Absolute motion's point of reference

[yoelhalb]

According to special relativity acceleration is an absolute motion, so according to what is it moving?

 

[JesseM]

Its velocity is changing relative to all inertial frames (frames where light always has a coordinate speed of c and the equations expressing the laws of physics take a certain special form), although different frames disagree on the value of the velocity at any given instant on the object's worldline.

 

[D H]

According to special relativity acceleration is an absolute motion

Better state: According to relativity, the magnitude of proper acceleration is Lorentz invariant. That doesn't mean the same as saying acceleration is absolute motion.

 

[yoelhalb]

My question is what does he think? what is by him considered rest and according to what is he moving?

 

[JesseM]

My question is what does he think? what is by him considered rest and according to what is he moving?

That depends on what spacetime coordinate system he chooses to use--there is no physical reason that any given observer must use one coordinate system or another, although the usual convention is that each observer uses a coordinate where his coordinate position doesn't change with coordinate time (a coordinate system where he is 'at rest'). For a non-inertial observer there would be many different possible non-inertial coordinate systems where this could be true, which would have different judgments about the velocities of distant objects. And while his own coordinate acceleration would be zero in such a coordinate system, that wouldn't change the fact that he feels G-forces, which would be explained in terms of some sort of "pseudo-gravitational force" in this system (similar to a fictitious force in Newtonian physics), see the equivalence principle analysis from the twin paradox FAQ for details on this.

 

[yoelhalb]

So in other words one who accelerates might claim that he is at rest

 

[yoelhalb]

But if this is true then why does not all physics laws hold true for him?
For example if he throws a ball will it fall right back to him?

 

[JesseM]

So in other words one who accelerates might claim that he is at rest

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).

 

[yoelhalb]

Do you have a good source that explains special relativity in such a level of detail?

 

[ghwellsjr]

Until someone, anyone, accelerates, they can consider themselves to be at rest. When they accelerate for some period of time, they end up with an absolute velocity with respect to their initial rest state before they started to accelerate. The answer to your question is: the absolute motion after acceleration is according to the rest state before acceleration.

 

[yoelhalb]

so if he was never at rest?

 

[ghwellsjr]

Anyone who is not accelerating can consider himself to be at rest. That was the brilliance of Einstein which nobody else was able to consider.

 

[yoelhalb]

If he is accelerating and was never to rest according to what is he accelerating?

 

[yoelhalb]

That depends on what spacetime coordinate system he chooses to use--there is no physical reason that any given observer must use one coordinate system or another, although the usual convention is that each observer uses a coordinate where his coordinate position doesn't change with coordinate time (a coordinate system where he is 'at rest'). For a non-inertial observer there would be many different possible non-inertial coordinate systems where this could be true, which would have different judgments about the velocities of distant objects. And while his own coordinate acceleration would be zero in such a coordinate system, that wouldn't change the fact that he feels G-forces, which would be explained in terms of some sort of "pseudo-gravitational force" in this system (similar to a fictitious force in Newtonian physics), see the equivalence principle analysis from the twin paradox FAQ for details on this.

If so then why does Galileo's ship which is clearly on Earth and feels gravity, how can all physics law's apply to him?

 

[ghwellsjr]

The question that I was answering for you was concerning special relativity. Nobody has been accelerating forever. But if you want to pretend, then you can pick a time that you can call his rest state and consider my answer to apply after that time.

 

[ghwellsjr]

If so then why does Galileo's ship which is clearly on Earth and feels gravity, how can all physics law's apply to him?

You are now asking about General Relativity instead of your original question which was limited to Special Relativity and which I tried to answer for you in a way I thought you could and would understand. Do you understand my answer to your original question?

 

[yoelhalb]

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?

 

[JesseM]

Do you have a good source that explains special relativity in such a level of detail?

I don't think any of my introductory SR texts goes into much detail on the issue of accelerating frames, but I often find one can find interesting-looking textbooks by entering keywords into google books...with keywords "relativity" + "accelerating" + "frame" I found http://books.google.com/books?id=LyVxtGv1RwEC&lpg=PA83&dq=relativity%20accelerating%20frame&pg=PA81#v=onepage&q=relativity%20accelerating%20frame&f=false , Dynamics and Relativity, and Explorations in mathematical physics: the concepts behind an elegant language (which has a very nice discussion of the derivation of Rindler coordinates, the most common type of accelerated frame, on p. 240), for example.

 

[yoelhalb]

No.
A person has to move according to something but now there is n o point of reference.

 

[JesseM]

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?

Just by analyzing things from the perspective of the inertial frame where A was at rest as B and C moved away. If you choose to use a non-inertial frame where C is at rest, then in this frame A was not at rest.

 

[yoelhalb]

Just by analyzing things from the perspective of the inertial frame where A was at rest as B and C moved away. If you choose to use a non-inertial frame where C is at rest, then in this frame A was not at rest.

Let's put it differently.
the same example again but n ow together with all of them also started D in the direction of B with the same acceleration of C in A's direction will he catch up with B?

 

[yoelhalb]

Just by analyzing things from the perspective of the inertial frame where A was at rest as B and C moved away. If you choose to use a non-inertial frame where C is at rest, then in this frame A was not at rest.

