The Swing of a Pendulum

[GammaMatrix]

► x[sub]0[/sub] is the origin from which the change in position is measured. Relative.

I'm sorry to jump in here... but position is not relative unless you have a second system to be relative to.

A change in position of a single particle

$$(x_1 - x_0)$$ only means you are talking about a relative position in with respect to the same system. Which isn't very interesting!

ps. it is so boring in fact, how can anyone actually call it a true relative change?

 

[Motor Daddy]

Motor Daddy:

Clearly, trying to discuss pendulums in accelerating cars is way too complex a problem for you to cope with at this stage. So, let me just go back over the whole relative-velocity problem you were having earlier in the thread.

James, Glad you decided to post. I always get a kick out of how you get all twisted and confused about your own science. The main thing is that you keep your faith, even if it isn't reality. I admire that quality in you, probably because I don't posses it myself.

First, let's dispense with the confusion about whether we're talking one or two velocities.

No confusion on my part. The confusion is only on your part created by bad theory.

To specify a relative velocity, we always need two velocities.

The concept of a relative velocity doesn't require two velocities, the concept of relative velocity is one velocity! That one velocity is a measure of change in distance between two objects. If the distance stays the same for 1 second then the relative velocity is 0 m/s. If the distance changes 20 meters in one second then the relative velocity is 20 m/s. Where do you get off trying to say a relative velocity is two velocities??

The velocity of object B relative to object A is always defined to be:

$$v_{rel} = v_B - v_A$$

So, if we say that car B is travelling 20 m/s faster than car A we have:

$$20 = v_B -v_A$$

Notice that this tells us nothing about the velocities of cars A and B, other than that one is 20 m/s greater than the other. Thus, it is possible that

$$X: v_A = 0, v_B=20$$

or

$$Y: v_A=80, v_B=100$$

or whatever.

What about this:

$$Z: v_A=-10, v_B=10$$

?

This is also fine.

"What's with the X,Y, and Z?", I hear you ask. X,Y and Z are what we call reference frames. I'm sure you remember the definition of a reference frame from our many previous discussions (think sticks and clocks etc. - remember?)

When we say "Car B is travelling 20 m/s faster than Car A" we haven't explicitly specified any particular reference frame. And until we do, we can't assign numbers to the velocities of cars A and B. One important caveat, of course, is that we do require a pre-existing concept of what a metre and a second are, or else the expression "20 m/s faster" is itself meaningless. But that's basic common sense.



Yes. Each of these situations corresponds to a different choice of reference frame.



This raises a slight complication.

Go figure.

$$W: v_A=-15, v_B=5?$$

In that case, B's velocity relative to A is still 20 m/s, but can we say that B is travelling faster than A? Clearly, in this particular choice of reference frame, the magnitude of the velocity (i.e. the speed) of B is less than the speed of A, but that does not change the fact that the velocity of B relative to A is still 20 m/s.

So, if you're having issues with "B is going faster than A", then I suggest you do not choose a frame such as frame W in the above example. You're better off working in a simple frame, and the simplest one to choose is the one where:

$$v_A = 0, v_B = 20$$

That way, you won't tie yourself in mental knots trying to work it all out.

You claim all frames have the same laws, do you not?

You have no point of reference to measure those -15 and 5 velocities. Explain to me how you determined those -15 and 5 velocities? What measurements were those speeds obtained from?

Right. A relative velocity assumes that we have already established a notion of what we mean by the term "velocity", because relative veloocity is just the difference between two velocities.

No it is not, not in my world. In my world relative velocity is a measure of changing distance between two objects.

I hope that's sorted now to your satisfaction. If you have any questions, please ask.

As I said before, I always enjoy your twisted version of reality. It's like going to a fun house, where everything is smoke and mirrors.

There's nothing absolute about that. In the rest frame of the sphere that always happens, whether or not the sphere is moving in some other reference frame.

The light can not possibly hit the walls simultaneously if the walls move, that would mean the light traveled faster than the speed of light in one direction, and that can't happen, as the light travel time is exactly the same for all points on the expanding light sphere, and light travel time defines the meter, so it is LOCKED. There is no possible way to differentiate from that!!!

