Length Contraction MMX

[butchmurray]

By Thorntone E. Murray
Houston, TX


Problem

For two identical light clocks in the same reference frame to be observed to have unequal lengths is contradictory to the constancy of light speed.

Hypothesis

Identical light clocks within a reference frame are always observed to have equal length as observed from any reference frame. Constancy of the speed of light and the formula VT=D – velocity multiplied by time equals distance – are the primary basis of this hypothesis.

Thought Experiment

There is a sphere within reference frame K’. Within the sphere there are two identical light paths that are perpendicular to each other. One end of each light path is the center point of the sphere. The other end of each light path is its point of intersection with the surface of the sphere. The length of the light paths and the radius of the sphere are equal. The equal light paths are the equivalent of identical single cycle light clocks. The sphere as well as the light paths are absolutely stationary with respect to reference frame K’. Reference frame K’ is in motion at an arbitrary constant velocity relative to reference frame K which is > than 0 and < C (light speed). The relative velocity of K’ has no affect on the appearance of the sphere and light paths as observed from within K’. The x-axis of K’ is parallel to the direction of motion relative to K. One of the light paths, D’x, is parallel to and the other light path, D’y, is perpendicular to the x-axis of K’.

Within K’, the center point of the sphere produces a light pulse which radiates into the equal light paths. The end points of the respective light paths at the surface of the sphere reflect the light pulses back to the center point. The light pulses arrive at the center point of the sphere concurrently and cause the center point to illuminate distinctively. The time interval for the light pulses to traverse the equal light paths is equal (T’x = T’y). The distinctive illumination is observable from within reference frame K’ as well as from any reference frame from which the sphere is observable. A distinctive illumination of the center point occurs if and only if both reflected light pulses reach the center point concurrently, that is if and only if T’x = T’y.

Within the sphere within K’ it is given that D’x = D’y and T’x = T’y. C is constant.

Without exception: Emission of a light pulse from the center point of the sphere results in a distinctive illumination of the center point, verification that T’x = T’y.
Without exception: The distinctive illumination is observable from within K’.
Without exception: The distinctive illumination is observable from any reference frame from which the sphere is observable independent of the relative velocity of the reference frames.

Data

(D) D’x = light path length parallel to the direction of motion.
(D) D’y = light path length perpendicular to the direction of motion.
(T) T’x = time interval for the D’x light pulse to radiate from and reflect back to center point
(T) T’y = time interval for the D’y light pulse to radiate from and reflect back to center point
(V) = C = the constant speed of light

Reference frame K’ is in motion at a constant velocity > 0 but < C relative to “at rest” reference frame K. The particular relative velocity is of no consequence. A light pulse is emitted from the center point of the sphere within K’. The distinctive illumination is necessarily observed from within K’ verifying the reflected pulses arrived at the center point of the sphere concurrently. The distinctive illumination is also observed from reference frame K. Therefore as observed from “at rest” reference frame K T’x = T’y. Of course, C is constant. Time delay and/or Doppler shift have no bearing in the matter.

As observed from “at rest” reference frame K:
(V) Velocity multiplied by (T) Time equals (D) Distance or VT=D
C * T’x = D’x substitute T’x for T’y C * T’x = D’x Therefore D’x = D’y
C * T’y = D’y C * T’x = D’y
T’ is equal for both as verified by a distinctive illumination. C is equal for both. It is therefore unequivocal that D’ is the same for both as observed from the “rest” frame.

As observed from reference frame K at relative rest, D’y, the length of the light path perpendicular to the direction of motion and D’x, the length of the light path parallel to the direction of motion are equal. Therefore, length parallel to the direction of motion did not contract relative to length perpendicular to the direction of motion. This finding directly contradicts Lorentz contraction.

The famous Michelson - Morley experiment and other experiments of the kind were considered to have failed with null results because the fringe shifts detected failed to approach the expected magnitudes. More importantly, for these intents and purposes, the lengths of the arms of the various interferometers had no detectable variations in length with respect to each other. Those results are consistent with and support the finding herein disclosed.

Conclusion

Equal lengths within a reference frame are always equal as observed from any reference frame independent of the relative velocity and/or orientation to the direction of motion.

Prediction

An actual experiment based on the one described herein will measure the rotational velocity and angle of the rotation of the earth relative to its stationary gravitational reference frame. Also, Lorentz transformation will be conclusively disproved.

 

[Jerromy]

I believe length contraction and relative velocity go hand and hand... a craft passing at near light speed will still appear the same length to the observer being passed but the craft travelling will measure itself to be shorter than it is while at a slower velocity.

 

[SpeedFreek]

I believe length contraction and relative velocity go hand and hand... a craft passing at near light speed will still appear the same length to the observer being passed but the craft travelling will measure itself to be shorter than it is while at a slower velocity.

