There are two cars facing the opposite directions on a road. One car takes off and travels at a steady speed of 60 MPH. After 1 minute he is 1 mile away from the other car, 2 minutes he is 2 miles away etc. At the 3 minute mark the other car starts up and travels the opposite direction at 60 MPH. At the 4 minute mark the cars are 5 miles apart and the distance between the cars is increasing at the rate of 2 miles per minute. Can I consider that either car is traveling 120 MPH ( 2 miles per minute) since the distance between the cars is increasing at the rate of 2 miles per minute?

Given your history, it seems likely that this question is somehow intended to be related to relativity, yet it is posed in a context where normal language would imply that all speeds are referenced relative to the road. This is a pointless exercise. If you really want to learn about relativity, remove the road, let the cars be spaceships in deep space, and let the speeds be 80% of c. Only then will it elicit answers that will be helpful to your misconceptions about relativity. As stated, you will learn nothing from the answers, as they will naturally assume the observer implied is one affixed to the road.

You can consider one of the cars to be traveling at almost 120 MPH in the frame of reference of the other car.

Almost, rather than exactly 120 MPH because of relativity, of course. The slight difference is of no practical importance in this particular case, but it would become significant at (much) higher speeds.

Alternatively, you can simply make up a frame of reference in which the car is traveling at exactly 120MPH. This has nothing to do with the other car. You can choose any of an infinite number of possible frames of reference.

Depending on what frame of reference you use, you can choose the speed of the car to be any value less than the speed of light.

How would that work as far as the circumference of the tires, and the RPM that the tires are turning? What of the direction of the torque on the axles of both cars? As even at a constant velocity there is torque on the axle as the engine is doing work.

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Depending on what frame of reference you choose to use, the circumference of the tires may appear reduced by relativistic spacial compression. The diameter of the tire will remain unchanged, but it will have an oval shape instead of a circular shape.

The RPM that the tires are turning may appear slower due to relativistic time dilation.

The torque on the axle will not be affected by your choice of frame of reference.

Each car will be travelling at 60 mph relative to the road and 120mph relative to each other, or as near as significant. But as Isaackuo stated you can propose the car to be travelling at any speed you like less than C depending on your frame of reference. As Ken stated, you may as well change the scenario to suit, so you get the answers you are looking for regarding relativity.

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I'm going to interpret this as a thread about how relativity works at Newtonian velocity scales, which might be a useful thing because it saves us from the extra complications of time dilation and whatnot. So the questions are about Galilean relativity. Note that even in Galilean relativity, inertial motion is entirely interpretable as purely relative, there is no need for a universal frame of rest to do Galilean relativity. That is also how cosmocrazy answered it. The RPM of the tires is only relevant to the issue of the relative motion between the cars and the road. It does not determine the speed of the cars in any kind of absolute way. Ever walk on a treadmill? Imagine a car driving against the grain on an airport moving walkway, for example.
All of these questions apply perfectly well to an airport moving walkway with a car on it. They demonstrate nothing of what you think they do.

I'm waiting for the real question before piping in.

You mean the question of, if I turn around and travel at 60 MPH in the same direction of travel as the other car, can I consider myself to be going 0 MPH? If he then turns around, how fast am I going?
When he brakes, my velocity goes down, or up (depending on the direction of travel)? That means if he applies a force to his car, my car accelerates?

You can always construct a frame in which you are going 0 MPH. It doesn't matter what other objects are doing, you'll just describe their motions relative to your position. This is actually standard classical mechanics. Isaac Newton proved that one could do this as long as any acceleration on the objects being considered was effectively parallel.

The only true zero velocity is one of which stays in the center of the light sphere. If each car was a light source, the car that emitted light and stayed in the center of the sphere of light would have a zero velocity. If neither car stayed in the center, neither would be a zero.

My velocity is not dependent on any other object. It depends on the distance and time I travel relative to the light I emit.

