Unknown velocity vector of a rail carraige

[RossBlenkinsop]

TL;DR Summary

find the unknown vector

referring to the image

in fig 1 there is a rail carriage subject to an unknown velocity vector Vu (velocity unknown). Vu has a constant velocity Vu in the direction as shown. In the ceiling of the carriage is a light shown in blue and a columnator on the floor.

The rail carriage is sitting on tracks and a person in the rail carriage can measure the velocity of the carriage wrt the tracks

By pure chance the tracks are oriented parallel to Vu

When the columnator was being built the rail carriage was still subject to the unknown velocity vector Vu. The person was instructed to build the columnator directly below the light source which, according to them, they did. According to the person in the carriage the photons from the light shine directly down the columnator, and therefore the columnator must be directly below the light. However as a result of Vu the the columnator is not directly below the light as is must be offset by some degree to allow for the movement of the carriage as a result of Vu.

Once all is set , the columnator is constructed, the person accelerates the rail carriage to multiple constant velocities Vk (velocity known) wrt the tracks. There are three scenarios Vk is less than Vu, Vk is equal to Vu and Vk is more than Vu (see fig 2). I have omitted the person in the carriage for simplicity

By pure chance the rail carriage is going in the opposite direction to Vu. Or the person could try multiple velocities in both directions. either way the result is the same.

As the columnator is offset, by my calculations, when Vk is equal to Vu the columnator will no longer work and when Vk is more than Vu the columnator will no longer work

is that correct ?

 

[Ibix]

is that correct ?

No. You forgot about relativistic aberration (edit: and/or the conservation of momentum), which means that the "columnator" (did you mean collimator?) will be below the source (edit: or colinear with whatever angle your source is emitting) and will detect light at any constant velocity. There is no way to detect your velocity without some external reference - the concept of velocity without some such reference is not defined.

See this post for the correct version of what happens in a frame where the carriage is moving - treat the yellow dot as the roof of your carriage and the blue dot as the floor.

I note that the poster I was conversing with in that thread was called Ross B, and held a similar misconception to you. Are you he?

 

[Ibix]

Whether or not you are Ross B, you are @Skeptick (see post #8 here) which means you've been struggling with this for over a decade.

Let me lay it out for you: relativity is derived from the principle of relativity. That means that it is explicitly based on the notion that there is no such thing as an absolute velocity. You cannot find an absolute rest frame by a thought experiment because of this.

Any experiment that you describe (accurately - your layout above cannot do what you say it will do) can be thought of as a collection of worldlines, some of which cross. The Lorentz transforms give you the representation of these worldlines and their crossings in another frame. No worldlines cross or uncross or start meeting or failing to meet as a result of applying the Lorentz transforms. They cannot. The crossing of worldlines is an event, which has one set of coordinates - it cannot transform to two distinct events. So if light falls on a detector (the worldline of the light meets the worldline of the detector) when the carriage moves at one constant velocity it will fall on the detector at any other.

 

[DrGreg]

I don't know if this animation may help (from an old post of mine four years ago). It shows a short burst of light (the red spot) being reflected up and down in a railway carriage, from two points of view.

 

[Pencilvester]

I know this doesn’t have anything to do with relativity, but I have to point this out:

By pure chance the tracks are oriented parallel to Vu

A rail carriage with velocity vector oriented parallel to the tracks is usually not a result of sheer dumb luck.

 

[RossBlenkinsop]

I agree

I now refer to the attached images figures a1 to a4

 

[RossBlenkinsop]

if you are in a frame that is subject to an unknown velocity vector the Lorentz transforms are based on the notion that it is impossible to measure that unknown vector. if an experiment is devised that can measure that vector then the Lorentz transforms will be rendered invalid as will your world lines theorey

 

[RossBlenkinsop]

referring to fig a1 there is a rail carriage that is subject to an unknown velocity vector Vu (velocity unknown)

the rail carriage contains two other rail carriages C1 and c2 both on rail tracks. there is a columnator attached to each of the smaller rail carriages C 1 and C2. C1 and c2 are identical in every way.

In the ceiling there is a strobe light depicted as a blue square.

C1 is positioned directly below the light , which corresponds with your post above, with which I agree. C1 at all times remains at rest wrt the larger outer carriage.

Carriage c2 is moving along the tracks at a constant velocity Vk (velocity known). it just so happens the train tacks are parallel to Vu and it also just so happens Vk is in the opposite direction to Vu and of the same magnitude.

At the time C1 is directly adjacent to C2 the strobe in the roof fires, call this T1.Fig a2 is the same scene at some later time. The photon that will be sampled by c1 is circled with a red circle.. This photon makes an angle theta wrt where the strobe was when it fired.

The yellow dots in a semi circle are the photons from the strobe.

 

[RossBlenkinsop]

the dotted blue square is the position of the strobe at the time it fired. The solid blue square is the position of the strobe at the later time, directly above C1, as expected.

The rest of the images are self explanatory but I will explain them anyway

I have omitted C2 from fig a2, just cos

 

[RossBlenkinsop]

referring to fig a3 -

This depicts the photon that is sampled by c1 (lets call this photon PC1, an acronym for photon C1). The photon is traveling along a vector that makes and angle theta wrt the point where the strobe fired. The vector has a magnitude (hypotenuse) of C (the speed of light). This vector can be devolved into its vertical and horizontal components Vh (horizontal) and Vv (vertical).

If the columnator has a length L the time it takes for PC1 to traverse the length L will be L divided by the magnitude of Vv, where Vv will always be less than C

 

[RossBlenkinsop]

referring to fig a4 -

This depicts the photon that is sampled by c2 (lets call this photon PC2, an acronym for photon C2). The photon is traveling along a vector that is perpendicular to the ceiling of the outer carriage and is at all times vertically directly below the point where the strobe fired.

The vertical competent of this vector is C (the speed of light )and it has no horizontal component .

As Vk = Vu and as the strobe fired when C2 was directly below the strobe, the rail carriage c2 will at all times be directly below the point where the strobe fired.

If the C2 columnator has a length L (the same length as C1) the time it takes for PC2 to traverse the length L will be L divided by C, let's call this time Tv. Tv will always be less than the C1 time.

 

[Dale]

if an experiment is devised that can measure that vector then the Lorentz transforms will be rendered invalid

Yes if such an experiment were devised then they would indeed be invalid. No such experiment has been performed to date.

 

[Ibix]

if an experiment is devised that can measure that vector then the Lorentz transforms will be rendered invalid as will your world lines theorey

Indeed. But all of your thought experiments are literally lines on paper. They can be rendered as worldlines, if only you'd draw Minkowski diagrams instead of your inaccurate cartoons (where you mix frames and times into a mess that - I suspect - is what confuses you). You would have to perform an actual experiment to detect a violation of Lorentz covariance. There are serious scientists working on that, because it might happen under some extreme circumstances. But not with a couple of carts inside another one.

Incidentally, I'm flattered that you regard worldlines as my "theorey", but the concept dates back to Minkowski in 1908.