Proper Time and Its Relation to Velocity and Acceleration

[Pantaz]

I'm having a hard time wrapping my head around your statement. Maybe you can help clear up my confusion about what you mean exactly by that statement.

If you and I are two cars on the highway we could be each traveling at a constant velocity in the same direction down the road, one in front of the other, like in traffic. We are each doing the same speed so the distance between us is always the same. The relative velocity between us is dependent on each of our motions. Since we are traveling the same speed in the same direction there is no relative motion between us.

If we each accelerate at the same rate at the exact same time there will be no change in distance between us.

If you base all your measurements on the distance between us then you have no justification to claim you are accelerating. According to you, if all there is is you and me, relative velocity (closing speed) AND acceleration are relative.

Looks like you have a bit of a contradiction on your hands.

Hang a pendulum from the rearview mirror of each car. At any steady velocity, the pendulum will hang motionless (relatively speaking). Acceleration is required to move the pendulum -- if both cars accelerate equally and simultaneously, you would see the effect on each pendulum. If only one car accelerates, then only that car's pendulum will move.

 

[Motor Daddy]

Hang a pendulum from the rearview mirror of each car. At any steady velocity, the pendulum will hang motionless (relatively speaking). Acceleration is required to move the pendulum -- if both cars accelerate equally and simultaneously, you would see the effect on each pendulum. If only one car accelerates, then only that car's pendulum will move.

So both pendulums swing simultaneously and the distance between the cars stays the same. What is the rate of acceleration measured in, ft/sec^2? What feet?

Acceleration is the rate of change of velocity. You have no choice but to say that the relative velocity between the cars is zero because the distance between the cars is the same at all times, even during the acceleration of each car. So the initial relative velocity was zero, and the relative velocity remained at zero, so there was no change in relative velocity. Acceleration equals zero if there is no change in velocity.

So there you have it, a conflict. On one hand you have a swinging pendulum which indicates change in velocity, and on the other hand the relative velocity didn't change. If the swinging pendulum indicates a change in velocity and it isn't the change in relative velocity then which velocity is it that changed? Are you trying to tell me that it's the absolute velocity that changed???

 

[Motor Daddy]

The crickets have arrived!!

 

[Cheezle]

The crickets have arrived!!

[video=youtube;rLprXHbn19I]http://www.youtube.com/watch?v=rLprXHbn19I[/video]

 

[AlphaNumeric]

Your right there wouldn't be more particles. The particles on this ship would just look to be more massive from the frame of reference of an observer at rest. I think your forgeting that E = mc^2. If the particles look to have more mass from a reference frame then they would also look like they have more energy when converted to energy.

Firstly anyone doing relativity with motion should use $$E^{2} = m^{2} + p^{2}$$ for momentum p (and in c=1 units), using $$E = \gamma m$$ (for rest mass m) leads to issues enforcing Lorentz invariance in a clean manner.

But it would only look like they had more energy from the frame of reference that is at rest, so then even though a ship was being observed by an outside observer the people on the ship would still measure the energy of their nuclear reactions to still just be goverened by E = mc^2. So then an outside observer looking into the experiments done by scientist inside the ship will not change the results the scientist on the ship would gather. The scientist will not measure their own mass to be different because of an outside observer, and the mass they measure would not be affected by multiple outside observer. There would be no need to determine what the scientist on the ship would measure because of being observed differently by outside observers. Different outside observers would all say the mass of the ship is different, but this would not change the laws of physics as seen by the scientist on the ship. So then there would be no need to corelate what they measure on the ship because outside observers didn't agree with what they measure as the mass of the ship. The laws of physics measured by the scientist on the ship would remain consistant.

The problem is you're not doing any quantitatively. As such you don't know if you're doing the relativity right, enforcing Lorentz invariance correctly. If you do all of this using frames, coordinates, worldlines etc then you'll find there isn't a problem.

The velocity of the particles coming out of the back of the ship would remain constant.

From the point of view of the person on the rocket. The other observer would have the impact of the relative velocity too. Plus the issue with the exhaust isn't just the velocity but the momentum they carry.

