When will the person at point B see train2 and why?

[dwspacetime]

hello everyone i am new here. i have been to some websites about relativity but still kind of suspicious about it. here i have a problem. could anyone give me a mathematical answer. by the way this is not a homework. i am not a student.

say we have a railroad from point A to point B and the length btw A and B is L=ct. c is the speed of light. now we have 2 trains, train1 and train2 pass point A towards point B at midnight or at time 0 oclock. train1 travels at v=c/2 relative to point A and train2 travels at v=3c/4 relative to train A. if there is a person at point B, when will he see train2. and why? thanks.

 

[Al68]

hello everyone i am new here. i have been to some websites about relativity but still kind of suspicious about it. here i have a problem. could anyone give me a mathematical answer. by the way this is not a homework. i am not a student.

say we have a railroad from point A to point B and the length btw A and B is L=ct. c is the speed of light. now we have 2 trains, train1 and train2 pass point A towards point B at midnight or at time 0 oclock. train1 travels at v=c/2 relative to point A and train2 travels at v=3c/4 relative to train A. if there is a person at point B, when will he see train2. and why? thanks.

Assuming the person is at rest with the track, and L is the proper distance between points A and B, train2 will reach him at L/0.909c. The velocity of train2 relative to the track is (v1+v2)/(1+v1v2/c^2)=0.909c.

If, for example, L= 1 light second, then train2 will reach him when his clock reads 1.1 seconds.

 

[dwspacetime]

thanks AL68. how did you get the equation. if you know a link please let me know. but i am still confused about time travel. people say if someone travels very fast away from earth, when he comes back he will be younger than his twin brother. but his twin brother also travels very fast away from his spaceship on the earth. why not his twin brother is younger?

 

[JesseM]

thanks AL68. how did you get the equation. if you know a link please let me know. but i am still confused about time travel. people say if someone travels very fast away from earth, when he comes back he will be younger than his twin brother. but his twin brother also travels very fast away from his spaceship on the earth. why not his twin brother is younger?

The time dilation equation only works in inertial frames, that is, the frames of observers who don't accelerate...whichever twin turns accelerates to move toward his brother after they've been moving apart for a while, he didn't remain in one inertial frame so he can't assume that his twin's aging will be given by plugging his relative velocity at different moments into the time dilation formula, and in fact the twin that accelerated will always be the one that's younger when the two reunite. Lots of different perspectives on this problem can be found at this twin paradox page. And for a good intro text on relativity in general, you could read http://www.oberlin.edu/physics/dstyer/Einstein/SRBook.pdf .

 

[dwspacetime]

thanks JesseM

sorry you said one of them will be younger? i don't understand. both of them accelerates in the exact same way to and away from each other in opposite directions i think. my intuition just tells me something is wrong here which i don't what it is. i will read more. is there any prove the speed of light is always c nomatter what?

 

[Al68]

thanks AL68. how did you get the equation. if you know a link please let me know. but i am still confused about time travel. people say if someone travels very fast away from earth, when he comes back he will be younger than his twin brother. but his twin brother also travels very fast away from his spaceship on the earth. why not his twin brother is younger?

http://en.wikipedia.org/wiki/Special_relativity. Look under "Composition of Velocities".

JesseM answered your last question.

 

[Al68]

thanks JesseM

sorry you said one of them will be younger? i don't understand. both of them accelerates in the exact same way to and away from each other in opposite directions i think.

The standard SR equations are only valid in inertial reference frames. The Earth twin is stationary in an (approximately) inertial reference frame, while the ship's twin is not. Simply put, an inertial reference frame is one in which if you let an object go, it will remain stationary in the frame if no forces act on it. This is not true of the ship's accelerated frame. So while it is true that the Earth had coordinate acceleration relative to the reference frame in which the ship is "stationary", Earth had no proper acceleration, ie in any inertial reference frame. Relative to any inertial reference frame, the ship, but not earth, accelerated.

is there any prove the speed of light is always c nomatter what?

