need the to use the velocity of the uniform motion.

No, the velocity is just the instantaneous velocity which is the first derivative of the function x(t) that gives position as a function of time (coordinate acceleration is the second derivative of x(t), or the first derivative of velocity as a function of time v(t), which is why I wrote the coordinate acceleration as dv/dt). I asked you a few times before if you were familiar with the idea of first and second derivatives from calculus, can you please answer this question? Understanding of basic calculus is pretty essential for all of modern physics from Newton onwards (if you don't understand the basics I would say you don't really understand what the words 'velocity' and 'acceleration' even mean in physics), so if you're not familiar with this stuff that's really where you need to start.

 

[yoelhalb]

No, please be careful with your wording. Their coordinate speed is far greater than c, but light's coordinate speed is even greater than that. So they are still not going faster than light.

Can you explain me this?
Light has been mesuared to be about c here on earth, clearly less then billions of light years per day.

 

[JesseM]

Can you explain me this?
Light has been mesuared to be about c here on earth, clearly less then billions of light years per day.

Again I recommend you read up on the http://www.einstein-online.info/spotlights/equivalence_principle (especially the third paragraph). As always, though, you're going to have trouble understanding any discussion of velocity if you don't understand the basic idea that instantaneous velocity at any given time t in a particular coordinate system is the first derivative of the position as a function of time x(t) in that coordinate system, i.e. v(t) = dx/dt. If you'd like to learn about derivatives I'm sure people here can recommend some good sources, but if you just keep ignoring the issue it's going to start seeming like you are not so much interested in learning about velocity and acceleration in relativity as just in finding reasons to criticize it.

 

[Dale]

Can you explain me this?
Light has been mesuared to be about c here on earth, clearly less then billions of light years per day.

Sure, I will use units of light-years for distance and years for time so that c=1. I will use capital letters to indicate an inertial frame and lower case letters to indicate Earth's non-inertial frame which rotates once per (sidereal) day, and the Z=z axis is aligned with celestial north.

The transformation between the inertial and non-inertial frames is given by:
x=X cos(ωT) - Y sin(ωT)
y=X sin(ωT) + Y cos(ωT)
z=Z
t=T

A star at rest wrt Earth and located 1 light year away on the X axis would have the coordinates:
R=(X,Y,Z)=(1,0,0)
r=(x,y,z)=(cos(2300t), sin(2300t), 0)
so at t=0 this gives a coordinate speed of
|dr/dt| = |(0, 2300, 0)| = 2300 > 1

A ray of light leaving that star at T=0 in the Y direction would have the coordinates:
R=(X,Y,Z)=(1,t,0)
r=(x,y,z)=(cos(2300t) - t sin(2300t), t cos(2300t) + sin(2300t), 0)
so at t=0 this gives a coordinate speed of
|dr/dt| = |(0, 2301, 0)| = 2301 > 2300

If you go out further than 1 light year the effect becomes greater. The coordinate speed of the stars becomes much greater than c, but the coordinate speed of light is even greater than that.

 

[yoelhalb]

If you'd like to learn about derivatives I'm sure people here can recommend some good sources.

Thanks, but I allready know it.

 

[yoelhalb]

Anyway, if C is "accelerating to the left" in the inertial frame of the ocean where A is moving at constant velocity to the left and B has constant velocity to the right, then he will be closer to A than B, but will remain between them (to the right of A, to the left of B) until he finally catches up to A. Just suppose that in the ocean frame, the horizontal axis is labeled with an x-coordinate, with -x being to the left and +x to the right. Then x(t) for A could be x(t)=-100*t (so for example at t=2 hours, A will be at x=-200 miles, where x=0 being the position where ABC started at t=0 hours) while x(t) for B could be x(t)=100*t. In this case if C is accelerating at 1 km/hour per hour, then C could have x(t)=-0.5*t2, which means it has v(t)=-1*t (so for example at t=1 hour, C is at position x=-0.5 miles with v=-1 mph, then at t=2 hours C is at position x=-2 miles with v=-2 mph, at t=3 hours C is at position x=-4.5 miles with v=-3 mph, until finally at t=200 hours both A and C meet at position x=-20,000 miles).