Where did this "direction" idea of yours come from? It sounds like you're assuming some frame of reference prior to the information you have given. In a particular given frame, we presumably know the velocity of at least one of the rockets. Then, observing that the distance between the two is increasing allows us to deduce the direction of travel of the other rocket in that given frame.

You start from a point in space. There is one dimensional distance in every direction from that point, no?

Sure. It's just a matter of picking the right frame of reference.

So why does the pendulum only swing when the absolute velocity changes? I know, do you??

Hope this helps!

I'm pretty sure it helped you more than me. Good day, James.

 

[GammaMatrix]

The concept of a relative velocity doesn't require two velocities, the concept of relative velocity is one velocity!

Not true... think about the word ''relative.''

I will assume you have relatives in your family? Think about then the assumption of what a relative is.... it requires someone else in the framework. I have mentioned myself that you might think of changing position relative to something itself... but it is very boring and usually not within the context of relativity. Relativity is about multivariable systems usually. Especially when talking about a velocity... you can't have a system change velocity without the respect of something else. If there is no system to compare a change in velocity, then how will you know you have?

 

[Aqueous Id]

I'm sorry to jump in here... but position is not relative unless you have a second system to be relative to.

I have no idea what you are trying to say. All I said was, there is no absolute position in spacetime.

A change in position of a single particle $$(x_1 - x_0)$$ only means you are talking about a relative position in with respect to the same system. Which isn't very interesting! ps. it is so boring in fact, how can anyone actually call it a true relative change?

Again, no clue what you're trying to say, or what you're up to. The definitive entry into this discussion is that there is no absolute position in space. That fact alone trumps all the bogus comments which claim that velocity is absolute.

I suppose you can add to the confusion by being vague, or you can try to counter it by trying to be clear and correct.

 

[GammaMatrix]

I have no idea what you are trying to say. All I said was, there is no absolute position in spacetime.

....


Sorry for a moment I read the last post thinking you got muddled up... but

A change in position does not mean a relative case exactly! What does a change in position mean when relative to itself? I assume that

(X_1 - X_0)

Is a change in position of a single system yes? If so, it is not exactly relative as such. You need other positions in space to accurately measure such a change. You could though loosely state it is relative changes in position to itself, but that wouldn't be right either since there is nothing to compare it to.

 

[GammaMatrix]

....


Sorry for a moment I read the last post thinking you got muddled up... but

A change in position does not mean a relative case exactly! What does a change in position mean when relative to itself? I assume that

(X_1 - X_0)

Is a change in position of a single system yes? If so, it is not exactly relative as such. You need other positions in space to accurately measure such a change. You could though loosely state it is relative changes in position to itself, but that wouldn't be right either since there is nothing to compare it to.

Aqueous

To also mention, I quoted your statement..

''x0 is the origin from which the change in position is measured. Relative.''

If there is a misunderstanding let me know.

 

[Aqueous Id]

....


Sorry for a moment I read the last post thinking you got muddled up... but

A change in position does not mean a relative case exactly! What does a change in position mean when relative to itself? I assume that

(X_1 - X_0)

Is a change in position of a single system yes? If so, it is not exactly relative as such. You need other positions in space to accurately measure such a change. You could though loosely state it is relative changes in position to itself, but that wouldn't be right either since there is nothing to compare it to.

Yes was doing a cut and paste and something triggered a "save". Then I tried to edit and couldn't. Just ignore the bottom 2/3 of the post.

The only point that I have made concerns the absurdity of claiming that there is an absolute position. I am trying to state this as simply as possible.

All positions are relative. Therefore all velocities are relative. "Systems" are relative. Another word: arbitrary.

 

[GammaMatrix]

Yes was doing a cut and paste and something triggered a "save". Then I tried to edit and couldn't. Just ignore the bottom 2/3 of the post.

The only point that I have made concerns the absurdity of claiming that there is an absolute position. I am trying to state this as simply as possible.

All positions are relative. Therefore all velocities are relative. "Systems" are relative. Another word: arbitrary.