No. But there is overwhelming evidence that it's always c relative to any inertial reference frame.

 

[JesseM]

thanks JesseM

sorry you said one of them will be younger? i don't understand. both of them accelerates in the exact same way to and away from each other in opposite directions i think.

The initial acceleration is irrelevant to the problem, it makes no difference whether the initial departure point consists of them starting out at rest next to each other and then accelerating away, or just crossing paths while moving at constant velocity. What's important is which one accelerates to turn around after they have been moving apart for awhile after the departure point, so that the distance between them begins to decrease after it has been increasing for a while, and eventually they can reunite and compare ages.

The fact that the one whose worldline contains a "bend" midway between the departure point and the reunion point always ends up being younger is closely how it works with distances along spatial paths, where if you have two paths between a pair of points in 2D space, and one is a straight line between those points while the other is bent, then the bent path will always have a greater length since a straight line in 2D is the shortest distance between points. Similarly, in spacetime a "straight line" (constant velocity) path between two events always has the greatest amount of "proper time" (time as measured by a clock that moves along that path). I expanded on this analogy a bit in this thread:

I think it's best to think in terms of a spacetime diagram with time on one axis and space on another, so you can see each twin's worldline as a path through spacetime. Here's one from the twin paradox page, with time as the vertical axis and space as the horizontal one, drawn from the perspective of the frame where the Earth twin (Terence) is at rest so his position in space doesn't change over time in this frame:

You can see that the length of the two paths is different--if these were ordinary paths in space, and you drove along each one with an odometer running, then even if the two cars had the same odometer reading when they departed from the point at the bottom of the diagram, they would have different odometer readings when they reunited at the top. In ordinary space, if a car travels in a straight line between two points with a separation $$\Delta x$$ along the horizontal x-axis, and separation $$\Delta y$$ along the vertical y-axis, then the distance traveled between the points (the amount the odometer reading will increase) is just given by the pythagorean theorem, it's $$\sqrt{\Delta x^2 + \Delta y^2}$$. In relativity clocks measure time elapsed along paths through spacetime in much the same way that odometers measure distance elapsed along paths through space, but the formula is slightly different--if a clock travels along a straight path between two points in spacetime (like Terence's path above, or like Stella's path between the 'start event' and the beginning of the 'turnaround'), and the two points in spacetime have a spatial separation of $$\Delta x$$ and a time separation of $$\Delta t$$, then the amount the clock will increase is given by $$\sqrt{\Delta t^2 - (1/c^2)*\Delta x^2}$$ (if you use a system of units where c=1, like light-years for distance and years for time, then this can just be written as $$\sqrt{\Delta t^2 - \Delta x^2}$$, which looks almost like the Pythagorean formula except for the minus sign). Because this formula is a little different than the Pythagorean formula, it actually works out that a straight-line path between two points in spacetime (like Terence's between the start event and the return event) will always correspond to a greater amount of clock time elapsed than a non-straight path between the same two points (like Stella's path), unlike with spatial paths where a straight-line path between two points in space always has a shorter distance than a non-straight path between the same points (because in Euclidean geometry a straight line is the shortest distance between points).

But aside from that difference, it's closely analogous. The reason the traveling twin ages less has to do with the overall shape of the paths, you can't pinpoint the moment where the Earth twin ages more, just like with spatial paths you can't pinpoint a particular section of the bent path that the extra distance is accumulated on the odometer. And just as different frames can disagree on which twin is aging more during a particular phase of the trip like the outbound leg, it's also true that different Cartesian coordinate systems in 2D space could disagree on which car had accumulated a greater odometer reading at a particular height along the y-axis. For example, suppose in the above diagram we have the y-axis oriented vertically and the x-axis oriented horizontally--in this case, if we pick the y-coordinate of the turnaround, Stella's car will have accumulated a greater odometer reading at that y-coordinate than Terence's car. But now suppose we orient the y-axis so it's parallel to the outbound leg of Stella's trip (which is equivalent to keeping the y-axis vertical and rotating the diagram so that the outbound leg of Stella's trip is vertical while Terence's is at an angle)--in this case, at the y-coordinate of the turnaround, it will be Terence who's accumulated a greater odometer reading than Stella. So until the two cars reunite at a common location, there is no objective frame-independent truth about which has accumulated a greater odometer reading at a given y-coordinate, just like in relativity there is no objective frame-independent truth about which clock has accumulated a greater amount of time at a given t-coordinate.