You have that back to front. A craft passing at near light speed will appear length contracted to a person at rest, whilst the craft travelling will measure itself to be the same length as it always was!

 

[SpeedFreek]

As observed from reference frame K at relative rest, D’y, the length of the light path perpendicular to the direction of motion and D’x, the length of the light path parallel to the direction of motion are equal. Therefore, length parallel to the direction of motion did not contract relative to length perpendicular to the direction of motion. This finding directly contradicts Lorentz contraction.

Light always propagates at c from a point at rest in relation to the observer, whatever the observers motion in relation to the source of that light, so your conclusion is incorrect. The sphere K' moves in relation to K, whilst the light propagates from a point at rest in relation to K. Of course, the light also propagates at c from a point at rest in relation to K' too! Hence, the relativity of simultaneity.

This belongs in the Unexplained forum.

 

[Jerromy]

Wow, this is all starting to make some sense. Should I quit whilst I'm a head? LOL I was warped over to the unexplained while reading a thread yesterday...

 

[butchmurray]

Light always propagates at c from a point at rest in relation to the observer, whatever the observers motion in relation to the source of that light, so your conclusion is incorrect. The sphere K' moves in relation to K, whilst the light propagates from a point at rest in relation to K. Of course, the light also propagates at c from a point at rest in relation to K' too! Hence, the relativity of simultaneity.

I do understand simultaneity. However, the fact remains that the reflected pulses arrived at the center point concurrently; verification that time is the same for both light paths. The speed of light is, obviously, the same for both light paths. Therefore, the lengths of the light paths are, necessarily, the same.

butchmurray

 

[SpeedFreek]

I do understand simultaneity. However, the fact remains that the reflected pulses arrived at the center point concurrently; verification that time is the same for both light paths. The speed of light is, obviously, the same for both light paths. Therefore, the lengths of the light paths are, necessarily, the same.

butchmurray

Of course time is the same for both light paths, light measures proper time, so if the observer K' is at the same coordinate in spacetime as both the first event (the simultaneous emissions of those lights) and the second event (the simultaneous detection of those lights) then K' can easily calculate the proper time between those two events. Both events are on the worldline of K'.

K will, however, measure things differently, as they are separated from those events by space and time, and those events occur at two different coordinates for K, whilst K is residing at a third coordinate. Those events are on a separate worldline to K and this is why K requires the Lorentz transformation in order to find out what the proper time was for K'.

 

[butchmurray]

The following should make this matter clear for most:

1. The sphere and the light clocks are absolutely stationary within a reference frame.

2. The light clocks are identical and synchronized.

3. The light clocks are not at all affected by the velocity of any external reference frame in relationship to this reference frame. The light clocks remain synchronized.

That being said:

If one of the light clocks appears to be contracted, the light pulse in that light clock has to appear to be slower because the light clocks remain synchronized. This is an obvious contradiction to the constancy of the speed of light.


Or

The light clocks have to appear to maintain equality of length because the light clocks remain synchronized.

Thank you,
butchmurray

 

[SpeedFreek]

The following should make this matter clear for most:

1. The sphere and the light clocks are absolutely stationary within a reference frame.

That would be the from the reference frame of K'

2. The light clocks are identical and synchronized.

Synchronised in the reference frame of K'

3. The light clocks are not at all affected by the velocity of any external reference frame in relationship to this reference frame. The light clocks remain synchronized.

Synchronised in the reference frame of K'

If one of the light clocks appears to be contracted, the light pulse in that light clock has to appear to be slower because the light clocks remain synchronized. This is an obvious contradiction to the constancy of the speed of light.

Not at all. It is an indication that, whilst the speed of light is constant to all inertial observers, simultaneity is not an absolute, but is relative.

You have been given the clues (in different ways) as to how to correct your thought experiment here, at BAUT, and at the AntiRelativity forums. Yet you continue to ignore them. Are you just going to continue to spam this nonsense all over the internet until you find a forum where you can convince people who don't understand relativity, that relativity is wrong? Those of us that do understand relativity can see the error you are making.

Once again, the sphere in K' is moving relative to K, whilst the lights propagate from a position at rest in relation to K. There's your problem.

 

[butchmurray]

Speedfreek,

Please believe me when I say that I truly do not intentionally intend to upset anyone. However, when a deep seeded belief is challenged, there are those anchored in their beliefs that will be offended. I am more knowledgeable about SR than you apparently think I am. And, yes I am challenging it.

The flat earth was challenged.
Earth as the center of the universe was challenged.
Earth as the center of the solar system was challenged.
The list goes on. But, someone has to do it. If no one does, there can be no progress.

There is the possibility that I am wrong.
There is the possibility that I am only partially right.
There is the possibility that I am right.