My math can be a bit rusty... I think relative positions should be

$$Position = \frac{(x_1 - x_0)}{(x'_1 - x'_0)}$$

 

[Russ_Watters]

Ehem: What you have described are three different relative velocities between three different objects.

Yes.

In the big picture all of those objects have an absolute velocity measured against the light sphere. Not only does my thought experiment reveal it...

You can keep on believing it, but it won't ever be true. Your experiment will always return a result of 0 because we are always stationary with respect to the speed of light.

...my thought experiment shows that there exist a frame in which the pendulum swings. No other frame does the pendulum swing except for the absolute frame!

Er, the pendulum swings in every frame of reference shown in the thought experiment! That's how the astronaut measures his acceleration and anyone in the other frames can watch with binoculars!

Again, this shows that acceleration is absolute, but velocity is not.

 

[Russ_Watters]

Why do I have to play by your rules?

You really only HAVE TO play by the universe's rules. "Winning" in here won't get you a Nobel prize because you won't ever be able to get your experiment to produce the results you want it to.

 

[Aqueous Id]

My math can be a bit rusty... I think relative positions should be

$$Position = \frac{(x_1 - x_0)}{(x'_1 - x'_0)}$$

Not sure what you mean there.

First of all, you need only recognize that identifying any point in space is arbitrary. Once you label an origin x[sub]0[/sub] you have imposed relativity on the universe. At this moment, all points are relative to your arbitrarily chosen origin.

Since all positions are relative to an arbitrarily chosen origin, then velocity is necessarily relative.

 

[Russ_Watters]

This is how acceleration works in the absolute frame:

No, that's how acceleration works in every frame.

Personally, I think you like to reboot and restart the argument over from scratch because you eventually get backed into a corner where the only other way out would be to acknowledge this all hangs on your assumption of an experimental result that contradicts reality.

 

[Aqueous Id]

No, that's how acceleration works in every frame.

Personally, I think you like to reboot and restart the argument over from scratch because you eventually get backed into a corner where the only other way out would be to acknowledge this all hangs on your assumption of an experimental result that contradicts reality.

The other entry point into this discussion is semantics. Here, you see the confusion over the words absolute and [/i]arbitrary[/i]. Completely different concepts.

 

[Motor Daddy]

No, that's how acceleration works in every frame.

Personally, I think you like to reboot and restart the argument over from scratch because you eventually get backed into a corner where the only other way out would be to acknowledge this all hangs on your assumption of an experimental result that contradicts reality.

In your next post tell me:

1. The initial velocities of the rockets.
2. The distance between the rockets at t=0.
3. The distance between the rockets at t=1.
4. The measured acceleration in units of m/s^2.

Thank you

 

[AlphaNumeric]

In your next post tell me:

1. The initial velocities of the rockets.
2. The distance between the rockets at t=0.
3. The distance between the rockets at t=1.
4. The measured acceleration in units of m/s^2.

Thank you

I gave you the mathematics for general separation L and general acceleration a. I am in no doubt you failed to understand it, despite it being something taught to 16 year old high school students, else you wouldn't be asking such a question. Unless you did understand it and you're being deliberately dishonest. I did it in 2 different inertial frames. The position, velocity and acceleration for all times, as defined in the inertial frames in question, were given. I know you struggle with algebra, the repeated posting you've done of your 'absolute box' where you include far too many decimal places (thus also showing you don't have a working understanding of physics) show you can only deal with specific numbers, not the fully general case. That's part of the reason you don't grasp what a frame, ie a choice of coordinates, is, given you cannot actually grasp coordinates used in physics to describe positions and times of events.

Funny how you complain when I don't reply to every one of your claims but then you are happy to ignore when people respond to your claims. If you were honest you wouldn't ask questions which have already been answered. If you don't understand the answer then you should be honest enough to admit it. Clearly you aren't.