is there any prove the speed of light is always c nomatter what?

Depends what you mean by that. In SR the coordinates of different inertial frames are related by the "Lorentz transformation", which says that if an arbitrary event has coordinates x,t in one inertial frame, then the coordinates x',t' of the same event in a different inertial frame moving at speed v relative to the first will be:

$$x' = \gamma * (x - vt)$$
$$t' = \gamma * (t - vx/c^2)$$
with $$\gamma = 1/\sqrt{1 - v^2/c^2}$$

It's possible to prove that, given this coordinate transformation, if something has a coordinate speed of c in one frame, it will have a coordinate speed of c in any other frame. However, it's another matter to demonstrate that if different observers construct physical coordinate systems out of grids and rulers and clocks at rest relative to themselves, then the readings on one physical coordinate system will be related to the readings on another by this transformation. It can be shown that this will be true if all the fundamental laws of physics (which govern the behavior of physical rulers and clocks along with everything else) have a property called "Lorentz-symmetry", which means the equations are such that if you write them down in one frame and then do a Lorentz transformation on them to see what the correct equations would be in another frame, the equations look exactly the same in both frames; so far, all the fundamental laws of physics which have been discovered so far do have this property. Also, tests which have tried to look for variations in the speed of light when it is measured in different directions (and measured at different points in the Earth's orbit) have failed to find any such variations. All of this is empirical evidence though, there's no way to prove relativity must be correct in a non-empirical way (the same is true of any other statement about the laws of physics of course).

 

[dwspacetime]

wow thank you guys. just came back from gym.

 

[dwspacetime]

i have another question before i read on. sorry if the answer is in the links you told me. say there are only two balls in the universe, ballA and ballB with nothing. suddenly two of them accelerat away from each other. how can you tell which one is accelerating. i mean which one gets the force from God. if you say ballA is at rest, to me ballA must be in a system that is at rest and there must be no relative movement between ballA and the system. but what is the system? the empty space? say i am ballA or ballB. do i feel a force that pushs me to accelerate? but what does that mean feeling a force?

 

[JesseM]

i have another question before i read on. sorry if the answer is in the links you told me. say there are only two balls in the universe, ballA and ballB with nothing. suddenly two of them accelerat away from each other. how can you tell which one is accelerating. i mean which one gets the force from God. if you say ballA is at rest, to me ballA must be in a system that is at rest and there must be no relative movement between ballA and the system. but what is the system? the empty space? say i am ballA or ballB. do i feel a force that pushs me to accelerate? but what does that mean feeling a force?

Think of what happens when you accelerate in a car--you get pushed back against the seat. Acceleration causes you to experience G-forces, even in empty space free of any actual gravity. So, whichever ball accelerates, someone traveling along with it will experience G-forces, while someone traveling along with a ball that doesn't accelerate will feel weightless in SR.

 

[dwspacetime]

ok. same situation only 2 balls in the universe. they remain relatively motionless. you think they are at rest? wait. God can make them both accelerating in the same manner. but they are accelerating away from what? so my question is is there an system independent of matter. or the empty space is matter.

 

[JesseM]

ok. same situation only 2 balls in the universe. they remain relatively motionless. you think they are at rest? wait. God can make them both accelerating in the same manner. but they are accelerating away from what? so my question is is there an system independent of matter. or the empty space is matter.