As C accelerates toward A (as long as A stays at the same motion) the difference in their relative speed will drop by one mile an hour, each hour. After 3 hours, A will be 600 mph away from B, as B is traveling 200 mph in respect to A. C will be 294 miles away from A, moving 99 mph away from A in the first hour, then 98 Mph in the second hour, 97 mph in the third hour.

A is still at rest, however C is slowing down as it is moving away from A.

After 100 hours, B is 2000 miles away, still going at a rate of 200 mph (A's 100 mph and B's 100 mph...to B, A is doing the same). C however is at rest in regard to A (C has reached 100 mph), having slowed down from 99 mph down to 1 mph in regard to A.

As each hour increases, C gains 1 mph in speed as it approaches A, until it eventually overtakes A. It can overtake A if it simply travels at 101 mph (or 1 mph in regard to A), but in this case, C will overtake A much sooner as it is accelerating toward A now.

While the boat never "literally" turns around (it is always facing the same direction) and might seem silly to assume it is going backward so fast and leave a wake BEHIND it...most questions of this nature actually start in featureless space where only a,b, and c are present.

In your scenario, it is easier to assume D is the at rest rate, where D is the Earth everyone is moving across. This is no more valid than anyone else's reference, but it has features one can refer to and all three can measure against.

D by the way is moving in F, the Milky Way (Skipping the solar system), which is traveling at about a million miles an hour toward Q, which is the Great Attractor...so, using D as a rest reference, and ignoring F and Q (and everything in between) makes things much simpler.

According to what you write it follows that C (from A's point of view) started with its direction to the right (since they are all together in the beginning and then C moves to the right side of A and A is the frame of reference), and then he changed directions and met A, that essentially means that he changed direction without rotating.
With this you are actually destroying the answer on the twin paradox.

Actually although this can really be, there are some instances that such a claim is invalid, I have no clue if a spaceship can be claimed to be backing up, but it is against physics and common sense to claim that a buggy can pull the horse, (and yes there might be something like that in space), actually special relativity in its answer on the twin paradox claims this to be true for any motion.
So there are situations that the direction is clear for all, and A's claim makes no sense and you would never believed it if some one would tell you such a story in real life, and I don't see why we have to believe it just to support an hypothesis that can never be tested.

 

[Dale]

C (from A's point of view) started with its direction to the right (since they are all together in the beginning and then C moves to the right side of A and A is the frame of reference), and then he changed directions and met A, that essentially means that he changed direction without rotating.
With this you are actually destroying the answer on the twin paradox.

Things change direction without rotating all the time. Throw a pencil straight up into the air and note that as it rises then falls it changes direction without rotating.

Your objection is irrelevant.

 

[yoelhalb]

Things change direction without rotating all the time. Throw a pencil straight up into the air and note that as it rises then falls it changes direction without rotating.

Your objection is irrelevant.

Then according to you two twins moving away and them moving back and meeting, and according to what you say they can change direction without rotation, so who will be younger?
Anyway a pencil can change directions, but a horse and buggy it is against common sense and physics to claim motion in 2 directions (is the principle of relativity a religion?).

 

[Dale]

Then according to you two twins moving away and them moving back and meeting, and according to what you say they can change direction without rotation, so who will be younger?

The one which underwent non-zero proper acceleration.

Anyway a pencil can change directions, but a horse and buggy it is against common sense and physics to claim motion in 2 directions

Show me a detailed derivation where the horse and buggy doesn't make sense. You are imagining a problem with relativity that does not exist.

 

[yoelhalb]

The one which underwent non-zero proper acceleration.

Why should anyone of them?

Show me a detailed derivation where the horse and buggy doesn't make sense. You are imagining a problem with relativity that does not exist.

Imagine A,B,C are togheter, C is a horse and buggy.
Now A and B move apart in a uniform motion, and C starts accelration till it meets A.
Since a horse and buggy can go only in one direction it must be that A is the one that moves.

 

[Dale]

Why should anyone of them?

Because otherwise they will not be able to reunite.

Imagine A,B,C are togheter, C is a horse and buggy.
Now A and B move apart in a uniform motion, and C starts accelration till it meets A.
Since a horse and buggy can go only in one direction it must be that A is the one that moves.