Let's say A is on the rocket and B is somewhere else. A watches N particles of exhaust leave the rocket every second. N particles with mass m at speed v carries Nmv momentum from A's point of view. From B's point of view the masses are $$m\gamma$$. The number of particles leaving the rocket every second from B's point of view is $$\frac{1}{\gamma}$$, since it appears to move slower in time. What about the velocity? I won't go through the specifics (I can but I'm sitting on a couch watching TV and I can't be bothered to do the equations) but as the relative velocity between A and B increases it seems from B's point of view the relative difference between A and the exhaust goes to zero. Therefore the impulse the exhaust gives the rocket appears to go down. Add into that the mass of the rocket appears to go up and despite A seeing everything behaving as usual the speed of light isn't obtained.

This is why it is important to do the mathematics before making conclusions, you don't know if you have included all of the aspects. SR takes care of all of it for you, as writing the system from A's point of view is easy, it is the same as in Newtonian mechanics, and then you apply the appropriate transforms. It is made more complicated by the non-inertial motion of B but it can be done.

The speed of light in the equations I posted above replaces the velocity variable in the velocity equation v = d/t.

So here is a problem which has already been pointed out to you. The velocity isn't constant, doing v = d/t gives you the average velocity. Even in Newtonian rocket you have a variable mass rocket (ie gets lighter as it emits thrust) providing constant thrust, so the acceleration isn't even constant. In a relativistic rocket you have the issue of time dilation effects too, coupled with relativistic mass issues. All of these combine in a complicated way (Newtonian rockets are fiddly enough). If you can't do the calculations then any conclusion you reach is at best dubious.

So then it would be no surprise that the mathmatics that assumes the speed of light is constant would also lead to velocity being constant because the speed of light has taken the place of velocity in one of the equations. So then it is if v = c, and c being constant then makes v act like a constant. For instance you could not have a rocket ship that reached a high velocity then have the rockets perform differently because Nasa that was at rest on Earth observed what was going on inside of the rocket from base. The people in the space ship could have functioning rockets, that behaive the same way regardless if Nasa was monitoring them or not.

I really suggest you get yourself an introductory book on special relativity and work through it. It'll cover such examples as the relativistic rocket exhaust problem.

I was expecting you to say that relativistic effects are just local.

"Local" has a particular meaning in physics literature. You need to define what you mean by 'local' to make sure we're not crossing wired.

I was expecting you to say that relativistic effects are just local.

"Local" has a particular meaning in physics literature. You need to define what you mean by 'local' to make sure we're not crossing wired.

The crickets have arrived!!

Oh I'm sorry, I had to drive cross country yesterday and didn't have the time or desire to reply to you. I still don't have the desire to deal with you, since all you do is rehash the same ignorance you've had for years.

If you want enough SR thread of your own go start one, here I'm talking to PL. He might not have much SR knowledge more than you but he looks like he is honestly interested. You've shown you have no wish to listen to people explain SR or to learn SR yourself. If you had bothered to learn SR you'd be able to do the calculations and see there is no contradiction. You're making the same mistake as PL, assuming that your wordy arm waving is an accurate description of what relativity says. It isn't. When you start your new thread please provide the explicit SR calculations which lead to the contradiction you claim exists. If you demonstrate you have enough intellectual honesty to do that then I'll respond to you further. Otherwise if you cannot be bothered to do the bare minimum for yourself then I'm not going to do it for you.

 

[Pantaz]

So both pendulums swing simultaneously and the distance between the cars stays the same. ...

I never said the pendulums swing simultaneously.

Continuing with my scenario: You are in Car A. Your pendulum appears motionless. The cars are moving at equal velocity. Suddenly, it appears that you are accelerating much faster than Car B, yet your pendulum remains motionless! How can this be?

 

[Motor Daddy]

I never said the pendulums swing simultaneously.

if both cars accelerate equally and simultaneously

Then what do you mean by the word simultaneously?

Continuing with my scenario: You are in Car A. Your pendulum appears motionless. The cars are moving at equal velocity. Suddenly, it appears that you are accelerating much faster than Car B, yet your pendulum remains motionless! How can this be?

The pendulum swings when the absolute velocity changes (acceleration). The pendulum is non-responsive to changes in relative velocity caused by the other car's changes in motion. What does that tell you?