To slam someone or burn him or her at the stake because they don’t believe what you believe is just plain wrong. Unfortunately, it is human nature and I accept that.

Again, I did not intend to offend you but I have the right to believe things that you don’t.

Thank you,
Butchmurray

 

[butchmurray]

All,

We must realize that when SR and the Lorentz transformations were formulated, the universe was thought to be static. The only bodies in the entire universe considered to be in motion were in our solar system.

That static universe had to be explained in terms that accounted for the consistency of light speed that did not vary with earth’s orbital position relative to the sun.

The concept of the universe as the one and only coordinate system that light speed is measured in relationship to is moribund. More than a hundred years have elapsed since those beliefs were formed. Our quantum leaps in technology must be used to discover new knowledge with deep and everlasting gratitude to those who gave us the best understanding possible with the tools they had to work with.

We must now pull up the anchors that are preventing progress. Of course, put new ideas through the wringer. There will be many false starts. There will be a few earth shattering discoveries that were not crushed in their infancy. The true facts must determine the legitimacy of an idea, not the fact that it does not fit with what we already know.

Thank you,
butchmurray

 

[SpeedFreek]

Speedfreek,

Please believe me when I say that I truly do not intentionally intend to upset anyone. However, when a deep seeded belief is challenged, there are those anchored in their beliefs that will be offended. I am more knowledgeable about SR than you apparently think I am. And, yes I am challenging it.

I am not upset or offended, as you are challenging none of my beliefs.

To slam someone or burn him or her at the stake because they don’t believe what you believe is just plain wrong. Unfortunately, it is human nature and I accept that.

I am not trying to slam you, just show you the errors in your conclusion for your thought experiment. If you want to use the central illumination to disprove Lorentz contraction, you are using the wrong experiment and it needs to be changed as, as it stands, it cannot be used for such a purpose.

If you understand SR better than I think you do, then consider this.

What you are doing is trying to find a way around the findings of the famous train and embankment thought experiment, with your spherical "train".

Let me please try to illustrate what I mean. Imagine a train carriage, moving past an embankment. In this version of the experiment, we have a light bulb at the centre of the carriage, with K' sitting below it. There is a detector at each end of the carriage that will flash when it detects light coming from the central bulb. So the central bulb lights up, the light propagates each way through the carriage and hits the detectors at each end at the same time. The detectors flash, and the light from those flashes propagates back up the carriage towards K'. K' sees both detectors flash at the same time.

This is exactly the same as your thought experiment - if the carriage were as wide as it were long, you could have detectors on the sides too and K' would still see all detectors flash at the same time.

However, the thought experiment is designed to show how simultaneity is relative rather than absolute, for events that are separated by space, due to the constancy of c.

From the view of the embankment, K, the light from the central bulb does not reach each end (or the sides) of the carriage at the same time, due to the carriage moving in respect to that light. K sees the detector at the back of the carriage flash before the detector at the front (after calculating out the light-travel time between those detectors and themselves). So, K can say the events of the central light reaching those separate detectors is not simultaneous, whereas K' will say they were simultaneous.

Now, where you are going wrong is that K can always calculate what the view would be for K', and knows that K' thinks the event were simultaneous. In the context of your experiment, K knows the lights from the edges of the sphere reach the centre at the same time. K sees that central illumination, because although the light hits the back before the front, the centre is moving forward so the light from the front takes less time to get back again! But that is not what is important, as the lights meet at a singular location - it is a singular event, rather than two events separated by space.

What is important is that K sees the light reach the edges of the sphere at different times, whereas K' sees that happen at the same time. Events separated by space are calculated to be simultaneous from one frame, whilst they happen at different times for another frame.

All you are saying is that K sees the central bulb illuminate, so they know that, for K', the light reached the edges of the sphere at the same time. But the same is not true for K, as the light did not reach the edges of the sphere at the same time.

In order to use the Lorentz contraction you need to be able to make measurements of events separated by space, so your experiment does nothing to disprove the Lorentz contraction. Your experiment is not flawed in itself, there is nothing wrong with the set up, but it does not prove what you think it proves. It proves the light reaches the edges of the sphere at different times for K.

 

[butchmurray]

Speedfreek,

Now I understand your point.

From inside the carriage the light pulse reaches both ends of the moving carriage at the same time. From the embankment that same pulse reaches two equidistant stationary targets at the same time. That is per the Lorentz transformations employing the light cone.

Respectfully, that is not the relationship to which I refer.

My scenario is based on length contraction in the direction of motion of a moving frame as observed from an at rest frame. For instance, from an “at rest” frame K the length in the direction of relative motion of frame K’ appears contracted by 50% when the relative velocity is .866 the speed of light. The length of K’ perpendicular to the direction of motion appears unaffected as observed from frame K.