So how will C ever meet him if he moved away?

 

[ghwellsjr]

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?

Your "similar question" can be interpreted many ways. I will try to interpret it the way I think you meant which is:

A, B and C are at rest with respect to each other. A and B accelerate together for awhile and then stop accelerating so that they are moving at a constant speed with respect to their initial rest condition and to C's current rest condition. Then C accelerates at a lower acceleration and as he approaches A (why is B in this?) he decelerates in such a way that he ends up at the same speed and in the same location as A. Now A, B and C are moving together with respect to their initial, at rest, condition.

If you didn't mean it this way, you will have to explain what you did mean in more detail.

Also, I don't know why you feel the need to ask "How can we claim that A was at rest?" As I said earlier, anyone who is not accelerating can claim to be at rest. This was the brilliance of Einstein. Don't feel bad if it doesn't seem clear to you, it didn't seem clear to anyone else except Einstein when he said it.

 

[JesseM]

So how will C ever meet him if he moved away?

Because in a non-inertial frame of C, A would move away but then move back towards C.

 

[JesseM]

Let's put it differently.
the same example again but n ow together with all of them also started D in the direction of B with the same acceleration of C in A's direction will he catch up with B?

Are you assuming B and A both go in opposite directions at the same speed in the frame where all four were originally at rest next to each other? Then C accelerates in the direction of A, D accelerates in the same way but in the direction of B? In this case, yes, B should catch up with B and C should catch up with A.

 

[ghwellsjr]

Let's put it differently.
the same example again but n ow together with all of them also started D in the direction of B with the same acceleration of C in A's direction will he catch up with B?

I'm afraid you're going to have to be much more precise in order to get a reasonable answer. You have now introduced D doing something like what B was doing and I don't even know why you had B in the first example.

You also stated in your first example that you were asking a similar question but I don't see what it is similar to or why you think it is similar. Please provide more details.

 

[yoelhalb]

Because in a non-inertial frame of C, A would move away but then move back towards C.

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)

 

[yoelhalb]

Sorry the second question can be answered because he needs to accelrate with a speed higher then 100 mph.
But what about the first question?

 

[JesseM]

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).

Do you mean each is moving at 100 mph in the other's rest frame, or do you mean that in the frame where both were originally at rest (the frame of the ocean) they are both moving at 100 mph in opposite directions? It doesn't really matter since it will only affect the specific numbers and not the overall analysis, so I'll assume the second one for now...

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?).

If C accelerates in the direction of A, he'll be closer to A than to B, although the distance from A to C is still increasing rather than decreasing (it's just not as increasing as fast as the distance from B to C)

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)

If C keeps accelerating by 1 mph every hour in the ocean frame, then eventually C's speed will exceed A's speed of 100 mph in this frame. At that point, in A's inertial rest frame, C should start moving back towards A.

 

[yoelhalb]

If C accelerates in the direction of A, he'll be closer to A than to B, although the distance from A to C is still increasing rather than decreasing (it's just not as increasing as fast as the distance from B to C)

Again ABC are togheter.

then A <-----------> B are moving apart with 100 mph.
C also starts accelerating to the left.
because he claims that he is accarating will he be to the left of A or B?

 

[yoelhalb]

Lets ask siimilar.
When C will meet A and he sees his time and calculates it according to his time (which has clearly been slowed down), will he find A's time to be slowed down?
And if c then accelrates till he meets B what will he find his clock to be?
(clearly he will find one of them to be slowed down, but which one?)

 

[yoelhalb]

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 imagine one in Earth (maybe even in Galileo's ship, making the question even worse), he sees the entire universe (10 billion light years) moving around every day, clearly more then the speed of light, who would he explain that?

 

[yoelhalb]

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?
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.
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?

 

[ghwellsjr]

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?

Sorry the second question can be answered because he needs to accelrate with a speed higher then 100 mph.
But what about the first question?

Again ABC are togheter.

then A <-----------> B are moving apart with 100 mph.
C also starts accelerating to the left.
because he claims that he is accarating will he be to the left of A or B?

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.

Your last question doesn't have enough information for us to give a meaningful answer. It seems obvious that the answer couldn't be "to the left of B" but since you asked the question this way, you must be thinking of something entirely differently than what your question seems to imply. I have no idea what.

 

[JesseM]

Again ABC are togheter.

then A <-----------> B are moving apart with 100 mph.

Again, is 100 mph a relative velocity or each one's velocity in the (ocean) frame where they were originally at rest relative to each other? In the first case, of course that just means that each one is moving at 50 mph in the ocean frame (unless you want them to have different speeds relative to the ocean frame). Either way, can we assume that C has an initial velocity of 0 relative to the ocean frame before he starts accelerating?

C also starts accelerating to the left.
because he claims that he is accarating will he be to the left of A or B?

What do you mean that C "claims he is accelerating"? In C's non-inertial rest frame he has no coordinate acceleration. Again, the claim the acceleration is objective is that all inertial frames agree whether something is accelerating, and any object accelerating relative to inertial frames will feel G-forces even if it isn't accelerating in its own non-inertial frame.

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)

 

[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.