Simple relativity questions.

[ydoaPs]

That's how you'd normally do it, and you'd get the wrong answer if you didn't take into account relativity. Which is the whole concept being applied here, apparently. I mean, a speedometer can show anything you want it to, if you don't wire it up properly. I've seen a speedometer which indicated 22 mph when the vehicle was standing still. BFD.

 

The bottom line is that a true, relativistically accurate speedometer does not measure speed in the way that has been indicated. An accurate speedometer would calculate the wheels' circumference rather than using a measurement from the rest frame.

 

So, in this case, speedometer=ladar?

[Sisyphus]

I thought it measured the RPM of the wheels and calculated the speed based on wheel size.

 

No, it measures the interval between electric pulses. Or the torque on a spring-loaded piece of aluminum, if it's an older one.

[swansont]

So, in this case, speedometer=ladar?

 

One could do it that way, and one would NOT get the proper velocity given by the OP.

[J.C.MacSwell]

No, it measures the interval between electric pulses. Or the torque on a spring-loaded piece of aluminum, if it's an older one.

 

Which measures "round trips" of some point in the wheel from the frame of the vehicle. Correct?

 

To OP et al:

 

I realize it is just accounting, but a corresponding point on the perimeter of the rigid ideal wheel must make that round trip as well. This point can never reach c in that frame, so the speedometer cannot register a speed of c or greater.

 

I understand the approaching infinite pseudospeed by using the time frame of the vehicle and the "yardstick" of the point on wheel the nearest the road, frame mixing as Swansont mentioned, but I don't think any vehicle speedometer is set up to do that. A device would have to stay continuously at the point of contact with the road, while also spinning with the wheel, which of course it cannot do.

Edited August 10, 2009 by J.C.MacSwell

[Ivan Gorelik]

...This point can never reach c in that frame...

 

Proper velocity can be more than c.

Coordinate velocity can NOT be more than c.

 

...so the speedometer cannot register a speed of c or greater...

 

Speedometer, installed in the IDEAL car, measures PROPER velocity, consequently, its maximal possible showed value is infinity. (But this does not mean, that the car moves faster than light, - the proper velocity of light is infinity.)

 

In order to measure COORDINATE velocity one must use at list two devices, and connect them with the road, but not with the car.

 

If you still do not understand, make a “relativistic tractor” picture, with the distance between track’s ribs equal to c, for example, and with the “Einstein’s light clocks”, made between brain cell’s of tractor’s driver. Proper velocity is measurable and even more: it is able to feel it by human senses. You can fly by dozens of trees per one day, you can fly by dozens of stars per one day, you can fly by dozens of galaxies per one day. But “one day” is the “proper one day.” Do not mix the notions: “proper velocity” and “coordinate velocity”.

[Sisyphus]

I really don't get what you're talking about with "proper velocity" vs. "coordinate velocity." How is the speed of light infinite in any way? What is a "distance of C?" I thought it was just "counting how many 1km interval markers go by per unit time," which is just an error in frame mixing, but now you're saying a lot of other stuff. How do "human senses" enter into it?

[J.C.MacSwell]

Proper velocity can be more than c.

Coordinate velocity can NOT be more than c.

 

 

 

Speedometer, installed in the IDEAL car, measures PROPER velocity, consequently, its maximal possible showed value is infinity. (But this does not mean, that the car moves faster than light, - the proper velocity of light is infinity.)

 

In order to measure COORDINATE velocity one must use at list two devices, and connect them with the road, but not with the car.

 

If you still do not understand, make a “relativistic tractor” picture, with the distance between track’s ribs equal to c, for example, and with the “Einstein’s light clocks”, made between brain cell’s of tractor’s driver. Proper velocity is measurable and even more: it is able to feel it by human senses. You can fly by dozens of trees per one day, you can fly by dozens of stars per one day, you can fly by dozens of galaxies per one day. But “one day” is the “proper one day.” Do not mix the notions: “proper velocity” and “coordinate velocity”.