This is not even approximately a derivation. Please do an actual derivation using explicit expressions for the various worldlines, transformations, and derived quantities of interest. Which derived quantity do you think is wrong? E.g. the tension between the horse and buggy should always be positive, do you think you get a negative tension in some frame, if so then derive the tension in that frame.

 

[yoelhalb]

Again A,B,C are together at one point.
C is a horse and a buggy.
Now A and B start moving apart, each one seeing the other one moving 100 m/s, A moves to the left and B to the right (from each others perspective), like this A<----------->B.
In the same second C also started an acceleration of 1 m/s² to the left.
Since it is clear the direction of the horse and buggy is clear it follows that every one must agree that C is moving left only.
Now if A is the point of reference then C should never be to his right, but just to his left, and will never meet him again as long C is not rotating, since according to A's perspective A is at the point of reference and where the motion started.
But if B's claim that he his the point of reference then C should be next to B, (in the first second he will be 1 m apart, the second 3 m, etc), until after a long time he will meet A.
Now we have clear proof who is moving.

 

[Dale]

You really don't seem to understand what a derivation is.

So I will ask you again: what are the worldlines of A, B, and C? And which derived quantity is concerning you?

You have asserted several times that a horse and buggy cannot go backwards, but have not said why you believe that and have not shown that whatever is troubling you is actually predicted by relativity. If you cannot even form a coherent argument how do you expect to have a rational discussion.

 

[JesseM]

According to what you write it follows that C (from A's point of view) started with its direction to the right (since they are all together in the beginning and then C moves to the right side of A and A is the frame of reference), and then he changed directions and met A, that essentially means that he changed direction without rotating.
With this you are actually destroying the answer on the twin paradox.

Actually although this can really be, there are some instances that such a claim is invalid, I have no clue if a spaceship can be claimed to be backing up, but it is against physics and common sense to claim that a buggy can pull the horse, (and yes there might be something like that in space), actually special relativity in its answer on the twin paradox claims this to be true for any motion.
So there are situations that the direction is clear for all, and A's claim makes no sense and you would never believed it if some one would tell you such a story in real life, and I don't see why we have to believe it just to support an hypothesis that can never be tested.

Your argument has nothing specifically to do with relativity at all! In basic Newtonian physics, suppose that in the frame of the ground a car is accelerating down the road so its speed relative to the road is increasing. Then if I am an inertial observer moving at constant velocity down the same road, if the accelerating car's velocity relative to the road goes from below mine to above mine, then in my frame the car's direction will change without it turning around. It's not hard to see why this must true--when the accelerating car's speed relative to the road is lower than mine, if I am in front the distance between me and the accelerating car is increasing, so in my frame (where I am at rest) the accelerating car must be moving away from me; but then when the accelerating car's speed exceeds mine while I am still in front, the distance between me and the accelerating car is now decreasing, so in my frame the accelerating car must now be moving towards me.

For a more mathematical demonstration, suppose the accelerating car's position as a function of time in the ground frame is given by x(t) = (1.5 meters/second^2)*t^2, and my own position as a function of time in the ground frame is given by x(t) = (27 meters/second)*t, so I have a constant speed of 27 m/s and we both start at position x=0 meters at time t=0. You said you were familiar with derivatives, can you calculate the instantaneous velocity as a function of time (i.e. first derivative of x(t) with respect to t) for the accelerating car, and therefore figure out the time t at which the accelerating car's velocity exceeds that of my car?

Then in Newtonian physics, the coordinates of events in my own rest frame x',t' are related to the coordinates x,t in the ground frame by the following simple transformation:

x' = x - (27 m/s)*t
t' = t

And the reverse transformation:

x = x' + (27 m/s)*t'
t = t'

So if the accelerating car has x=(1.5 m/s^2)*t^2 in the ground frame, we can substitute x=x' + (27 m/s)*t' and t=t' to conclude x' + (27 m/s)*t' = (1.5 m/s^2)*t'^2, which means x'(t') in my frame is x'(t') = (1.5 m/s^2)*t'^2 - (27 m/s)*t'. Again, can you take the first derivative of this to find the velocity as a function of time of the accelerating car in my own rest frame?