Acceleration doesn't need to be "away from" anything physical, even with only a single ball in flat spacetime, it's defined as accelerating if the laws of physics as seen by an observer on the ball would be different from those that apply in inertial reference frames (including the fact that an accelerometer which measures G-forces should always give a reading of zero when it's at rest in an inertial frame).

 

[dwspacetime]

well. i have to say i am not satisfied with your answer this time JesseM. I will put this question aside for now. if there is one ball only in the space, when its speed changes from 0 to none 0. it is moving away from a system whose v=0 obviously. the system may not have anything physical. well it does not make 100% sense to me. we may not have an answer now or we may have an answer somewhere already.

 

[JesseM]

well. i have to say i am not satisfied with your answer this time JesseM. I will put this question aside for now. if there is one ball only in the space, when its speed changes from 0 to none 0. it is moving away from a system whose v=0 obviously. the system may not have anything physical. well it does not make 100% sense to me. we may not have an answer now or we may have an answer somewhere already.

If it helps, you can talk about various inertial coordinates in empty space even if there are no physical objects at rest in these systems. So if the ball changes velocity, there will have been some inertial frame where it was previously at rest but it is now moving. On the other hand, there will be a different inertial frame where it was initially in motion, and the change in velocity brought it to rest. In relativity the laws of physics work exactly the same in all inertial frames so there is no basis for preferring anyone frame over the others, which means there is also no notion of absolute rest or absolute motion, all statements about rest vs. motion are relative to an arbitrary choice of reference frame.

 

[dwspacetime]

i think i understand what you said. my concern if the space itself is matter. in a absolute empty space with nothingness in it it seems there is no differece of anywhere in the space. and it is emptyness anywhere. if a ball moves from v=a to v=b. its position changes from where it was when v=a to where its v=b. the position when its v=a can't be anywhere like a space with nothing in it. it must be that particular location and this should not change if we take out the ball out of the space if we can.

if we observe the only 2 balls in the space accelerate away from each other and if we for some reason say one is at rest or in a constant speed while the other is accelerating. there must be a difference btw the way the balls change their positions. but to what reference frame? if we use either of the ball as reference frame we can't tell which one is accelerating. so the referenc frame must not be any of the balls but something independent of them . what is that? the nothingness space? you see my point?

 

[atyy]

but to what reference frame? if we use either of the ball as reference frame we can't tell which one is accelerating. so the referenc frame must not be any of the balls but something independent of them . what is that? the nothingness space? you see my point?

JesseM said with respect to an inertial frame.

I don't think it's too cheating to think of an inertial frame as a system of rulers and clocks "stationary" wrt to each other, where "stationary" is defined by some conventions involving light being sent back and forth from different points on the various rulers.

Less cheating is to say that to define an inertial frame we use light - the electromagnetic field - which *is* a form of "matter" - so an inertial frame is defined wrt to "matter" and not "nothingness".

 

[dwspacetime]

that is a very good book. i mean relativity for questioning mind. i am halfway through. just finished chapter 9. do they teach this in high school. i didnt learn it when i was in high school.

 

[Cleonis]

But to what reference frame? if we use either of the ball as reference frame we can't tell which one is accelerating. so the referenc frame must not be any of the balls but something independent of them . what is that? the nothingness space? you see my point?

Your question is valid.

The thing is, your question comes from a widespread deficiency in special relativity introductions. In my opinion all introductions to special relativity are wrongfooting the reader. (Yeah, that's a big claim, let's see if I can back that up.)

By implication relativistic physics attributes physical properties to space. (Well, the arena of relativistic physics is referred to as spacetime, but that's not my emphasis now.) By implication relativistic physics assumes that any matter or energy located in space is subject to the phenomenon of inertia. Since inertial mass cannot be its own source of inertia the existence of inertia must be a property of space. Peculiarly, this implicit assumption is rarely or never made explicit. In fact, many introductions cloud the issue. Many introductions shift the attention away from space, by emphasizing the aspect that 'Special relativity has done away with the ether'.

