Absolute motion's point of reference

[yoelhalb]

Again since ABC are together, then when C from his point of view accelerating to the left now if A is at absolute rest then C most be to the left of A, but if B is at absolute rest then C will be to B's left and A's right.
this is the question I started with, what is c's point of reference?
And don't answer me what A and B will think because i want to know what c will think, (actually A and B have no way of proofing that C is accelerating instead of them accelerating int the opposite direction, so all what we claim that C is moving comes from C's point of view)

 

[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)

Actually that's what i wanted to proof that you can't get away with acceleration without having some absolute point of reference such as the ocean

 

[ghwellsjr]

Of course you would say because when he accelerates he feels motion, but my question is why is this?
All of this together (and I have more questions) causes me to think that special relativity is rather incomplete, is there someone who can help me trying to work this out?

No, we would not say that acceleration makes you feel motion, it does not, it makes you feel a force pushing you in a direction that may not be related to the direction of your motion and there may not be any motion as in the case of gravity which is identical to the force you feel when you are accelerating. Or consider the case of being in free fall on an amusement park ride when you don't feel any force (ideally) but you are experiencing a lot of motion.

And please, before you ask more questions, please wait a long enough time for you to get an answer that makes sense to you from your previous question. If an answer doesn't make sense to you, explain why, instead of going off in a completely different direction.

 

[JJRittenhouse]

Let m e explain the whole question again.
ABC are at the same position one next to the other.
Now A and B are moving apart with a constant speed of 100 mph (imagine ships in the water).
Also according to C in the same second A and B took apart, he started accelrating with a speed of 1 mph in the direction of A's travel.
(actually the question starts here will he be a mile close to A or to B?).
A initially sees this as C moving away from him with 99 mph.
The next hour C speeds up with another 1 mph to a total of 2 mph, and so on till he meets A.
According to A how can this happen? C initially moved away form him and never moved back.
(As you can see there are actually 2 questions)

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.

 

[JesseM]

Yes, but he would know the coordinate system where he remains at rest is not an inertial frame, so the usual equations of SR such as the time dilation equation won't apply in this frame (though at any single instant on his worldline there will be some inertial frame where he is instantaneously at rest).

so why isn't he at rest?

"at rest" and "in motion" have no absolute meaning, they only have meaning relative to some coordinate system. In his non-inertial rest frame, he is at rest throughout the journey. At any given point on his worldline, you can also find an inertial frame where he is instantaneously at rest, but since he is accelerating in this frame his velocity is constantly changing so it won't remain at zero for any extended length of time.

If that doesn't answer your question "why isn't he at rest", then I don't understand what you're asking, please be specific about what frame you're talking about.

consider when discussing if an object is big or small, there would never be a claim as absolute big, because there is not point of reference, so why is motion different.

"Motion" in the sense of velocity isn't any different (you understand the difference between acceleration and velocity right? that velocity is the first derivative of position with respect to time, while velocity is the second derivative with respect to time?), there is no absolute truth about whether an object is "at rest" or "in motion" at a given instant. There also isn't an absolute truth about whether an object is "accelerating" or "not accelerating" with regards to arbitrary coordinate systems, but there is an absolute truth about whether an object is accelerating with regards to inertial coordinate systems, and the laws of physics do take a special "preferred" form in inertial coordinate systems although you are free to use a non-inertial frame as long as you understand the equations for the laws of physics will look different in this frame. This might be compared to the situation in 2D Euclidean geometry where if you want to figure out the length of a straight line between two points, if you know the coordinates (x₁, y₁) and (x₂, y₂) of the endpoints in anyone of an infinite number of Cartesian coordinate systems you can use the Pythagorean theorem to calculate the length as $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ (and you will get the same answer regardless of what Cartesian coordinate system you use), but this equation wouldn't correctly give you the length in some non-Cartesian coordinate system on the plane. And the question of whether a given line is "straight" or "curved" also has an absolute answer in the sense that every Cartesian coordinate system will agree on whether the slope dy/dx is constant or changing along the line, even though for a curved line where dy/dx is changing in every Cartesian coordinate system, you could still define a non-Cartesian coordinate system where dy/dx was constant along that line.

 

[yoelhalb]

No, we would not say that acceleration makes you feel motion, it does not, it makes you feel a force pushing you in a direction that may not be related to the direction of your motion and there may not be any motion as in the case of gravity which is identical to the force you feel when you are accelerating. Or consider the case of being in free fall on an amusement park ride when you don't feel any force (ideally) but you are experiencing a lot of motion.

And please, before you ask more questions, please wait a long enough time for you to get an answer that makes sense to you from your previous question. If an answer doesn't make sense to you, explain why, instead of going off in a completely different direction.