 

[yoelhalb]

Your argument has nothing specifically to do with relativity at all! In basic Newtonian physics, suppose that in the frame of the ground a car is accelerating down the road so its speed relative to the road is increasing. Then if I am an inertial observer moving at constant velocity down the same road, if the accelerating car's velocity relative to the road goes from below mine to above mine, then in my frame the car's direction will change without it turning around. It's not hard to see why this must true--when the accelerating car's speed relative to the road is lower than mine, if I am in front the distance between me and the accelerating car is increasing, so in my frame (where I am at rest) the accelerating car must be moving away from me; but then when the accelerating car's speed exceeds mine while I am still in front, the distance between me and the accelerating car is now decreasing, so in my frame the accelerating car must now be moving towards me.

It has with the principle of relativity.
Before special relativity there was claimed to be absolute motion (such as the ether) so you would never claim that the car changed directions.
Such a claim was only introduced by Einstein, and it can never be proved, and as I show it is against common sense.

 

[Dale]

as I show it is against common sense.

You certainly have not shown any such thing. You have merely asserted it with no proof, derivation, nor even an explanation about why you might think such an absurd thing.

 

[yoelhalb]

You certainly have not shown any such thing. You have merely asserted it with no proof, derivation, nor even an explanation about why you might think such an absurd thing.

Then please explain it to me.
I will tell you the story and you will explain me just what is going on.
Imagine 3 objects are at together A,B,C.
Then A and B are moving away with a uniform motion A<----------->B, at 100 m/s.
C also starts to accelerate to the left, C is a horse and buggy, accelerating from C's view 1 m/s² from the initial point.
So in the first second after the beginning of the motion, (C has moved 1 m from the initial point) will C be 1 m to the left of B or 1 m to the left of A?, and how will A and B interpret this.

 

[JesseM]

It has with the principle of relativity.
Before special relativity there was claimed to be absolute motion (such as the ether) so you would never claim that the car changed directions.

Even before relativity, there'd be nothing stopping you from having a road moving inertially relative to the ether frame (after all the Earth is not the center of the universe, so we wouldn't expect the surface of the Earth to remain at rest relative to the ether), and a car moving relative to the road at just the right velocity so it was at rest in the ether frame. In this case, if you have a second accelerating car initially at rest relative to the road, but then accelerating in a constant way so that its velocity relative to the road eventually exceeded the inertial car's velocity, then naturally the accelerating car will turn around without rotating in the inertial car's frame--and here we have set things up so the inertial car's rest frame is the ether frame, so the accelerating car turns around without rotating in the ether frame too.

 

[Mentz114]

Then A and B are moving away with a uniform motion A<----------->B, at 100 m/s.

I presume you mean moving apart. In which case they must have experienced some acceleration before the state of motion you describe.

This period is crucial in working out if C will overtake A. But if the system was completely specified there would be no doubt about the positions of A,B and C, and all observers will agree.

 

[yoelhalb]

Even before relativity, there'd be nothing stopping you from having a road moving inertially relative to the ether frame (after all the Earth is not the center of the universe, so we wouldn't expect the surface of the Earth to remain at rest relative to the ether), and a car moving relative to the road at just the right velocity so it was at rest in the ether frame. In this case, if you have a second accelerating car initially at rest relative to the road, but then accelerating in a constant way so that its velocity relative to the road eventually exceeded the inertial car's velocity, then naturally the accelerating car will turn around without rotating in the inertial car's frame--and here we have set things up so the inertial car's rest frame is the ether frame, so the accelerating car turns around without rotating in the ether frame too.

My question is different then your example, since in my example both started at the same place, and my question is not because he passes him but because A must claim him backing up, (also a car can back up without rotating and is not the same as a horse and buggy), here is what your example might look like on Earth before relativity.
Imagine two horse and buggies are initially at the same spot, then suddenly one horse and buggy accelerates backward and then suddenly he passes the other horse and buggy, all without rotation.
(However nobody would make such a claim before relativity, and you would never believe such a story).

This is analogous to what I am speaking, A,B,C are initially together, then A and B move away with linear motion and A is to the left, if A is the point of reference then how can C (who is accelerating to the left) be to the right side of A.
Thus, clearly showing that although A moves with a linear motion B is the point of reference.