Actually, what special relativity abandoned was the following aspect of ether theories: in ether theories it is assumed that objects located in the ether have particular velocity to the ether. One may be unable to determine that velocity, but it is assumed that 'velocity relative to the ether' does exist. What Special relativity has abandoned precisely is the concept of attributing a velocity vector to ether, or equivalently, what is abandoned is the concept of a velocity vector for velocity of an object relative to the ether.

The twin scenario illustrates the things that special relativity does use: the traveling twin travels a longer pathlength, which corresponds to a smaller amount of proper time elapsing. This difference in pathlength effect is a property of space!

If you are pushed by something pushing against you, or you are pulled by some string, then you can certainly feel that, and an accelerometer will give a reading. What is sensed is acceleration with respect to space. Special relativity does use acceleration vectors that represent acceleration relative to space There is a crucial distinction here; relativistic physics has - as a matter of principle - no such thing as a velocity vector relative to space. What relativistic physics does have (as a fundamental necessity) is an acceleration vector relative to space

The contrast with classical physics couldn't be bigger. In classical physics velocity is a derivative of position, and acceleration is a derivative of velocity; not just mathematicaly, but also in physical interpretation. Not so in relativistic physics. While you cannot have velocity relative to spacetime, you can and do have acceleration relative to spacetime.

The problem with introductions to special relativity is that the authors are leaving out essential information. All novices are puzzled and start asking the same questions that you do. You have been wrongfooted.Cleonis

 

[atyy]

Your question is valid.

The thing is, your question comes from a widespread deficiency in special relativity introductions. In my opinion all introductions to special relativity are wrongfooting the reader. (Yeah, that's a big claim, let's see if I can back that up.)

By implication relativistic physics attributes physical properties to space. (Well, the arena of relativistic physics is referred to as spacetime, but that's not my emphasis now.) By implication relativistic physics assumes that any matter or energy located in space is subject to the phenomenon of inertia. Since inertial mass cannot be its own source of inertia the existence of inertia must be a property of space. Peculiarly, this implicit assumption is rarely or never made explicit. In fact, many introductions cloud the issue. Many introductions shift the attention away from space, by emphasizing the aspect that 'Special relativity has done with the ether'.

Actually, what special relativity abandoned was the following aspect of ether theories: in ether theories it is assumed that objects located in the ether have particular velocity to the ether. One may be unable to determine that velocity, but it is assumed that 'velocity relative to the ether' does exist. What Special relativity has abandoned precisely is the concept of attributing a velocity vector to ether, or equivalently, what is abandoned is the concept of a velocity vector for velocity of an object relative to the ether.

The twin scenario illustrates the things that special relativity does use: the traveling twin travels a longer pathlength, which corresponds to a smaller amount of proper time elapsing. This difference in pathlength effect is a property of space!

If you are pushed by something pushing against you, or you are pulled by some string, then you can certainly feel that, and an accelerometer will give a reading. What is sensed is acceleration with respect to space. Special relativity does use acceleration vectors that represent acceleration relative to space There is a crucial distinction here; relativistic physics has - as a matter of principle - no such thing as a velocity vector relative to space. What relativistic physics does have (as a fundamental necessity) is an acceleration vector relative to space

The contrast with classical physics couldn't be bigger. In classical physics velocity is a derivative of position, and acceleration is a derivative of velocity; not just mathematicaly, but also in physical interpretation. Not so in relativistic physics. While you cannot have velocity relative to spacetime, you can and do have acceleration relative to spacetime.

The problem with introductions to special relativity is that the authors are leaving out essential information. All novices are puzzled and start asking the same questions that you do. You have been wrongfooted.


Cleonis

Nope.

 

[matheinste]

Your question is valid.

