Simple relativity questions.

[Ivan Gorelik]

Simple relativity questions.

1. What does speedometer of ideal car measure?

2. Can it show, for example, 10c, where c=299792458m/s?

3. Is SR correct?

 

My answers:

1. ...

2. Yes.

3. Yes.

[Klaynos]

1. Distance/Time (instantaneous speed) relative to the earth.

 

2. No.

 

3. Yes.

[Ivan Gorelik]

1. Distance/Time (instantaneous speed) relative to the earth.

 

2. No.

 

3. Yes.

 

1. Proper Velocity = Distance / Proper Time. (Proper time = the time in the moving car. Proper Time interval is shorter then the time interval measured by system of synchronized watches, resting along the road.)

 

2. Yes, because the limit of proper velocity is infinity.

 

Compare: the limit of coordinate velocity is 299792458 m/s.

 

More details about coordinate velocity, proper velocity, rapidity (or hyperbolic velocity), quantable velocity (or trigonometric velocity) you can find in my web-page, or from Wikipedia.

 

Paradox: most physicists-relativists do not know, what physical value is measured by their car’s speedometer.

[swansont]

If you are using the clock in the car and the distance measurement in the road's frame, yes, the limit is infinite. But you are mixing frames, so what's the point?

[Ivan Gorelik]

...you are mixing frames, so what's the point?

 

No. That not me, who mix the frames. The speedometer does it.

 

Speedometer is the physical device.

It measures proper velocity.

In order to measure coordinate velocity one need to invent another device, containing at least two clocks.

It can be named coordinate-velocity-meter with finite limit.

But speedometer is the proper-velocity-meter with infinite limit.

 

By the way different types of velocities explain one and the same motion but math is different.

They are sin, cos, tg, ctg of relativity…

 

4. In front of you there is the map of Universe. Can you cover the distance between Milky Way and Andromeda in the period of one second, measured by your rocket clock?

[swansont]

No. That not me, who mix the frames. The speedometer does it.

 

The speedometer will not measure the speed as you have described. The distance will contract, and you will get an answer that is < c

[Ivan Gorelik]

Let's ask physicists from CERN to help us to solve this problem...

[Sisyphus]

A speedometer measures the relative velocity between car and road, and that can't be greater than C.

[Ivan Gorelik]

Let's ask physicists from CERN to help us to solve this problem...

 

I think they also will make the same error.

 

That is why, I’ll write here an example problem.

 

Let’s simplify the problem.

Let the length of car wheel is equal to 1c.

Let the speed of light is equal to 1c.

Let car moves with the coordinate velocity equal to 0.8c.

What will be the reading of the speedometer?

 

Solution:

The point of car’s wheel, contacting with the road, does not move relatively the road. Consequently, this region of the wheel does not contract.

Consequently, the wheel will make 8 full rotations per 10 time units, relatively the road watches.

The wire of speedometer will also make 8 full rotations per this time.

But the time interval of these rotation inside the car is not 10 time units, but smaller by 1/sqrt(1-0.64)=5/3, or 6 “car time units”.

The readings of the speedometer: (8/6)c. That is more then speed of light, 1c, and more then coordinate velocity, 0,8c.

 

Question: Does our car moves faster then light?

Answer: No. The coordinate velocity of light is 299792458 m/s, or 1c.

The proper velocity of light is infinity.

 

To make comparative conclusions, we must compare the same types of velocities.

Light is faster in both cases.

[Klaynos]

the edge of the wheel is moving at a relativistic speed compared to the car, therefore there will be a length contraction effect on that which will negate this effect. See swansonts post above...

[Ivan Gorelik]

I am in shock.

This is much easier problem, comparatively with “Magnetic Hole”, moved to “Pseudoscience and Speculations”… http://www.scienceforums.net/forum/showthread.php?p=507167#post507167

And no one can say correct answer on this simple problem.

 

Magnetic hole is much harder to understand and consequently it will be made!

[swansont]

The point of car’s wheel, contacting with the road, does not move relatively the road. Consequently, this region of the wheel does not contract.

Consequently, the wheel will make 8 full rotations per 10 time units, relatively the road watches.