Is the distance increasing or decreasing between the cars? What justification do you have to claim you are accelerating (changing velocity) with the pendulum not swinging?

 

[Motor Daddy]

If you want enough SR thread of your own go start one, here I'm talking to PL. He might not have much SR knowledge more than you but he looks like he is honestly interested. You've shown you have no wish to listen to people explain SR or to learn SR yourself. If you had bothered to learn SR you'd be able to do the calculations and see there is no contradiction. You're making the same mistake as PL, assuming that your wordy arm waving is an accurate description of what relativity says. It isn't. When you start your new thread please provide the explicit SR calculations which lead to the contradiction you claim exists. If you demonstrate you have enough intellectual honesty to do that then I'll respond to you further. Otherwise if you cannot be bothered to do the bare minimum for yourself then I'm not going to do it for you.

That's what I thought, you don't have the intestinal fortitude to answer my questions because they prove you wrong. I expected as much.

 

[Aqueous Id]

For people who are competent and comfortable doing basic calculus and vectors learning about non-Euclidean geometry by starting with the other two types of constant curvature geometries (positive curvature is spherical and negative is hyperbolic) is a good place to start.

For example you can obtain spherical geometry by taking the definition of a sphere's embedding in flat Euclidean space and then doing what is technically known as a pull back onto the sphere's surface. For example, consider the 3d case (this generalised in an obvious way), where we embed a 2d sphere into 3d Euclidean space. The equation of a 2d sphere is $$x^{2} + y^{2} + z^{2} = R^{2}$$. The sphere is 2 dimensional so we parametrise it using two coordinates which we can decide to be the polar angles via $$x = R\,\sin\theta \, \cos \phi$$, $$y = R\,\sin\theta\,\sin\phi$$ and $$z = \,R\cos\theta$$. We know the Euclidean metric $$\delta_{ab}$$, where $$ds^{2} = \sum_{a,b}\delta_{ab}dx^{a}dx^{b} = dx^{2} + dy^{2}+dz^{2}$$, and we can compute the Jacobian of this transform $$J_{ia}$$, which is a 2x3 matrix (pulling the 3d metric back onto the 2d surface). The metric on the surface is then $$g_{ij} = \sum_{a,b}J_{ia}J_{jb}\delta_{ab}$$, which simplifies to $$g_{ab} = \sum_{a}J_{ia}J_{ja}$$. If you do this you get $$ds^{2} = R^{2}(d\theta^{2} + \sin^{2}\theta d\phi^{2})$$, the spherical metric!! Using similar principles you can work out area elements on the sphere too.

It's a nice exercise and gives some insight into how to construct non-Euclidean structures with little more than a Euclidean structure and a surface Here gives 5 different ways of embedding a hyperbolic surface into Euclidean space on page 12 and then the resultant pullbacks on page 13, should anyone want to see if they can do it for themselves

Thanks for this, Alpha, this moves the discussion into 3rd year math. I think this is where a huge rift opens between the nuts and regular folks. Nuts will never be able to conceptualize curved space, certainly not in the abstract mathematical sense. Regular folks will either have a handle on it, or else try to figure it out. Thanks for the post. Great explanation.

 

[AlphaNumeric]

That's what I thought, you don't have the intestinal fortitude to answer my questions because they prove you wrong. I expected as much.

Motor Daddy, I know you want to delude yourself into thinking you aren't squandering your time but the mountain of times you've had your ignorance exposed speaks for itself. No one here thinks you are finding problems with relativity. JamesR has shown your ignorance more than enough times. If you don't have the intellectual honesty to learn special relativity, even a little, why should anyone give you the time of day? If you don't have enough respect for yourself to learn then I don't have respect enough for you to teach you.

If you really think you have a disproof of relativity send it to a journal. Hell, if you write up your 'disproof' in a format similar to those found in papers I'll even do the additional formatting necessary to make it conform to journal requires (many have their own LaTeX requirements) for you, so your work is judged purely on its 'scientific merits' and not presentation. That's how little I fear your claims. For example, your pendulums issue was easily resolved, all of it was just your lack of knowledge in relativity. It is always your lack of knowledge. You just don't understand the concept of inertial frames in relativity.