The thing is, your question comes from a widespread deficiency in special relativity introductions. In my opinion all introductions to special relativity are wrongfooting the reader. (Yeah, that's a big claim, let's see if I can back that up.)

The contrast with classical physics couldn't be bigger. In classical physics velocity is a derivative of position, and acceleration is a derivative of velocity; not just mathematicaly, but also in physical interpretation. Not so in relativistic physics. While you cannot have velocity relative to spacetime, you can and do have acceleration relative to spacetime.

The problem with introductions to special relativity is that the authors are leaving out essential information. All novices are puzzled and start asking the same questions that you do. You have been wrongfooted.


Cleonis

Do you mean all introductions to special relativity or just the ones you have read.

Isn't acceleration absolute?

Matheinste.

 

[Al68]

if we observe the only 2 balls in the space accelerate away from each other and if we for some reason say one is at rest or in a constant speed while the other is accelerating. there must be a difference btw the way the balls change their positions. but to what reference frame? if we use either of the ball as reference frame we can't tell which one is accelerating.

Sure you can. If you use an accelerating object as the frame origin, it will be an accelerated reference frame, and will show itself as such by the presence of fictional forces.

For example, if there are two cars, one accelerating away from the other, fictional G-forces make it obvious which one has proper acceleration.

 

[JesseM]

that is a very good book. i mean relativity for questioning mind. i am halfway through. just finished chapter 9. do they teach this in high school. i didnt learn it when i was in high school.

Don't think it's normally taught in high schools, I didn't have a relativity class until college. "Relativity for the Questioning Mind" looks like a great intro to the subject based on the parts I looked at, glad you're enjoying it--you can thank flatearther for discovering it, I only heard about it thanks to flatearther's mention at the end of this thread.

 

[Cleonis]

Do you mean all introductions to special relativity or just the ones you have read.

I'm in the habit of glancing through any introduction that I encounter, over the course of that I have framed the hypothesis that all introductions share the defiency that I refer to. In general the mindset that I encounter is one of avoiding to write in terms of properties of space.

I started to understand relativistic physics only when I moved on to the work of historians of science such as John Stachel, John Norton, Michel Janssen, and a number of others working in the same field. They are authors who were originally trained as physicists, but later shifted to philosophy of physics. They are, or have been, members of the board of editors of the 'Einstein papers project', the exhaustive publication of Einstein's writings (ncluding Einstein's scribbled investigation notes.) They have relativistic physics for breakfast, lunch and dinner. As historians of science, their special interest is the development of fundamental ideas.

Isn't acceleration absolute?

In physics, the word 'absolute' is used in a number of meanings.
In terms of special relativity spacetime is a homogenous, isotropic structure, that is immutable. In terms of special relativity acceleration as registered by accelerometers is acceleration with respect to spacetime.

For many people the expression 'absolute' is associated with the concept of an absolute space with an assumption that absolute position in space exists.
To avoid that association I don't want to use the word 'absolute'. It's probably sufficient to define acceleration operationally, and just locally, as 'that which is registered with an accelerometer'.

Cleonis

 

[matheinste]

In terms of special relativity acceleration as registered by accelerometers is acceleration with respect to spacetime.

Cleonis

I don't believe novices like myself are being mislead by most authors of introductory SR texts . They may not go into certain aspects too deeply but this is probably because for beginers, such as me, it takes some time and a lot of wider reading before we even realize that there are philosophical depths to the fundamentals of the workings and structure of space and time, even when considered seperately let alone when combined into spacetime. As you will know, there are many authors such as Weyl, Eddington, Reichenbach and Grunbaum who go much more deeply into the fundamental concepts. If these are misleading then I am at a loss as to where to turn for enlightenment.

That said, the above description of acceleration is something I do not understand.

Matheinste.