You might claim that C will never be to A's right, but this is not true, consider two ships moving away with a uniform motion do you think the water between them will be emptied out?.
So C might stay to his right, and thus proving that a is not the frame of reference, (Actually this is what I started the whole thread that there must be some global reference and not that every body can claim to be his own point of reference).

 

[ghwellsjr]

Then please explain it to me.
I will tell you the story and you will explain me just what is going on.
Imagine 3 objects are at together A,B,C.
Then A and B are moving away with a uniform motion A<----------->B, at 100 m/s.
C also starts to accelerate to the left, C is a horse and buggy, accelerating from C's view 1 m/s² from the initial point.
So in the first second after the beginning of the motion, (C has moved 1 m from the initial point) will C be 1 m to the left of B or 1 m to the left of A?, and how will A and B interpret this.

You claimed in post #67 that you already know about derivatives but now it is clear that you do not. If C is accelerating at 1 m/s^2, then after 1 second, C will have moved 1/2 m from the initial point, not 1 m. You seem to be getting the position confused with the speed which is 1 m/s after 1 second.

And your example has nothing to do with relativity. We can't even figure out what your issue is. You give us a multiple choice question where all the answers are incorrect. Or maybe I should say, the only way one of your answers could be correct is if we interpret the question in a way that I'm sure you didn't mean.

The way I think you mean is: After one second, A has moved to the left 50 m, B has moved to the right 50 m, and C has moved to the left 1 m. But then why are you asking us if C is 1 m to the left of A or 1 m to the left a B?

So you must have meant that A is moving to the left and is 100 m from the starting point and B is stationary so then the correct answer would be: C is 1 m to the left of B.

But you could have meant that B is moving to the right and is 100 m from the starting point and A is stationary so then the correct answer would be: C is 1 m to the left of A.

(Keep in mind, I am using your incorrect understanding of the actual position of C after 1 second.)

Can you see why your example is so confusing? You have been presenting this example since post #17, and you still haven't presented it in an unambiguous way that would allow us to respond in any meaningful way.

 

[ghwellsjr]

My question is different then your example, since in my example both started at the same place, and my question is not because he passes him but because A must claim him backing up, (also a car can back up without rotating and is not the same as a horse and buggy), here is what your example might look like on Earth before relativity.
Imagine two horse and buggies are initially at the same spot, then suddenly one horse and buggy accelerates backward and then suddenly he passes the other horse and buggy, all without rotation.
(However nobody would make such a claim before relativity, and you would never believe such a story).

This is analogous to what I am speaking, A,B,C are initially together, then A and B move away with linear motion and A is to the left, if A is the point of reference then how can C (who is accelerating to the left) be to the right side of A.
Thus, clearly showing that although A moves with a linear motion B is the point of reference.

You might claim that C will never be to A's right, but this is not true, consider two ships moving away with a uniform motion do you think the water between them will be emptied out?.
So C might stay to his right, and thus proving that a is not the frame of reference, (Actually this is what I started the whole thread that there must be some global reference and not that every body can claim to be his own point of reference).

You seem to think that special relativity is saying that every person, horse, buggy, ship, car, etc. can all claim to be a different point of reference all at the same time. But it does not say that. It says you can pick anyone to be the point of reference and analyze what everyone else is doing from that reference frame. Then, if you want, you can pick another one to be the point of reference and analyze everything from that reference frame and there are ways to convert the answers you get from one reference frame into another reference frame. The number you get for speed, positions and times can be all different in each reference frame but they will be consistent with each other with regard to the order of events. You can even pick a frame of reference for which there is no object.

So let's do it for your example. If we decide that the initial starting point where A, B, & C are stationary is the frame of reference, then we could say that A moves to the left at 50 m/s, B moves to the right at 50 m/s and C accelerates to the left at 1 m/s^2. In this case, after 1 second, C would be to the right of A by 49 m and to the left of B by 51 m. (Again, I'm using your incorrect understanding of position due to acceleration.)

Or we could decide to use the frame of A's motion as the reference frame. Then after 1 second, C would be to the right of A by 49 m and B would be to the right of C by 51 m.

Or we could decide to use the frame of B's motion as the reference frame. Then after 1 second, C would be to the left of B by 51 m and A would be to the left of C by 49 m.

Do you see that these all give the same answers, even though we assume different reference frames?