So he might claim resting?
so that why I asked about seeing the entire universe going faster then the speed of light.
(again there are 2 explanations here 1) that jesseM gave, that acceleration can claim rest to his own frame of reference. 2) what ghwellsjr gave, that acceleration uses the previous point of view of his own rest. and I have to overthrow both of you. anyway I am in a hurry)

 

[JJRittenhouse]

this is the question I started with, what is c's point of reference?

From C, both A and B are always accelerating. B always away from C, one mph per hour, and A negatively (deceleration) away from 99 mph to 1 mph, and then stops, and slowly accelerates back toward C.

C will feel constant pressure though from it's own acceleration, while A and B will not, however C can simply assume it is within a very weak field of gravity instead of assuming it is the one accelerating.

If A, B and C were in space, C could not determine if he were accelerating toward A or away from B, or simply standing stationary within a weak field of gravity.

 

[yoelhalb]

"Motion" in the sense of velocity isn't any different (you understand the difference between acceleration and velocity right? that velocity is the first derivative of position with respect to time, while velocity is the second derivative with respect to time?), there is no absolute truth about whether an object is "at rest" or "in motion" at a given instant. There also isn't an absolute truth about whether an object is "accelerating" or "not accelerating" with regards to arbitrary coordinate systems, but there is an absolute truth about whether an object is accelerating with regards to inertial coordinate systems, and the laws of physics do take a special "preferred" form in inertial coordinate systems although you are free to use a non-inertial frame as long as you understand the equations for the laws of physics will look different in this frame. This might be compared to the situation in 2D Euclidean geometry where if you want to figure out the length of a straight line between two points, if you know the coordinates (x₁, y₁) and (x₂, y₂) of the endpoints in anyone of an infinite number of Cartesian coordinate systems you can use the Pythagorean theorem to calculate the length as $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ (and you will get the same answer regardless of what Cartesian coordinate system you use), but this equation wouldn't correctly give you the length in some non-Cartesian coordinate system on the plane. And the question of whether a given line is "straight" or "curved" also has an absolute answer in the sense that every Cartesian coordinate system will agree on whether the slope dy/dx is constant or changing along the line, even though for a curved line where dy/dx is changing in every Cartesian coordinate system, you could still define a non-Cartesian coordinate system where dy/dx was constant along that line.

Again so what distinguishes an inertial frame of reference form a non inertial and why?
(If there would be an absolute frame of reference it would be understood, also for an object under gravity it is understood, but not for an accelrating object with no absolute point of rest)

 

[JesseM]

Actually that's what i wanted to proof that you can't get away with acceleration without having some absolute point of reference such as the ocean

But you could analyze exactly the same situation from the perspective of a different inertial coordinate system (or even a non-inertial coordinate system), my choice of using the ocean frame was an arbitrary one. Assuming that x,t represent the coordinates in the ocean frame, then in Newtonian physics if we want to transform into an inertial coordinate system x',t' moving at speed v in the +x direction relative to the ocean frame, we'd use the Galilei transformation:

x' = x - vt
t' = t

(in relativity you'd need a different transformation called the Lorentz transformation, but the speeds in your problem are so small compared to light speed that Newtonian physics is a good approximation)

This transformation can be reversed to give x and t in terms of x' and t':

x = x' + vt'
t = t'

So for example, if we want to use the frame where B is at rest, the v=+100 mph. So, if we know A has x=-100*t in the ocean frame, then in B's frame we can substitute x = x' + 100*t' and t = t' to get x' + 100*t' = -100*t', and subtracting 100*t' from both sides gives x' = -200*t', so that's the position as a function of time for A in B's rest frame. Likewise since C had x=-0.5*t² in the ocean frame, making the same substitution of x = x' + 100*t' and t = t' gives x' + 100*t' = -0.5*t'², so the position as a function of time of C in B's rest frame must be x' = -0.5*t'² - 100*t'. Take the derivative of that with respect to time and you find that C has v' = -1*t' - 100 in B's frame, so C is still accelerating at a rate of -1 mph per hour in this frame.

Similarly you can pick a coordinate transformation to a non-inertial frame where C is at rest if you like:

x = x' - 0.5*t'²
t = t'

In this case, since C has x=-0.5*t² in the ocean frame, substituting in the above transformation equations gives x' - 0.5*t'² = -0.5*t'², which reduces to x'=0. Similarly since A had x=-100*t in the ocean frame, substituting gives x' - 0.5*t'² = -100*t' which means x' = 0.5*t'² - 100*t'. So in this frame A has a positive coordinate acceleration towards C. But since this is a non-inertial frame, the laws of physics don't work the same in this frame as they do in an inertial frame like the ocean frame or B's rest frame; instead there are fictitious forces present in this frame, which explains why C feels a G-force even though C is at rest in this frame.