If I could disprove relativity I'd publish the work. It'd make me famous and it would change the shape of particle physics forever. The fact I'm not asking to co-author a paper with you is I don't think you have anything. No one but you does. But go on, put your physics where your mouth is and submit it to people whose opinions of special relativity you cannot dismiss, like you do with us. Perhaps you can do more than try to get rises out of people on forums. In the mean time the rest of us have actual physics to do.

 

[Motor Daddy]

Motor Daddy, I know you want to delude yourself into thinking you aren't squandering your time but the mountain of times you've had your ignorance exposed speaks for itself. No one here thinks you are finding problems with relativity. JamesR has shown your ignorance more than enough times. If you don't have the intellectual honesty to learn special relativity, even a little, why should anyone give you the time of day? If you don't have enough respect for yourself to learn then I don't have respect enough for you to teach you.

If you really think you have a disproof of relativity send it to a journal. Hell, if you write up your 'disproof' in a format similar to those found in papers I'll even do the additional formatting necessary to make it conform to journal requires (many have their own LaTeX requirements) for you, so your work is judged purely on its 'scientific merits' and not presentation. That's how little I fear your claims. For example, your pendulums issue was easily resolved, all of it was just your lack of knowledge in relativity. It is always your lack of knowledge. You just don't understand the concept of inertial frames in relativity.

If I could disprove relativity I'd publish the work. It'd make me famous and it would change the shape of particle physics forever. The fact I'm not asking to co-author a paper with you is I don't think you have anything. No one but you does. But go on, put your physics where your mouth is and submit it to people whose opinions of special relativity you cannot dismiss, like you do with us. Perhaps you can do more than try to get rises out of people on forums. In the mean time the rest of us have actual physics to do.

If I haven't been able to get through to you in literally thousands of posts explaining how velocity and acceleration work in an absolute frame, what makes you think I can write a paper and change people's minds? I know how it works, you don't. I would like to teach people how absolute velocity works. At the same time I realize human nature precludes people from understanding. Oh well, sucks to be them.

 

[origin]

If I haven't been able to get through to you in literally thousands of posts explaining how velocity and acceleration work in an absolute frame, what makes you think I can write a paper and change people's minds? I know how it works, you don't. I would like to teach people how absolute velocity works. At the same time I realize human nature precludes people from understanding. Oh well, sucks to be them.

At some point you should ask yourself, "why is everyone crazy except me"? This might lead you to the conclusion that maybe they aren't the crazy ones....

 

[Motor Daddy]

At some point you should ask yourself, "why is everyone crazy except me"? This might lead you to the conclusion that maybe they aren't the crazy ones....

In chronological order, I am the first to know this information. Everyone that learns the information learns it at a later time. You seem to be implying that time runs backwards, and that it's everyone else that has learned it and I don't know it yet.

Your brain is not quite right if you think everything in the universe except you is in motion. My motion is not dependent on your motion!

 

[AlexG]

At some point you should ask yourself, "why is everyone crazy except me"? This might lead you to the conclusion that maybe they aren't the crazy ones....

Crazy people never do that.

 

[Read-Only]

Come on now, people; crazy/insanity has nothing to do with it. The real problem is quite simple, Motor Daddy just doesn't understand Relativity. And it's most likely that is an indication that his amount of education isn't up to the task. What he's been doing - which is VERY common among people who haven't studied the requisite physics - is to apply what would be called "everyday common sense" to to problem. That doesn't work of course because SR and GR just aren't intuitive - they are special cases of physics which are quite different from classical Newtonian physics.

You would not call a young child "crazy" if he tried to explain how an airplane can fly when he knows it's heavier than air. He might conclude the wings are filled with birthday helium balloons and that's what is keeping it up. And that little comparison is very valid: the child doesn't understand aerodynamics and Motor Daddy hasn't learned advanced physics.

 

[AlexG]

The problem is not that he hasn't learned relativity. He's been exposed to SR and GR in pretty fair detail for years now. MD affirmatively denies relativity, and furthermore, claims he's the only one who's right.