(These speeds are good enough because they are so slow, it would be a little more complicated if the speeds approached the speed of light.)

 

[Dale]

Then please explain it to me.

Sorry, I cannot read your mind and I cannot make sense out of nonsense. Post 83 by ghwellsjr outlines the same problems that I am having with your scenario. It is not up to me to try to guess your intentions and do both sides of the argument. If you have a point to make then it is up to you to convey it clearly and unambiguously.

To make your point you need to do the following:
1) explicitly state the worldlines of A, B, and C in some inertial frame (as I have requested 3 times now).
2) explain what condition prevents a horse and buggy from going backwards.
3) show that that condition arises in your example.

If you cannot do 1) and 3) then you should still at least be able to do 2). You have provided no explanation for why a horse and buggy cannot go backwards other than asserting "common sense". So, explain, what prevents a horse and buggy from going backwards, do you imagine that the horse explodes, if so what causes the explosion, if not then what else could prevent it from going backwards?

 

[JesseM]

My question is different then your example, since in my example both started at the same place, and my question is not because he passes him but because A must claim him backing up, (also a car can back up without rotating and is not the same as a horse and buggy), here is what your example might look like on Earth before relativity.

In my example the accelerating car's wheels were still rolling forwards when it was initially going backwards in the rest frame of the inertial car at rest in the ether, it wasn't "backing up" in the traditional sense of making its wheels go backwards. That's because in this frame the road was itself moving backwards (think of a treadmill), so even though the accelerating car was going forwards relative to the road, it was still going backwards in the frame of the inertial car until its speed relative to the road matched that of the inertial car, at which they were both at rest relative to the ether, and after that the accelerating car's continued acceleration would cause it to start moving forward relative to the ether.

Nothing about this example would change if you imagined that we replaced the two cars with two horse-and-buggies, and imagined that both started at the same position on the road. It would still be true that if the road was moving backwards at speed v relative to the ether, and the inertial horse-and-buggy was moving forward at speed v relative to the road, then the inertial horse-and-buggy would be at rest relative to the ether. And if the accelerating horse-and-buggy started out at rest relative to the road, then it would start out moving backwards relative to the ether. If it later accelerated until it was moving at a speed greater than v relative to the road, then it would be moving forward relative to the ether. Do you disagree?

 

[yoelhalb]

You seem to think that special relativity is saying that every person, horse, buggy, ship, car, etc. can all claim to be a different point of reference all at the same time. But it does not say that. It says you can pick anyone to be the point of reference and analyze what everyone else is doing from that reference frame. Then, if you want, you can pick another one to be the point of reference and analyze everything from that reference frame and there are ways to convert the answers you get from one reference frame into another reference frame. The number you get for speed, positions and times can be all different in each reference frame but they will be consistent with each other with regard to the order of events. You can even pick a frame of reference for which there is no object.

So let's do it for your example. If we decide that the initial starting point where A, B, & C are stationary is the frame of reference, then we could say that A moves to the left at 50 m/s, B moves to the right at 50 m/s and C accelerates to the left at 1 m/s^2. In this case, after 1 second, C would be to the right of A by 49 m and to the left of B by 51 m. (Again, I'm using your incorrect understanding of position due to acceleration.)

Or we could decide to use the frame of A's motion as the reference frame. Then after 1 second, C would be to the right of A by 49 m and B would be to the right of C by 51 m.

Or we could decide to use the frame of B's motion as the reference frame. Then after 1 second, C would be to the left of B by 51 m and A would be to the left of C by 49 m.

Do you see that these all give the same answers, even though we assume different reference frames?

(These speeds are good enough because they are so slow, it would be a little more complicated if the speeds approached the speed of light.)

The question here is simple (it is a logical and not a mathematical question), since C was initially together with A, and since C is an horse and buggy heading to the left, then if A is the point of reference then C should not never arrive to his right.
To illustrate this in real life, consider the typical relativity example.
You are in a train and there is a train next to it, then both trains start to move apart, so you claim that the other train moves away from you, but the people on the other train claim that you are moving.
Now let's change the example and instead of another train this time a horse and buggy is next to your train, and again your train and the horse and buggy move apart, so you think that the horse and buggy has moved.
But then you look out and you see that while your train and the horse and buggy still move apart, the horse is still facing your train, that means in other words that the buggy is pulling the horse away from you.
Can this be?.
So you are actually the one who moves.