 

[JesseM]

Again so what distinguishes an inertial frame of reference form a non inertial and why?

The form of the equations that correctly predict the motion and behavior of objects (i.e. the equations expressing the laws of physics) in terms of the coordinates of that frame; the equations take the same special form in all inertial frames, but the equations are different in non-inertial frames. For example, if you have a type of clock that ticks at a rate of 10 ticks per second in its own rest frame, then in any inertial frame where it's moving at speed v, it will tick 10*$$\sqrt{1 - v^2/c^2}$$ every second, whereas if it's moving at speed v in a non-inertial frame this equation would no longer work. Did you understand my analogy about 2D Euclidean geometry in post #40, and in particular do you understand that the pythagorean formula $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ will accurately compute the length along a straight path between two points with coordinates (x₁, y₁) and (x₂, y₂) if we are using a Cartesian coordinate system, but not if we are using a non-Cartesian coordinate system?

 

[JJRittenhouse]

"Here is a similar question.
"Imagine A,B,C are at one position, then A and B starts to move away with uniform motion.
C moves with acceleration starting with a lower speed and eventually catching up with A.
How can we claim that A was at rest?"

Here we have a problem, and I ignored it at first because I thought we were just assuming automatic speed.

If A, B and C can all say that they are in rest in regard to each other at the start of this, then there is no way for A and B to be moving 100 mph away from each other in the next instant. A and B must accelerate to 100 mph (or each view the other as accelerating to 200 mph twice as fast if you use one or the other as your reference).

Now you can set this up differently, where A is going 1,000 mph, B is going 1,000 mph opposite of A (and just passed each other a moment before we start this) and C is traveling at 900 mph in the same direction as A (A having just passed C just prior to the initial condition).

I'm using D as a reference as you were assuming when you set up the example (by stating everyone's rate seperately where no one is at rest, you must assume that your explanation starts from a reference apart from A, B, or C and then asks for one of their reference frames). I use the larger numbers to illustrate that any speeds can be used with the same result, as long as A, B and C ignore D (as they would in an empty space where only A, B and C exist, and D is an imagined reference)..and it all comes out the same.

D only exists, however, because of how you set up the conditions. Everyone was in motion, so none have the at rest reference. You set up the question with D as an assumed fourth reference, however D doesn't need to exist at all.

 

[ghwellsjr]

I really think you are having problems stating your questions and examples because you don't understand the difference between speed and acceleration and this makes it impossible for us to answer your questions.

you understand the difference between acceleration and velocity right?

I have to overthrow both of you.

I'm in good company.

Can you demonstrate to us that you know the difference between speed, velocity and acceleration? Otherwise, I would prefer to remain overthrown.

 

[yoelhalb]

I am seeing that none of you understands what I am asking, so let me clarify.
First of all, science is not a religion, and it has to be understood by common sense.
Second of all, the principle of relativity (that objects can allways clain to be at rest) has never been proved and it can't actually be proved.

So now my question is WHAT IS ACCELERATION?
Initially einstein considered accelaration to be clearly in motion, and that's the reason why he has not included it in special relativity, and why he want on to develope general relativity.

However as of the general relativity it is no longer clear that you are moving as you can be at rest in a gravity field.
So we have to take a look on accelaration from two views, and see if it can fit with with common sense.
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?
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).

2) so let's assume that accelaration can not claim to be at rest.
in other words the g-forces (when there is no big mass on the horizon) means accelaration, and the more force you feel the more faster you accelrate.
a) so first we have to understand accordng to what is he moving (and you can't say according to his intial speed, because what if he never had one, and just started wirht accelaration?)
b)also we have now a clear moving body so if two objects are moving away with linear motion and an accelerating body catches up with one of them, this object must also be clearly moving, which is contraditing to the idea of special relativity.

AT EITHER WAY there is another question.
this is clear that his clock his slowing down absulotly, so if he find an object travaling in uniform motion and he finds his clock to be also slow while he then finds the object moving in the opposite direction much older then he clearly knows who is moving, (for exampleint he twin paradox just send along an acelrationg objet and you will know clearly for which of the twins the time slows down).

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

 

[ghwellsjr]

One of the reasons none of us understands what you are asking is because your posts are so full of typos, misspelled words, and bad grammar. Please go back and edit your post and clean it up so that you can read it yourself. Maybe then we will have some hope of communicating.