 

[Read-Only]

The problem is not that he hasn't learned relativity. He's been exposed to SR and GR in pretty fair detail for years now. MD affirmatively denies relativity, and furthermore, claims he's the only one who's right.

Yes, I'll agree with that.

Perhaps I should have stated it this way: The difference is that the child in my analogy will most likely be willing to learn, however, Motor Daddy REFUSES to learn.

And I'll also state that a refusal to learn stands at the very top of my "repugnant list."

 

[AlphaNumeric]

If I haven't been able to get through to you in literally thousands of posts explaining how velocity and acceleration work in an absolute frame

If your pendulum on cars example is anything to go by you are demonstrably ignorant of what relativity says since it provides a description of the system without needing an absolute reference frame. Therefore, despite you asserting it, the requirement of an absolute frame in that scenario is false. Thus illustrating your grasp of such things is not as good as you think it is.

what makes you think I can write a paper and change people's minds?

I personally think you lack the capacity to even understand basic kinematics and the high school level mathematics necessary to describe the systems you like to talk about. Considering doing novel physics, writing papers and getting them published is most of a decade beyond introductory kinematics I don't think you could write such a paper anyway, even if the universe does work as you assert.

I know how it works, you don't.

An assertion you admit you have no evidence for. You have no experience with experimental data, you have no working valid models of your own, you have no grasp of the mainstream models you dismiss. By every single yardstick you lack justification for your claim you know. You know how the universe works despite having never examined it in this regard. That's plain delusional.

I would like to teach people how absolute velocity works.

Plenty of people grasp how absolute motion might work, it is a fairly simple concept to grasp. The issue is not one of not understanding, it is an issue of it not being physically valid, given all experimental data known at present. I can give you an infinite number of different ways of modelling distances and motion in space, how do I know if any of them are right? What does 'right' mean? It means accurately reflecting reality, so experimental data is needed. The experimental data is consistent with relativity, therefore the concept of no absolute frame is consistent with reality. As such your assertion you know things are absolute is unjustified. How do we know your notion of motion is valid, when there are so many invalid ones? Where's your evidence? Why do you know without evidence but if I were to just assert SR is right you'd complain?

It is one rule for you and one rule for everyone else. There is a fundamentally dishonest approach. You've had it pointed out enough time to you you cannot be unaware of it. This leads me to conclude you are either deliberately lying or you're too stupid to grasp it.

At the same time I realize human nature precludes people from understanding. Oh well, sucks to be them.

Why is it everyone else is wrong, due to human nature, but not you? Why doesn't human nature affect you? What makes you special? Farsight is the same, he likes to quote Feynmann about how the easiest person to fool is oneself but then doesn't apply it to himself.

I have no problem saying relativity might well be wrong. Hell, I believe that it will one day be replaced by something else, mostly in the realms of quantum gravity, but that doesn't mean your claims are true. There are many concepts of absolute motion, why is yours right? How do we know motion is absolute, it could be a different notion of relative motion. Which one is it? For that we need to use experimental evidence, not blind assertion. You do exactly what you complain mainstream physicists do, assert without proof, which makes you a hypocrite.

In chronological order, I am the first to know this information.

Without any experimental data you just know how the universe works? Is this divine knowledge? Did voices tell you? Aliens? Did you just wake up one morning and know?

Your brain is not quite right if you think everything in the universe except you is in motion. My motion is not dependent on your motion!

I am currently not moving relative to myself. This is a tautology. I am not claiming I am special and it is everyone else who is moving and I am at absolute rest but rather I am stationary with respect to me and there are some things which are not stationary relative to me. Conversely there are some things which are stationary relative to themselves to which I am not stationary with respect to.