Describe your speedometer. I can't see how any speedometer, even using ideal assumptions, would measure proper velocity as you describe it.

[swansont]

Describe your speedometer. I can't see how any speedometer, even using ideal assumptions, would measure proper velocity as you describe it.

 

A speedometer that measured passage of the trees/markers placed at regular intervals (as described earlier) would do this, if it were calibrated to the rest frame distance of the trees. i.e. your speed would be measured in trees-per-second, and converted to proper speed by knowing the rest frame distance between the trees.

 

However, this is not how most speedometers are configured, and it would not be a true speedometer, since it is measuring this contrived "proper speed." It would be a "properspeed"-ometer.

 

The obvious followup is: why would one bother to do this?

[J.C.MacSwell]

A speedometer that measured passage of the trees/markers placed at regular intervals (as described earlier) would do this, if it were calibrated to the rest frame distance of the trees. i.e. your speed would be measured in trees-per-second, and converted to proper speed by knowing the rest frame distance between the trees.

 

However, this is not how most speedometers are configured, and it would not be a true speedometer, since it is measuring this contrived "proper speed." It would be a "properspeed"-ometer.

 

The obvious followup is: why would one bother to do this?

 

Seriously. Are any? The OP seems to claim they are.

[Sisyphus]

I guess a GPS that approximated its own speed would essentially be that. Obviously that's not a self-contained system, though, and requires pre-calibration to some other arbitrary ("proper?") frame.

[Klaynos]

I guess a GPS that approximated its own speed would essentially be that. Obviously that's not a self-contained system, though, and requires pre-calibration to some other arbitrary ("proper?") frame.

 

Because of the way GPS works with time intervals this would cause more problems as you are frame mixing with time and space

[swansont]

Seriously. Are any? The OP seems to claim they are.

 

Not that I am aware. But roads often have markers that would allow one to attempt this kind of measurement, so I am happy to concede that this type of measurement is possible.

 

But I agree, the claim that standard speedometers measure "proper velocity" has not been supported and has been shown to be wrong.

[Ivan Gorelik]

Describe your speedometer. I can't see how any speedometer, even using ideal assumptions, would measure proper velocity as you describe it.

 

Any speedometer, connected with moving vehicle or with moving object, measures the proper velocity.

 

Any speedometer compares the length of passed way and the period of time, spent on this way. Any speedometer uses its proper time. Proper time period is always shorter than corresponding coordinate time period. Proper velocity is always bigger than corresponding coordinate velocity.

 

Imagine a huge man, with the length of one step, equal to one c (299792458 m). If he made 10 steps per one second, measured by his internal brain clock, he will have the proper velocity, equal to 10 c (10*299792458m/s). In order to compute his coordinate velocity, the man must have inherent internal speedometer and another device, - calculator: v_t = v_tau/gamma; gamma=sqrt(1+( v_tau/c)^2); v_tau=10c; v_t=0.995c.

Edited August 13, 2009 by Ivan Gorelik

[J.C.MacSwell]

Any speedometer, connected with moving vehicle or with moving object, measures the proper velocity.

 

Any speedometer compares the length of passed way and the period of time, spent on this way. Any speedometer uses its proper time. Proper time period is always shorter than corresponding coordinate time period. Proper velocity is always bigger than corresponding coordinate velocity.

 

Imagine a huge man, with the length of one step, equal to one c (299792458 m). If he made 10 steps per one second, measured by his internal brain clock, he will have the proper velocity, equal to 10 c (10*299792458m/s). In order to compute his coordinate velocity, the man must have inherent internal speedometer and another device, - calculator: v_t = v_tau/gamma; gamma=sqrt(1+( v_tau/c)^2); v_tau=10c; v_t=0.995c.

 

You described what you claim it does. Unless you believe you have a "huge man taking steps" somewhere in your vehicle you've made no attempt to describe your speedometer.

[swansont]

Any speedometer, connected with moving vehicle or with moving object, measures the proper velocity.