 

[atyy]

I started to understand relativistic physics only when I moved on to the work of historians of science such as John Stachel, John Norton, Michel Janssen, and a number of others working in the same field. They are authors who were originally trained as physicists, but later shifted to philosophy of physics. They are, or have been, members of the board of editors of the 'Einstein papers project', the exhaustive publication of Einstein's writings (ncluding Einstein's scribbled investigation notes.) They have relativistic physics for breakfast, lunch and dinner. As historians of science, their special interest is the development of fundamental ideas.

Hole problem?

 

[Al68]

In terms of special relativity acceleration as registered by accelerometers is acceleration with respect to spacetime.

That would be new to me. Accelerometers measure applied force, and relate it to proper acceleration. Proper acceleration is the coordinate acceleration relative to an inertial reference frame, not "spacetime".

 

[JesseM]

By implication relativistic physics attributes physical properties to space. (Well, the arena of relativistic physics is referred to as spacetime, but that's not my emphasis now.) By implication relativistic physics assumes that any matter or energy located in space is subject to the phenomenon of inertia. Since inertial mass cannot be its own source of inertia the existence of inertia must be a property of space.

Why do you say "inertial mass cannot be its own source of inertia"? What do you even mean by the words "source of inertia"? Physics only tells us how things behave in a quantitative sense (like the fact that objects accelerate differently when subjected to the same force depending on their inertial mass), not why they behave that way (unless it's explaining aspects of one theory in terms of a more fundamental theory, but then the behavior of things in the more fundamental theory is left unexplained).

If you are pushed by something pushing against you, or you are pulled by some string, then you can certainly feel that, and an accelerometer will give a reading. What is sensed is acceleration with respect to space. Special relativity does use acceleration vectors that represent acceleration relative to space There is a crucial distinction here; relativistic physics has - as a matter of principle - no such thing as a velocity vector relative to space. What relativistic physics does have (as a fundamental necessity) is an acceleration vector relative to space

Both velocity and acceleration are defined relative to inertial frames, not "space".

The contrast with classical physics couldn't be bigger. In classical physics velocity is a derivative of position, and acceleration is a derivative of velocity; not just mathematicaly, but also in physical interpretation.

What does "also in physical interpretation" mean? What would it mean for velocity to be a derivative of position only mathematically and not in physical interpretation?

Not so in relativistic physics.

Mathematically it is so--coordinate velocity is the derivative of coordinate position, and coordinate acceleration is the derivative of coordinate velocity (and proper acceleration at a given point on an object's worldline is just the coordinate acceleration in the object's instantaneous inertial rest frame at that point, which will match the reading on a co-moving accelerometer at that point). Do you agree that in the mathematical sense this is as true in relativity as it is in classical physics? If you do agree, are you saying that even though it's true mathematically, it's not true "in physical interpretation" in relativity? See my above question about the meaning of that phrase.

 

[Cleonis]

[...] coordinate velocity is the derivative of coordinate position, and coordinate acceleration is the derivative of coordinate velocity (and proper acceleration at a given point on an object's worldline is just the coordinate acceleration in the object's instantaneous inertial rest frame at that point, which will match the reading on a co-moving accelerometer at that point). Do you agree that in the mathematical sense this is as true in relativity as it is in classical physics? If you do agree, are you saying that even though it's true mathematically, it's not true "in physical interpretation" in relativity? [...]

I find this a very interesting subject, and worth a thread of its own. I've decided to transfer this discussion to a new thread, with the name: "Acceleration and velocity: Newtonian versus relativistic interpretation."

Cleonis

 

[Cleonis]

Both velocity and acceleration are defined relative to inertial frames, not "space".

Well, in this case the distinction is moot.

No matter what word one happens to use, in both cases the concept must be defined operationally, and the operational definition is identical for both cases.

When I say <<I'm accelerating with a G-count of 1 with respect to the local inertial frame>>, then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.

When I say <<I'm accelerating with a G-count of 1 with respect to space>> then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.