 

The point in contact with the road will not contract. You cannot say that about the rest of the wheel, since it does have a speed with respect to the road. What is the circumference of the wheel, measured in the road's frame?

[Ivan Gorelik]

The point in contact with the road will not contract.

 

Yes

 

...You cannot say that about the rest of the wheel, since it does have a speed with respect to the road...

 

Yes. The car is ideal. Wheel is ideal. Wheel does not change the form because of the centrifugal forces. But SR is correct and the rest of wheel does, contract. But that does not change the result. The wheel copies the road. "The well measures" the length of road in the lengths of wheel, or in meters, if the length of a wheel is equal to one meter. This result does not depend of the value of velocity. The distance measured between points A and B will be always the same, - velocity independent.

 

The same independence is applicable to the quantity of rotations of the rotor of speedometer, made of the way from A to B.

 

But the time rate inside the car is dependent of velocity.

 

Speedometer divides the quantity of rotations of its rotor by the quantity of “tick-tock” of the light clock inside the car.

 

Speedometer measures the proper velocity of a car and its limit value is infinity.

It's really simple!

[swansont]

Yes. The car is ideal. Wheel is ideal. Wheel does not change the form because of the centrifugal forces. But SR is correct and the rest of wheel does, contract. But that does not change the result. The wheel copies the road. "The well measures" the length of road in the lengths of wheel, or in meters, if the length of a wheel is equal to one meter. This result does not depend of the value of velocity. The distance measured between points A and B will be always the same, - velocity independent.

 

You can't have it both ways. If the wheel contracts, then you can't just say that the length is constant. Show it.

[Ivan Gorelik]

You can't have it both ways. If the wheel contracts, then you can't just say that the length is constant. Show it.

 

I repeat: the part of wheel, contacting with the road, does not contract, as a result, wheel measures notcontracted length of road.

Speedometer measures proper velocity of a car.

 

Proper velocity is measurable physical value.

 

The rate of motion can be described by four types of velocities:

 

Coordinate velocity, proper velocity, rapidity or hyperbolic velocity, quantable velocity or trigonometric velocity.

 

The second type of velocity was discovered by several authors (including me, independently) and its properties you can find already in Wikipedia.

 

The forth type (quantable) was opened by me in 2007.

 

These four types of velocities remind the trigonometric functions sin, cos, tg, ctg.

 

To be more precise here are some connections:

v_t/c = sin(v_q/c);

v_tau/c = tg(v_q/c);

gamma = 1/cos(v_q/c);

v_t/c = th(v_psi/c);

v_tau/c = sh(v_psi/c);

gamma = ch(v_psi/c).

 

Here:

v_t – coordinate velocity;

v_tau – proper velocity;

v_q – quantable velocity;

v_psi – rapidity;

gamma =1/sqrt(1 – (v_t/c)²) = sqrt(1 + (v_tau/c)²)

 

By the way, there are eight types of uniform rectilinear acceleration.

 

Home task:

1. What acceleration must be constant in order the spaceman would feel himself comfortable, i.e., fill constantly g-acceleration?

2. What acceleration must be constant in order an electron would make one full rotation along the whole Universe in the period of time, equal to electrons classical period?

[swansont]

I repeat: the part of wheel, contacting with the road, does not contract, as a result, wheel measures notcontracted length of road.

 

The point of contact is a point. That is the only part that does not contract; the rest of the wheel does, with respect to the road. The speedometer is not located on the wheel rim, at the point of contact with the road.

[Ivan Gorelik]

The point of contact is a point. That is the only part that does not contract; the rest of the wheel does, with respect to the road. The speedometer is not located on the wheel rim, at the point of contact with the road.

 

 

You are very opinionated!

 

Proper velocity is more than real, - one can fill it.

I would like to show this as follows.

 

Let’s improve the speedometer in your insistence.

 

One counter of speedometer counts the kilometer poles, flying past a moving car. The other counter counts the tick-tock of Einstein's light clock, located inside the vehicle. The calculator divides the first result into another result, and gives us the value of proper velocity, but not the coordinate velocity.