You're so enamoured with your notion of absolute motion you cannot grasp what relativity is saying. Hence why it is so daft of you to try these approaches, you always make the most trivial of errors. Relativity doesn't say your motion depends on mine but rather than your motion relative to me depends on me. If two cars are driving around then the motion of Car 1 relative to Car 2 depends on how Car 2 moves AND how Car 1 moves. If the positions of Cars 1 and 2 are $$\mathbf{x}_{1}(t)$$ and $$\mathbf{x}_{2}$$ then their velocities are $$\mathbf{v}_{1,2}(t) = \dot{\mathbf{x}}_{1,2}(t)$$. The values of the components of $$\mathbf{x}_{1,2}(t)$$ and $$\mathbf{v}_{1,2}(t)$$ are dependent upon our choice of frame, our choice of coordinates. Relativity says that if you're considering velocities then an important thing is $$\mathbf{v}_{1}-\mathbf{v}_{2}$$, the relative velocity. Clearly this depends on the motion of both cars. Consider if they crash head on. The important thing is their relative speed. Suppose they both have the same mass M. There is a frame where they crash together and the resultant clump of metal ends up being stationary. This is the centre of momentum frame, so $$\mathbf{v}_{1} = -\mathbf{v}_{2} $$. If they had a relative speed of say 200kph then this means one drive to the right at 100kph and the other to the left at 100kph. If you changed to a frame where one is going at +1,000,000kph and the other at 1,000,020kph caught up and crashed into it the relative velocity is the same. Has the damage changed? The speeds are higher but no, since the momentum isn't zero in this frame, the clump of metal continues to move after collision in this frame. The importance is the difference in velocities, not the value of the speeds.

These sorts of thought exercises are something anyone doing an introductory course in relativity (or even Newtonian mechanics in some cases, as that covers the notion of different frames) would do. The fact you haven't is obvious, you don't grasp any of this but assume you do and assume you know how things work. That's ignorant, delusional and flat out dishonest.

 

[Prof.Layman]

Firstly anyone doing relativity with motion should use $$E^{2} = m^{2} + p^{2}$$ for momentum p (and in c=1 units), using $$E = \gamma m$$ (for rest mass m) leads to issues enforcing Lorentz invariance in a clean manner.

Momentum is governed by mass as well, if an object was seen to have more mass then it would also have more momentum. Say a scientist on the ship had measured the momentum of the exhaust, and then another scientist at rest measured the momentum of the particles to be different because he was traveling at another relative speed, they would both conclude that the particle of the exhaust would have the same velocity even without considering relativity even though they said it had a different momentum.

The problem is you're not doing any quantitatively. As such you don't know if you're doing the relativity right, enforcing Lorentz invariance correctly. If you do all of this using frames, coordinates, worldlines etc then you'll find there isn't a problem.

If like you say being observered by an outside observer changed what observations someone else made then it would cause all kinds of problems. Say if one observer measured the mass of the particles to be 50, and then another measured the particles to be 100 from his frame, then how could you ever be able to figure out what actually happened on the ship? The mass of the particles as seen from the frame of reference can't be 50 and 100 at the same time because he is just being observed by two different outside observers.

From the point of view of the person on the rocket. The other observer would have the impact of the relative velocity too. Plus the issue with the exhaust isn't just the velocity but the momentum they carry.

Let's say A is on the rocket and B is somewhere else. A watches N particles of exhaust leave the rocket every second. N particles with mass m at speed v carries Nmv momentum from A's point of view. From B's point of view the masses are $$m\gamma$$. The number of particles leaving the rocket every second from B's point of view is $$\frac{1}{\gamma}$$, since it appears to move slower in time. What about the velocity? I won't go through the specifics (I can but I'm sitting on a couch watching TV and I can't be bothered to do the equations) but as the relative velocity between A and B increases it seems from B's point of view the relative difference between A and the exhaust goes to zero. Therefore the impulse the exhaust gives the rocket appears to go down. Add into that the mass of the rocket appears to go up and despite A seeing everything behaving as usual the speed of light isn't obtained.

This is why it is important to do the mathematics before making conclusions, you don't know if you have included all of the aspects. SR takes care of all of it for you, as writing the system from A's point of view is easy, it is the same as in Newtonian mechanics, and then you apply the appropriate transforms. It is made more complicated by the non-inertial motion of B but it can be done.