Yes, with the earth moving at 60 MPH in the opposite direction. Or you can consider both to be traveling at 60 mph, with the earth being stationary. Or you can consider both to be traveling 100,000 km/hr or so because they are on the surface of the earth, which is itself moving. Or you can consider both to be moving 26.2 mph, with the earth moving 33.8 mph in the opposite direction, for no particular reason. All of these are valid perspectives, and the laws of physics work equally well in each of these reference frames. This it the principle of relativity, which was established long before Einstein's theory of relativity.

A real world example (which exactly happened to me a few days ago) - have you ever been on a train in a station, looked out the window at a train on the next track, and notice that you are moving? And then realize that (relative to the track and the earth) you are perfectly stationary, and it is the other train that has begun to move?

If you consider each car to be traveling at 0 MPH before he turns around, then in this inertial reference frame, you continue to travel at 0 MPH, and the other car is then moving at some speed other than 0 MPH. Even if the other car has a perfectly smooth ride, a passenger in that car who is blindfolded will still be able to tell that the speed of the car has changed. The acceleration requires a force acting on the passenger, which can be felt. If the passenger were holding a glass of water, the water in the glass would slosh around as the car changed speed.

In both the physics of Newton and the more accurate physics of special relativity, there is no such thing as absolute motion. You may take the perspective of an observer for whom the earth is stationary, and the cars are moving. Or you may take the perspective of the passenger of one of the cars, and consider the earth to be moving. Or you may take the perspective of the sun, and consider the earth and the cars both to be moving. All perspectives, or inertial reference frames, are equally valid, and the laws of physics work equally well in all of them. But an absolutely critical point is that the perspective of the observer must be inertial, or not accelerating. When the second car turns around, it leaves one inertial reference frame, and enters another one. From the perspective of the reference frame the other car was in before it turns around, the first car was stationary, and it remains stationary after the other car turns around. From the perspective of the reference frame the other car enters after it turns around, the first car is moving, and was moving before the other car turns around.

This is a very important point. There is no such thing as absolute velocity. There is such a thing as absolute acceleration (note to anyone reading - I think it is best to avoid general relativity in this discussion at this point). So you are free to define the velocities of all objects relative to the earth, relative to one of the cars, relative to some other car/vehicle, relative to a distant galaxy, and the laws of physics will work perfectly well from this perspective, provided the reference frame you choose is not accelerating. Once it accelerates (changes velocity), as in the case of the car that turns around, all bets are off.

If he applies a force to his car, his velocity changes. Your velocity remains the same in the reference frame his car was in before, and your velocity remains the same in the reference frame his car was in after he applies braking or some other force. So it may seem that there is action at a distance, in that the acceleration of the other car also accelerates your car, but to come to this conclusion, you have to take the perspective of a reference frame that is accelerating. And that's a big no-no.

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Your example with the cars works perfectly well in Newtonian physics, but once light is introduced, we have to consider special relativity.

But in either of those physics, there is no such thing as "My velocity." There is only your velocity relative to other objects.

I don't know what you're doing right now, but are you remaining still, with a velocity of zero? Are you perhaps traveling in a plane, train, or automobile, at speeds somewhere between 10 and 1,000 km per hour? Or are you rushing through space at 100,000 km per hour, because you are attached to the earth which is orbiting the sun at a very high rate of speed. Which of these is "My velocity"?

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"My velocity" is not dependent on the sun , the earth, or the moon, it is dependent on the light I emit. If the light I emit is equal distance away from me at all times, then I am a zero velocity.

Sure, we can refer to roads, moons, suns, etc, and relate our motion to those objects, but that is relative motion, not actual velocity. A zero velocity is that of which the light is equal distance away from me in all directions for any given time interval.

Doesn't that mean that everything is at zero velocity?

I assume your light sphere is hypothetical; you are not actually glowing...

The reason I have a hard time with that statement is that your speed relative to light is a constant. It never changes. No matter how you move, or how you measure it, your speed relative to light never changes.