 

Any speedometer compares the length of passed way and the period of time, spent on this way. Any speedometer uses its proper time. Proper time period is always shorter than corresponding coordinate time period. Proper velocity is always bigger than corresponding coordinate velocity.

 

Imagine a huge man, with the length of one step, equal to one c (299792458 m). If he made 10 steps per one second, measured by his internal brain clock, he will have the proper velocity, equal to 10 c (10*299792458m/s). In order to compute his coordinate velocity, the man must have inherent internal speedometer and another device, - calculator: v_t = v_tau/gamma; gamma=sqrt(1+( v_tau/c)^2); v_tau=10c; v_t=0.995c.

 

No, this is wrong. Speedometers generally do NOT measure proper velocity.

 

Your example is flawed. You can't treat the man as being in a single frame of reference for this example. The legs are moving with respect to the man's head, and you would have to take length contraction effects into account, which you haven't done.

[J.C.MacSwell]

Any speedometer, connected with moving vehicle or with moving object, measures the proper velocity.

 

Any speedometer compares the length of passed way and the period of time, spent on this way. Any speedometer uses its proper time. Proper time period is always shorter than corresponding coordinate time period. Proper velocity is always bigger than corresponding coordinate velocity.

 

Imagine a huge man, with the length of one step, equal to one c (299792458 m). If he made 10 steps per one second, measured by his internal brain clock, he will have the proper velocity, equal to 10 c (10*299792458m/s). In order to compute his coordinate velocity, the man must have inherent internal speedometer and another device, - calculator: v_t = v_tau/gamma; gamma=sqrt(1+( v_tau/c)^2); v_tau=10c; v_t=0.995c.

 

Just to add:

 

If that is it, "huge man taking steps", then describing his step as 299792458 m means what? I can do that with respect to some frame, take ten 299792458 m steps, measured in a frame that is moving almost c wrt me, in one second of my time, but wrt that frame I am still moving at less than c.

 

I can easily produce a speedometer that will register 10c. I simply scratch out kph on the display and replace it with "c" and it will accurately measure your description of "proper velocity" in some frame's distance and my time, but unless you recalibrate your speedometer to do this it will never register 10 c.

[Ivan Gorelik]

No, this is wrong. Speedometers generally do NOT measure proper velocity.

 

Your example is flawed. You can't treat the man as being in a single frame of reference for this example. The legs are moving with respect to the man's head, and you would have to take length contraction effects into account, which you haven't done.

 

 

Let my huge man has tractors track's instead the legs. He made on the road the marks ||||. Distance between marks is equal to "c" and does not depend of tractor's velocity.

 

Imagine relativistic tractor's track.

||||||||||||||||||||| - traces on the resting frame K, made by resting bottom part of the moving tractor's track. I don't care the velocity of the upper part of the track. (It's rapidity is two times more than the rapidity of the tractor itself. Rapidity is the third type of velocities, - it is the additive velocity. It's limit is also infinity.)

 

|\

| \

|_"o"

Rotating bar with the inclined weight, denoted by "o". It points out into the scale v_tau. The more rotations per second - the more inclination of "o". The quantity of rotations is measured in the tractor's system, i.e., it is counted per proper second of tractor.

 

I repeat: any speedometer, connected with the moving object, measures the proper velocity of the object. The limit of the proper velocity is infinity.

[swansont]

Let my huge man has tractors track's instead the legs. He made on the road the marks ||||. Distance between marks is equal to "c" and does not depend of tractor's velocity.

 

Imagine relativistic tractor's track.

||||||||||||||||||||| - traces on the resting frame K, made by resting bottom part of the moving tractor's track. I don't care the velocity of the upper part of the track. (It's rapidity is two times more than the rapidity of the tractor itself. Rapidity is the third type of velocities, - it is the additive velocity. It's limit is also infinity.)