 

Such speedometer is our eyes and brain. If we could move with relativistic velocities, we could feel the speed by the frequency of the flicking of flying-by kilometer poles. Frequency of flicking corresponds to our proper velocity, but not to the coordinate velocity.

Let me remind you: the limit of proper velocity is infinity; proper velocity is measurable and one could fill it, if he could move with relativistic velocities.

 

To make a speedometer, indicating the coordinate velocity, it is necessary to put synchronized clock under every kilometer pole.

Speedometer reads the values at the kilometer poles and readings of clocks under the kilometer poles. Then computes: V = (L2-L1) / (T2-T1). It will be the coordinate velocity and its limit is 299792458 m/s.

 

Home task: Astronaut flies beside the row of stars and fills flicking:

A. 10 flashes per second;

B. 100 flashes per second.

Is the frequency of flashes proportional to coordinate velocity, or to proper velocity?

(Distance between stars is the same and equal L).

Edited August 8, 2009 by Ivan Gorelik

[Klaynos]

The km posts along the road are not spaced one km apart from the frame of the car, you are frame mixing!

 

The synchronised clocks, in which frame are they synchronised and with what?

[swansont]

You are very opinionated!

 

Opinion has nothing to do with it.

 

 

Klaynos has already noted the failing of your recent example.

[Ivan Gorelik]

...

Klaynos has already noted the failing of your recent example.

 

That means that you both made the same error.

 

Be careful.

Proper velocity is measurable quantity.

“To measure” means “to compare” with etalon.

 

We can compare proper velocity, but in order to compare coordinate velocity we must use at least two separated devices, or to use nonlinear computation in transition from measurable proper velocity to computable coordinate velocity.

 

Example.

Let we have a road with trees, growing at the same distance from each other.

Yesterday I went along the raw of trees and passed by one tree per second.

Let it be etalon of proper velocity, named, for example, “tree”.

Today I went along the raw of trees and passed by ten trees per second.

It is clear that my today’s proper velocity is ten trees.

It is clear that my today’s proper velocity is ten times bigger than yesterday’s proper velocity.

 

Question: Can we say that my today’s coordinate velocity is ten times bigger than yesterday’s coordinate velocity.

 

My answer: No! But it is almost true, if the velocities are much smaller than speed of light.

 

If the distance between trees, for example, is one light second (299792458 m) then:

 

My yesterday’s proper velocity is: v1_tau = 1c = 299792458 m/s.

My yesterday’s coordinate velocity is: v1_t = v1_tau / (1+ (v1_tau/c)^2)^(1/2) = 0.7071c.

My today’s proper velocity is: v2_tau = 10c = 2997924580 m/s.

My today’s coordinate velocity is: v2_t = v2_tau / (1+ (v2_tau/c)^2)^(1/2) = 0.9950c.

 

The ratio of my today’s and yesterday’s coordinate velocities is: 1.407.

As you can see, this result is quite different from 10 times, as it would be at small velocities. But the ratio of proper velocities is the same, independent of the value of etalon. That means that proper velocity is comparable with etalon. That means that proper velocity is measurable value. That means that speedometer measures the proper velocity, which limit is infinity.

[swansont]

The distance between the trees is not constant in your frame. The speedometer does not use the trees' frame to measure the distance. How would it "know" these distances?

[J.C.MacSwell]

Simple relativity questions.

1. What does speedometer of ideal car measure?

2. Can it show, for example, 10c, where c=299792458m/s?

3. Is SR correct?

 

My answers:

1. ...

2. Yes.

3. Yes.

 

1. rotational speed measured in the time frame of the vehicle multiplied by the wheel circumference measured when the wheel is at rest (or some other preset distance)

2. no

3. yes

[Klaynos]

If you are travelling at a different speed relative to the trees today than yesterday then if you measure the distance between them it will be different today than yesterday.

 

Your comment:

 

If the distance between trees, for example, is one light second (299792458 m) then:

leads to the question, in which frame?

[ydoaPs]

A speedometer measures the relative velocity between car and road, and that can't be greater than C.

 

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

[swansont]

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

 

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.