In special relativity the fundamental object of consideration is Minkowski spacetime; special relativity explores the ramifications of Minkowski spacetime geometry. In these explorations the concept of 'frame of reference' is a tool, not an object of the theory.

Cleonis

 

[A.T.]

In special relativity the fundamental object of consideration is Minkowski spacetime; special relativity explores the ramifications of Minkowski spacetime geometry. In these explorations the concept of 'frame of reference' is a tool, not an object of the theory.

Well, that distinction is moot. Minkowski spacetime and frames of reference are both mathematical tools.

 

[matheinste]

When I say <<I'm accelerating with a G-count of 1 with respect to the local inertial frame>>, then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.

When I say <<I'm accelerating with a G-count of 1 with respect to space>> then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.


Cleonis

I hate to spoil a discussion by bringing logic into it but these statements imply that spacetime is the local inertial frame. As there are an infinity of "local inertial frames" then we have an infinity of background spacetime structures. So their is no preferred or absolute spacetime to which we can refer acceleration, but we already knew that.

Matheinste.

 

[JesseM]

Well, in this case the distinction is moot.

No matter what word one happens to use, in both cases the concept must be defined operationally, and the operational definition is identical for both cases.

When I say <<I'm accelerating with a G-count of 1 with respect to the local inertial frame>>, then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.

Yes. Another way to define what you mean experimentally would be to say that if you are moving past an inertial coordinate grid made out of physical rulers and clocks, which can be used to define your position as a function of time x(t) in this frame based on a series of local measurements on the grid, then at the moment the first derivative of x(t) is zero (meaning you are temporarily at rest relative to the grid), the second derivative of x(t) is 1G.

When I say <<I'm accelerating with a G-count of 1 with respect to space>> then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.

If you want to define it that way, fine. But unlike with movement relative to an inertial frame, "acceleration relative to space" is not accepted terminology with an accepted meaning in physics, so it wasn't clear what you meant before you gave this definition. And it's also not clear if you associate some extra conceptual baggage with the phrase beyond the experimental definition you've given; any implications of "acceleration with respect to space" that go beyond the standard implications of "nonzero proper acceleration" might be ones that not all physicists would accept.

 

[Cleonis]

[...] And it's also not clear if you associate some extra conceptual baggage with the phrase beyond the experimental definition you've given; [...]

Well, the particular phrasing you refer to was written for dwspacetime, who started the thread. The phrasing was intended to be tangible.

In your reply you gave a phrasing that was designed to eliminate all ambiguity. Unfortunately, that level of precision makes it sound like http://en.wikipedia.org/wiki/Legal_writing#Legalese".

In an essay for an audience of specialists I would push for utmost precision, but not in a posting that primarily needs to be accessible.

When I read someone else's postings I don't attribute extra conceptual baggage to the other person, at least that is what I try. If I err in interpretation I strive to err on the side of caution.

Cleonis

 

[dwspacetime]

i do see both sides using legalese. :)

i did some search online. there is a university website about how to define the inertial frame which i don't remember what it is. there are some nonsense in it. but regardless, an inertial frame or a non-inertial frame or any kind of reference frame is an arbitraty coordinate system for us to measure the movement in spacetime. the movement happens in spacetime but not a reference frame. i use a ruler to measure my table to be 3.281ft long means my table takes 3.281ft long spacetime in the english (reference) frame and 1 meter long in the metrics reference system. my table takes space but not ruler. without necessity of measurement there is not need for reference frame. without reference frame things don't move? they move with or without referece frame in spacetime!

when a ball moves from pointA to point B in spacetime under any reference frame. there must be another reference frame in which we measure the spacetime moves from point B to point A relative the ball.

maybe there is not such a thing as a ball gets a force from nowhere and start to accelerate 'cause action and reaction is always a pair. how does a rocket get reaction to propell?

anyway i think i personaly want to go ahead to finish the book. it is really interesting to me.