 

|\

| \

|_"o"

Rotating bar with the inclined weight, denoted by "o". It points out into the scale v_tau. The more rotations per second - the more inclination of "o". The quantity of rotations is measured in the tractor's system, i.e., it is counted per proper second of tractor.

 

I repeat: any speedometer, connected with the moving object, measures the proper velocity of the object. The limit of the proper velocity is infinity.

 

The track is moving with respect to the head. The separation of the track marks changes with speed, due to length contraction.

 

Every example you have come up with so far has this relative motion, which you ignore. Proof by repeated assertion is invalid.

[Ivan Gorelik]

Just to add:

 

If that is it, "huge man taking steps", then describing his step as 299792458 m means what? I can do that with respect to some frame, take ten 299792458 m steps, measured in a frame that is moving almost c wrt me, in one second of my time, but wrt that frame I am still moving at less than c..

 

Let we have a source of short-living particles.

 

Let the life-time of that particles will be one second exactly.

 

Which distance will cover the particle if it moves with proper velocity:

1 m/s;

10 m/s;

….

1 c;

10 c;

1000000000000000 c.

 

Answers:

L=v_tau*tau

1 m;

10 m;

….

1 c;

10 c;

1000000000000000 c.

 

In the last case the particle had covered the distance 1000000000000000*299792458 meters per second!

Did it moved faster than light?

No. That second is the proper second of the particle.

 

According to synchronized devises, connected with the source of the particles, its coordinate velocity is about c, and the particle lived about 1000000000000000 seconds.

 

To Swansont: Do you want, I take pencils and make a detailed figure?

[swansont]

 

To Swansont: Do you want, I take pencils and make a detailed figure?

 

Only if it helps you figure out where you are wrong. Any model that is not using a rigid object will likely have the problem that has plagued your examples. Once the object is free to move relative to another part of itself, you cannot describe length and time with a single reference frame. A wheel or track moves relative to the body of a car, so an observer (which includes a speedometer) in the car will see it length-contract. A revolution will not be the same length as when measured in the rest frame.

 

The common crank response is to come up with a different, more complicated example, rather than address the flaw in the simple model. Please stop giving crank responses.

[swaha]

i didnt understand one thing ideal car, ideal roads should have only one point of contact. to measure the distance shouldnt we consider 2 points 1st???!

[Ivan Gorelik]

i didnt understand one thing ideal car, ideal roads should have only one point of contact. to measure the distance shouldnt we consider 2 points 1st???!

 

In order to measure proper velocity one needs the road marked by “km” poles and one clock, connected with the moving object.

 

[math]v_\tau = \frac {dr}{d\tau}[/math]

 

In order to measure coordinate velocity one needs the road marked by “km” poles and at least two synchronized clocks connected with the road.

 

[math]v_t = \frac {dr}{dt}[/math]

 

At low velocities the values and almost coincide.

But at high velocities the difference must be computed:

 

[math]v_t = \frac{v_\tau }{\gamma}[/math]

 

[math]\gamma=\sqrt{1+ v_\tau ^2/c^2}=1/\sqrt{1- v_t ^2/c^2}[/math]

 

But what does measure an ideal speedometer, depends of it’s construction.

In the next letter I’ll describe some constructions of speedometer and results.

The simplest speedometer, which is our own internal speedometer, measures the proper velocity.

The limit of proper velocity is infinity.

---

Merged post follows:

Consecutive posts merged

Coordinate velocity and proper velocity are physical quantities with equal rights. Their values coincide under small velocities. But at large velocities they give different results. Nevertheless any of them describes the one and the same motion. It is possible to develop two independent math formalisms, which will give correct answers, according to used definitions. These differences explain us the cause of debates between people, who says that mass does not depend of velocity, with the people, who says about mass dependence of velocity.

 

The equal rights of coordinate and proper velocities lead not only to equal rights of math formalisms but also to the possibility to construct vehicles, the speedometer of which, will measure proper velocity or coordinate velocity, depending of the construction of vehicle.