 

[JesseM]

I am seeing that none of you understands what I am asking, so let me clarify.
First of all, science is not a religion, and it has to be understood by common sense.
Second of all, the principle of relativity (that objects can allways clain to be at rest) has never been proved and it can't actually be proved.

It's meaningless to ask about whether it can be "proved" since it's not a physical claim at all, whether an object is "at rest" or not just depends on your choice of spacetime coordinate system (whether the position coordinate changes at different coordinate times or stays constant), and a coordinate system is just an arbitrary way of assigning labels to different points in spacetime. The physical content of relativity is the claim that the laws of physics will obey the same equations in all the different inertial coordinate systems where light has a coordinate speed of c, and that is something that can be tested by experiment.

So now my question is WHAT IS ACCELERATION?

"Acceleration" in a given coordinate system is just the second derivative of coordinate position with respect to coordinate time, i.e. the rate that the coordinate velocity is changing (with velocity defined as the first derivative of coordinate position with respect to coordinate time). Do you know some basic calculus so you're familiar with the term "derivative" or do you not understand the meaning of this term?

Initially einstein considered accelaration to be clearly in motion

What do you mean by "in motion"? Do you think Einstein would disagree that for any accelerating object, you can always find an inertial coordinate system where it is instantaneously at rest at any given moment?

However as of the general relativity it is no longer clear that you are moving as you can be at rest in a gravity field.

In general relativity we still have the notion of a "local inertial reference frame" in a region of spacetime small enough so that the effects of spacetime curvature can be ignored--are you familiar with the equivalence principle? So at any given point on an object's worldline, there is still an objective truth about whether an object is accelerating or not accelerating relative to a local inertial frame at that point (though of course you can have other non-inertial frames which have different answers to whether the object is accelerating or not--again this is not a disagreement over a real physical question, it is just a different convention about how humans choose to label points in spacetime with position and time coordinates)

1)let's assume that acccelration can claim resting, then we have the follwoing questions.

Are you talking about finding a non-inertial frame where the "accelerating" object (accelerating relative to all inertial frames) is at rest for an extended period of time, or are you talking about finding the inertial frame where the object is instantaneously at rest at one particular instant? Please be specific.

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?

The laws of physics aren't any different for him if he uses an inertial frame where he is instantaneously at rest. If he uses a non-inertial frame, it's true the laws of physics will be different in this frame, but I'm not sure what you mean when you ask "why". If you have two different coordinate systems A and B and you know the equations for the laws of physics in A, then to find the correct equations for the laws of physics in B you take the coordinate transformation between A and B and apply it to the equations of the laws of physics in A to find the equation in terms of the coordinates of B (I can give you a simple Newtonian example if you aren't clear what I mean by this). It so happens that the equations of the laws of physics in our universe have the mathematical property of "Lorentz-invariance", meaning if you have the equation in one inertial frame and apply the Lorentz transformation to find the corresponding equation in a different frame, the equation will be unchanged. These equations would not be invariant under a different coordinate transformation which transforms from an inertial to a non-inertial frame though. No one knows why the equations of the laws of physics are the way they are, this isn't the type of question physics can answer--I guess you'd have to ask God ;) However, given the equation in one inertial frame (determined by experiment), it's a purely mathematical question whether that equation will be invariant under a given coordinate transformation, like the Lorentz transformation or a coordinate transformation into a non-inertial frame.

for gravity we clearly know the answer, mass warps space

What question is that supposed to be an answer to? I don't see how it answers the second part of your previous question, "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?" How does "mass warps space" tell us "why are the laws of physics different for him"? "Mass warps space" is simply a factual description of how the laws of physics work in the presence of mass, it doesn't tell us why the laws of physics should look different in a coordinate system in a region near a massive object than they do in a coordinate system far from any large mass.

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.

The coordinate speed of light is only supposed to be c in an inertial coordinate system where the laws of physics take that special form, in non-inertial coordinate systems there is no law saying that light must move at c, or that massive objects must move slower than c.

(and there is no answer that because of accelaration the laws of physics are different [again why?]

Again, physics can only give you the correct equations, it can never tell you "why" it's those equations and not some others that correctly describe nature, such a why question is totally outside the domain of science (anyone who claims to have an answer must either be a philosopher or a theologian)

because speed of light can never be exceeded).

Yes it can, in non-inertial frames.

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

That doesn't make any sense as an assumption. What would stop us from coming up with a coordinate system where different points on the object's worldline have a constant position coordinate but different time coordinate? Again, coordinate systems are human labeling conventions, nothing can stop us from choosing any convention we like for assigning position and time coordinates to different events.

 

[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?).