 

[Motor Daddy]

I gave you the mathematics for general separation L and general acceleration a. I am in no doubt you failed to understand it, despite it being something taught to 16 year old high school students, else you wouldn't be asking such a question. Unless you did understand it and you're being deliberately dishonest. I did it in 2 different inertial frames. The position, velocity and acceleration for all times, as defined in the inertial frames in question, were given. I know you struggle with algebra, the repeated posting you've done of your 'absolute box' where you include far too many decimal places (thus also showing you don't have a working understanding of physics) show you can only deal with specific numbers, not the fully general case. That's part of the reason you don't grasp what a frame, ie a choice of coordinates, is, given you cannot actually grasp coordinates used in physics to describe positions and times of events.

Funny how you complain when I don't reply to every one of your claims but then you are happy to ignore when people respond to your claims. If you were honest you wouldn't ask questions which have already been answered. If you don't understand the answer then you should be honest enough to admit it. Clearly you aren't.

So just humor me, tell me what the initial velocities are in m/s. Just post something like 10 m/s and 10 m/s, or 362 m/s and 362 m/s, or 10 m/s and 35 m/s. Just give me the initial velocities and tell me how you came to those numbers.

 

[Motor Daddy]

Maybe you are trying to say that you have no idea of what those velocities are because you have no way of knowing any initial velocity of any object? Furthermore, since you don't know any initial velocity you can't know any final velocity. If you don't know any initial or final velocity then you have no way of measuring a change in velocity using units of m/s^2. So once again, you are trapped in a world of measuring distance between objects at specific points in time, which is what you refer to as relative motion, "dat's it!"

 

[quantum_wave]

MD, I can't help but point out that everyday circumstances make the use of reference frames seem to be second nature to human experience. You often refer to aspects of your examples correctly in terms of frames, at least to my understanding of them, and yet you always seem to be going for the larger initial or start frame that encompasses all of the individual naturally experienced frames. It is as if you picture the universe as having a start point in time and space that establishes an "absolute" point in space and time. It is as if you perceive everything to backtrack to that absolute beginning, meaning that any and all changes that occur from t=0 to now are all relative to that one single point in space and time. Is there any truth to my perception or am I completely off track? If I'm completely off track can you tell me in 100 words or less how you would phrase your view of the "beginning" and your view of the concept of backtracking all local frames to one initial absolute frame?

 

[AlphaNumeric]

So just humor me, tell me what the initial velocities are in m/s. Just post something like 10 m/s and 10 m/s, or 362 m/s and 362 m/s, or 10 m/s and 35 m/s. Just give me the initial velocities and tell me how you came to those numbers.

You're now showing you either didn't read or didn't understand the post I made about this. You pick an arbirtrary inertial frame with coordinates (x,t). The vehicles start at $$x_{1}$$ and $$x_{2}$$. They move with speed v in this frame. They then experience an acceleration a for T seconds. And so on, as I described in my previous post.

You're asking for a value for v. There is no unique answer, since the value of v depends on the coordinates you use. If they experience an acceleration for time T then their velocities will change by the amount $$\Delta v = aT$$. So we could consider 2 particular inertial frames, the one where initially they are stationary, F, and the one where they end up stationary, F'. In F their velocities start at v=0 and end at v=aT. In F' their velocities start at v=-aT and end at v=0. We don't have to restrict ourselves to those two frames, we could pick a third frame, F'', which is moving at speed V with respect to F. Then the vehicles start at speed -V and end at speed -V+aT. The frames F,F',F'' are defined by our choice of coordinates (x,t), (x',t') and (x'',t''), where they are related by Galilean transforms if everything is Newtonian and Lorentz transforms if everything is relativistic, ie for F' in terms of F under a Galilean transform we can have $$x' = x-vt$$ and $$t' = t$$ where v=aT by the definition of F'.

You cannot grasp this general formalism, you are only enable to work with specific numbers and it is clearly hindering your ability (or inability) to understand this. Everything always comes back to short comings in your understanding, nothing more. You've had this explained to you by myself and by others. A child, literally a child, can understand this.

 

[Motor Daddy]

You pick an arbirtrary inertial frame with coordinates (x,t). The vehicles start at $$x_{1}$$ and $$x_{2}$$. They move with speed v in this frame.

Prove it. There is 2 rockets in space. You are claiming they are moving but the distance between them remains the same at all times. What causes you to think they are moving?