 

[yoelhalb]

In my example the accelerating car's wheels were still rolling forwards when it was initially going backwards in the rest frame of the inertial car at rest in the ether, it wasn't "backing up" in the traditional sense of making its wheels go backwards. That's because in this frame the road was itself moving backwards (think of a treadmill), so even though the accelerating car was going forwards relative to the road, it was still going backwards in the frame of the inertial car until its speed relative to the road matched that of the inertial car, at which they were both at rest relative to the ether, and after that the accelerating car's continued acceleration would cause it to start moving forward relative to the ether.

Nothing about this example would change if you imagined that we replaced the two cars with two horse-and-buggies, and imagined that both started at the same position on the road. It would still be true that if the road was moving backwards at speed v relative to the ether, and the inertial horse-and-buggy was moving forward at speed v relative to the road, then the inertial horse-and-buggy would be at rest relative to the ether. And if the accelerating horse-and-buggy started out at rest relative to the road, then it would start out moving backwards relative to the ether. If it later accelerated until it was moving at a speed greater than v relative to the road, then it would be moving forward relative to the ether. Do you disagree?

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.
(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).

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?

 

[ghwellsjr]

The question here is simple (it is a logical and not a mathematical question), since C was initially together with A, and since C is an horse and buggy heading to the left, then if A is the point of reference then C should not never arrive to his right.
To illustrate this in real life, consider the typical relativity example.
You are in a train and there is a train next to it, then both trains start to move apart, so you claim that the other train moves away from you, but the people on the other train claim that you are moving.
Now let's change the example and instead of another train this time a horse and buggy is next to your train, and again your train and the horse and buggy move apart, so you think that the horse and buggy has moved.
But then you look out and you see that while your train and the horse and buggy still move apart, the horse is still facing your train, that means in other words that the buggy is pulling the horse away from you.
Can this be?.
So you are actually the one who moves.

The problem with your examples is that you don't say enough about what is going on. When you say that A and C move apart without specifying which one (or both) is accelerating and then want to draw some conclusions based on which way a horse and buggy are facing, it shows that you don't understand some basic principles of physics which have nothing to do with relativity.

I want you to consider another example: You get in a stopped train at the railroad station. You sit in a seat. The shades are pulled down so you can't see out the windows. You consider this to be your reference frame. After a while, you feel a new force pushing you backwards into your seat. Now you know that you are accelerating. That means you are starting to move forward. As long as you continue to feel the force pushing you back into your seat, you know you are gaining speed. After a while, the force pushing you into the back of your seat diminishes until it is gone. Now you know that you have stopped accelerating and you are traveling at a constant speed. But you also know that as soon as you first felt the force, you were no longer stationary in your initial reference frame. You have been and continue to be moving in your initial reference frame. You don't need to look at anything outside your train to know that you are now moving with respect to your initial condition. Do you understand and agree with all of this?

 

[yoelhalb]

Sorry, I cannot read your mind and I cannot make sense out of nonsense. Post 83 by ghwellsjr outlines the same problems that I am having with your scenario. It is not up to me to try to guess your intentions and do both sides of the argument. If you have a point to make then it is up to you to convey it clearly and unambiguously.

To make your point you need to do the following:
1) explicitly state the worldlines of A, B, and C in some inertial frame (as I have requested 3 times now).
2) explain what condition prevents a horse and buggy from going backwards.
3) show that that condition arises in your example.

If you cannot do 1) and 3) then you should still at least be able to do 2). You have provided no explanation for why a horse and buggy cannot go backwards other than asserting "common sense". So, explain, what prevents a horse and buggy from going backwards, do you imagine that the horse explodes, if so what causes the explosion, if not then what else could prevent it from going backwards?

My question is that it is impossible to happen ny internal forces, yet it is possible to happen by external forces (even while it is itself accelerating on the opposite direction).
Imagine the horse and buggy are not on Earth but traveling in water, then the water can surely take them backwards.
But if this is true, then the external force can also take them back without any acceleration or rotation, now when they will meet together who will be younger?.

 

[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?.