You say yourself that you have not done those calculation and then make conclusions and then turn around and say how important it is that you don't do what you just said that you have done. All you have to do is assume that there are objects that travel at a relativistic velocity in space, and these objects could detect light in such a way that they count as being an observation. The laws of physics don't change because of this, so then the reactions between objects do not change because of relativity or being seen from another frame of reference. I think velocity in relativity should be used in much the same way as thermodynamics is used to find the validity of a theory. Instead of thinking is mass and energy conserved, they should be thinking is the velocity the same as seen from all frames of references. The act of observation can't take away or add energy to a frame of reference. I can't be traveling really fast and look over at a ship and just say oh the mass of your particles in the exhaust is 50 now, and your ship will blow up accordingly. So I am realy just assuming that the act of observation at relativistic velocities does not break the laws of thermodynamics.

So here is a problem which has already been pointed out to you. The velocity isn't constant, doing v = d/t gives you the average velocity. Even in Newtonian rocket you have a variable mass rocket (ie gets lighter as it emits thrust) providing constant thrust, so the acceleration isn't even constant. In a relativistic rocket you have the issue of time dilation effects too, coupled with relativistic mass issues. All of these combine in a complicated way (Newtonian rockets are fiddly enough). If you can't do the calculations then any conclusion you reach is at best dubious.

Well, c = d/t and v = d/t, this has to be done in the calculation because the speed of light is a velocity regardless if velocity can be the speed of light or not. These are the same equations used in Einsteins 1905 paper. So then other variables are assigned for distance and time in order to keep the speed of light as a constant. So then velocity wouldn't be affected from anything in this relation because it has an equivalent relation to distance and time even though it can be a different value. So then it isn't a true constant, but then it is not affected by anything else in the equations either because if the value of d/t affected velocity then it could also have different effect on the speed of light, making it to where it is no longer a constant.

I really suggest you get yourself an introductory book on special relativity and work through it. It'll cover such examples as the relativistic rocket exhaust problem.

Do you know of a good one in particular? All the ones at my library are just for laymen, they won't let me graduate so I have derived my own equations independently as part of my hobby.

"Local" has a particular meaning in physics literature. You need to define what you mean by 'local' to make sure we're not crossing wired.

I am not sure exactly what other people mean by this when told this when talking about the relativistic effect of other galaxies. I just assumed that it was because they think that motion with the expansion of the universe itself just doesn't count as a relativistic velocity or expanding with space makes an object immune to relativistic effects. The expansion of space could be a very strange thing indeed if this was true. But, I haven't read much of any work or mention of trying to find a mass increase in distance galaxies or if that increase in mass is just relative to the Milky Way. It is a point that is just left out of most laymens descriptions and I have had a hard time finding the answer on the internet even. So I just assumed that there is no relative mass increase of distant galaxies traveling with the expansion of space for a while just because it has been left out in mostly everything that would mention it if they had found out such a thing. You would think that would be big news in the scientific communitiy. But, I don't see how we could detect this increase in mass if it was just relative to us, because they are just so far away, and I don't think there has been much work put into this area so then I think it creates the possiblity that scientist have just not been able to find the increase in mass that is just felt by us being in the Milky Way. If it was found to be true then it could take away a lot of the woo woo of cosmological expansion.

 

[Pantaz]

Then what do you mean by the word simultaneously?

Sorry, I worded that incorrectly. Your original response ignored the following sentence, "If only one car accelerates, then only that car's pendulum will move." So, I should have written, "I never said the pendulums ALWAYS swing simultaneously."

Is the distance increasing or decreasing between the cars?

As I stated, "it appears that you are accelerating much faster than Car B", which indicates the cars are moving away from each other.

What justification do you have to claim you are accelerating (changing velocity) with the pendulum not swinging?

Read it again: "Suddenly, it appears that you are accelerating much faster than Car B, yet your pendulum remains motionless!"
I didn't say Car A is accelerating, said it appears to be accelerating. You assumed that because Car A is overtaking Car B, then Car A must be increasing its velocity. In reality, Car A is maintaining velocity, while Car B is slowing! (The pendulum in Car A remains steady, but in Car B it swings forward.)

Relative acceleration can be demonstrated quite easily with an old prank performed at intersections (sometimes unintentionally) when stopped next to another car. Put your car in reverse and very, very slowly begin backing-up. The other driver will often notice the movement in his peripheral vision, and begin stomping the brake, believing his car is creeping forward into traffic. (It works even better if you have a friend do it at the same time on the opposite side of the victim's car.)