 

The common demands:

there are no slippage of wheels along the road;

the power of engine is not limited;

there are no deformations, resulting from centrifugal forces.

 

Demands to vehicle with speedometer, measuring the proper velocity.

In the reference system of a car the rim of a wheel contracts exactly the same as the road.

Consequently, the needles of the wheel contract under the influence of the rim.

In the reference system of a tank the tracked tape contracts exactly the same as the road.

Consequently, the rod(beam) with infinitely small rollers at the ends of the rod, contract under the influence of the tape.

 

Demands to vehicle with speedometer, measuring the coordinate velocity.

In the reference system of a car the needles of the wheel do not contract.

Consequently, the rim can not undergo the relativistic contraction.

In the reference system of a tank the rod(beam) with rollers does not contract.

Consequently, the tracked tape can not undergo the relativistic contraction.

 

Example.

 

Let the tracked tape has 20 tracks.

Let the length of the rod with rollers is 1, the length of one track is 0.1.

If the velocity of a tank is 0.8c, then the length of rigid rod is 0.6.

Bottom part of the tape is in the state of rest relatively the road and must consist from 6 tracks.

The upper part must have 20-6=14 tracks. But computation leads to other result.

 

The cause is clear:

If the rod is rigid as the tape, then some of them must broke.

 

Then let the rod can contract under the influence of relativistically contracting tape.

 

In the reference system of tank the bottom and upper parts of tape move with velocities 0.8c; contract to 0.6 of initial length. The same length (0.6) will have the rod in the reference system of tank.

In the reference system of road the rod will contract to 0.36 of initial length.

 

On this length there will be 3.6 tracks, resting relatively the road.

 

The upper part of tape moves with velocity (0.8+0.8)/(1+0.8^2)= 0.975609756…

Gamma of upper part of the tape is: 4.555555555…

 

It is clear that upper part of tape must have 20-3.6=16.4 tracks; any of them have the length 0.1.

Dividing 1.64 by 4.55555... we’ll have 0.36, i.e., the length of the rod in the reference system of the road.

 

Thus, there are no problems. If the tape has one internally directed tooth, linking two contacts, after every full rotation of the tape, then it can measure the road in rest-lengths of the tape, [math]L = n l_{track}[/math].

 

Dividing this value by the proper time, the speedometer will show the value of proper velocity.

 

If we want to create the tank with speedometer, measuring the coordinate velocity, then the rod must be absolutely rigid, able to undergo the relativistic contraction only. The tape will expand on it the more, the more velocity of tank. Traces of such tape on the road will depend now from velocity of the tank. The more velocity, - the greater traces.

 

As for me, the tank, leaving the traces of different length, is not completely ideal.

 

Our own speedometer, measuring the proper velocity, seems to be more convincing.

[swansont]

Demands to vehicle with speedometer, measuring the coordinate velocity.

In the reference system of a car the needles of the wheel do not contract.

Consequently, the rim can not undergo the relativistic contraction.

In the reference system of a tank the rod(beam) with rollers does not contract.

Consequently, the tracked tape can not undergo the relativistic contraction.

 

Demand all you want, but this simply isn't what relativity tells us. The wheel or track is no longer in Euclidean space, so the circumference is not 2*pi*R. Simply stating that the circumference is unaffected does not make it so.

[Ivan Gorelik]

Demand all you want, but this simply isn't what relativity tells us.

 

In a couple of months, after the launch of discussed machine, we’ll know, who was correct.

 

I say: our proper internal speedometer measures the proper velocity. The maximal value of proper velocity is infinity.

 

http://en.wikipedia.org/wiki/Proper_velocity

 

Best wishes to You.

[Spyman]

The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity.

 

In its original formulation as presented by Paul Ehrenfest 1909 in the Physikalische Zeitschrift, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius R as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R₀ when stationary. However, the circumference (2πR) should appear Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that R=R₀ and R<R₀.

http://en.wikipedia.org/wiki/Ehrenfest_paradox