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yoelhalb

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In summary, according to special relativity, C would feel an acceleration due to its motion relative to A and B, but according to general relativity, C would not feel an acceleration because it is moving with a uniform velocity relative to all inertial frames.

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yoelhalb

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JesseM

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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 said:According to special relativity acceleration is an absolute motion

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yoelhalb

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JesseM

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That depends on what spacetime coordinate system he chooses to use--there is no physical reason that any given observeryoelhalb said:

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yoelhalb

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

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yoelhalb

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For example if he throws a ball will it fall right back to him?

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JesseM

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

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yoelhalb

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

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ghwellsjr

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yoelhalb

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so if he was never at rest?

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ghwellsjr

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yoelhalb

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

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yoelhalb

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JesseM said:That depends on what spacetime coordinate system he chooses to use--there is no physical reason that any given observermustuse 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?

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ghwellsjr

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ghwellsjr

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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 said: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?

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yoelhalb

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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?

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JesseM

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

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yoelhalb

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No.

A person has to move according to something but now there is n o point of reference.

A person has to move according to something but now there is n o point of reference.

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JesseM

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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 said:

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?

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yoelhalb

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JesseM said: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?

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yoelhalb

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So how will C ever meet him if he moved away?JesseM said: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.

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ghwellsjr

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yoelhalb said:

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.

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JesseM

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Because in a non-inertial frame of C, A would move away but then move back towards C.yoelhalb said:So how will C ever meet him if he moved away?

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JesseM

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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.yoelhalb said: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?

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ghwellsjr

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yoelhalb said: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.

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yoelhalb

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JesseM said: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)

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yoelhalb

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But what about the first question?

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JesseM

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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...yoelhalb said: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).

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)yoelhalb said: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 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 said: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)

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yoelhalb

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Again ABC are togheter.JesseM said: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)

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?

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yoelhalb

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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?)

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yoelhalb

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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?JesseM said: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 isinstantaneouslyat rest).

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yoelhalb

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so why isn't he at rest?JesseM said: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 isinstantaneouslyat 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?

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ghwellsjr

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yoelhalb said:

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?

yoelhalb said:

But what about the first question?

yoelhalb said: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.

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JesseM

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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?yoelhalb said:Again ABC are togheter.

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

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 allyoelhalb said:C also starts accelerating to the left.

because he claims that he is accarating will he be to the left of A or B?

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*t

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