What do you consider to be "actual velocity"?

Always true. So, without other objects, how do you know?

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No, because after objects emit light, if they have a velocity, they are no longer the center of the light sphere.

If the sun emits a sphere of light, if it were a zero velocity, the sun would stay in the center of that sphere. If it emits a light sphere, and then travels a distance, it is no longer in the center of the original light sphere.

By this definition (which is totally different than the normal definition of velocity), as pointed out by Henna Oji-san, you (and every other person and object) is moving at a velocity of zero. This is confirmed by experimentation to an extremely high degree of precision.

So what is your velocity right now?

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The outermost circle is the oldest light. The object was in the center of that circle when that light was emitted. The object has since moved, which means it has a velocity for that time interval.

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But if the speed of light is constant (relative to any observer, whatever his velocity) surely you can never move away from the center of the light sphere?

This has been refuted experimentally. Many times. The velocity of the earth has been measured at precisely zero by this type of method.

This issue was resolved roughly 100 years ago.

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The earth does not stay in the center of its own light, it has a velocity.

Yes it does. This has been confirmed many times.

Have a look here, for example.

By the usual definition of "velocity," it does. By your definition, which bears no resemblance to the normal definition, it doesn't.

If you want me (or anyone else) to just throw away the wealth of empirical evidence against what you are claiming, I think you're going to have to offer some evidence.

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This is getting pretty tiresome MDT-1. You don't understand relativity, and you have no desire to understand. On this thread you had a chance to understand Galilean relativity and just be 100 years behind in your physics, but you won't even do that, placing you 400 years behind. You are wasting our time.

First of all, that is not what the object sees. Second, even an outside observer will not see the cross hairs outside of any circle because that would imply the object is moving faster than light.

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MDT-1, from your post #18:

”If the sun emits a sphere of light, if it were a zero velocity, the sun would stay in the center of that sphere. If it emits a light sphere, and then travels a distance, it is no longer in the center of the original light sphere.”

From your post #20:

Your drawing is similar to this one, on a NASA website:
http://imagine.gsfc.nasa.gov/YBA/M31...s/doppler3.gif

Notice that the light emitter is not in the center of the earliest expanding light spheres that it emitted.

It’s the third illustration down on this NASA webpage:
http://imagine.gsfc.nasa.gov/YBA/M31...r-shift-2.html

See the caption: ”You will recognize it as the same as the fire truck approaching the stationary observer except now the source is emitting light instead of sound. Notice that the right region where a perceived increase in the frequency is noticed is referred to as "blueshifted", and the region which would appear to be of a lower frequency to an observer on the left is referred to as "redshifted."”

In this illustration, the background space would act like a light-speed-regulating “medium” or an “ether”, such as the way the air acted as the sound-speed-regulating medium in the example with the moving fire truck. However, this drawing doesn’t conform to the results of the Michelson-Morley experiment, since they found no evidence of such a “medium” or “ether” at the surface of the earth where their experiment was performed, so there might be some doubt about the validity of this NASA illustration. My opinion is that no one knows yet how to illustrate what really happens.

Isn't that mixing up wavelength and distance travelled (because it is trying to explain the former in a simple way analagous to sound)? What you really need is something like a series of concentric circles each with a circumference of ripples that are stretched or squashed.

But you may be right, that it is hard/impossible to give a realistic representation.

That is exactly what happens. The radius of the sphere is expanding at the rate of ~186,000 miles per second. So one second after the light is emitted from a point in space, the light is ~186,000 miles from that point in all directions from that point. If the light source changes position during that one second, the source will move closer to one edge and further from the opposite edge. The light sphere radius continues to expand at the rate of ~186,000 miles per second, regardless of the motion of the source after that old light was emitted.

The source changing position after the light sphere was formed has nothing to do with the rate at which the original radius expands. The radius expands at the rate of ~186,000 miles per second from the original point of emission, regardless if the source is at that original point some time later or not..