That being said, let the “at rest” length of two identical light clocks in reference frame K’ be 1 light second with the light clocks being perpendicular to each other. One of the light clocks is parallel to the direction of impending motion relative to frame K.

When frame K’ is moving at .866 light speed relative to frame K the light clock in K’ parallel to the direction of motion appears to have the length of .5 light seconds as observed from frame K. The light clock perpendicular to the direction of motion in K’ appears to maintain the length of 1 light second as observed from frame K.

The issue is: how can the light pulse in the light in the direction of motion appear to go half the distance of the light pulse in the identical light clock perpendicular to the direction of motion when the speed of the two pulses has to be the same – the speed of light?

One answer is that time dilated in the direction of motion by the reciprocal of the factor that the length in the direction of motion was contracted by. The problem with that is time is not directional in a reference frame. If time dilates in one direction time dilates for the entire frame. Therefore the length perpendicular to the direction of motion is equally affected and the ratio of the inequality is maintained as observed from frame K. That is, time can’t go at one rate if you are lying down and a different rate if you are standing.

Thank you,

butchmurray

 

[SpeedFreek]

When frame K’ is moving at .866 light speed relative to frame K the light clock in K’ parallel to the direction of motion appears to have the length of .5 light seconds as observed from frame K. The light clock perpendicular to the direction of motion in K’ appears to maintain the length of 1 light second as observed from frame K.

The issue is: how can the light pulse in the light in the direction of motion appear to go half the distance of the light pulse in the identical light clock perpendicular to the direction of motion when the speed of the two pulses has to be the same – the speed of light?

The answer to this problem is simple - it doesn't appear to go half the distance.

I should point out that your above calculation is incorrect.

Ok, so your sphere in the frame K' is moving at 0.866 c relative to K, where gamma is 2. Let's look at the length contraction from the frame of K.

From the frame of K, the sphere is contracted by half in its direction of travel, so the parallel light clock is now half the length of the perpendicular light clock. But the spacecraft is moving at 86.6% of light speed. So, how long is the PERIOD of the contracted parallel light clock from the frame of K?

If both clocks have periods of 1 second in the frame of K', the parallel clock does not have a period of 0.5 seconds in the frame of K, as you claim. Do you know why?

Because, from the frame of K, the sphere is moving in relation to the light in that clock! (You have been repeatedly told this!)

For K, the sphere is moving at 0.866 c, so as the parallel light moves forward towards the front of the (contracted) sphere, the front of the sphere moves away from that light, nearly as fast as the light is chasing it!

If the period of the parallel light clock (the time it takes the light from the centre to reach the front and come back to the centre again) is 1 second in the frame of K', then the sphere has a radius of 0.5 light seconds in the frame of K'. How long does the parallel light take to even reach the front of the contracted sphere, from the frame of K, let alone make the return journey to the centre?

If the sphere has a radius of 0.5 light seconds in the frame of K', then that length is shortened to 0.25 light seconds in the direction of travel, for the frame of K. So, after 0.25 seconds, will the light from the parallel clock have reached the front of the sphere for K?

No. After 0.25 seconds, the front of the sphere, which is moving at 86.6% of c, will have moved forwards a further 0.2165 light seconds. So after 0.25 seconds, the light will have travelled 0.25 light seconds but still has 0.2165 light seconds to travel, just to reach the front of the sphere!

A further 0.2165 seconds later, from the frame of K, and the sphere has moved forwards another 0.187 light seconds! After another 0.187 seconds, the sphere has moved on another 0.162 light seconds! After another 0.162 seconds the sphere has moved on another 0.140 light seconds!

How long before the light even reaches the front of the sphere, from the frame of K? He has been watching the light chase the sphere for nearly a second so far, and it is still 0.140 light seconds from the front of the sphere, which is still moving away from that light at 86.6% of c. And the light still has to make the return journey to the centre (which will, of course, be a lot shorter)!

And as for the perpendicular clock, the length of the apparatus might still be 0.5 light seconds, giving a total length of 1 light second for K', but from the frame of K, due to the motion of the sphere, the light takes a triangular path relative to the source, bouncing off the inside of the sphere at the apex of that triangle, so the light also travels a longer path.

How much longer is are the paths? How slow does a clock tick, when travelling at 0.866 c, relative to you?

(The answer is 2 seconds)

This is yet another way at looking at the reason why you are using the wrong experiment if you want to disprove the Lorentz contraction. You are using light clocks!

Of course, any clock in the frame of K' will be time-dilated in relation to K, which is why the period of both clocks is 2 seconds from the frame of K.

Should I go on?

 

[SpeedFreek]

Suffice to say, I think I might have finally got the message through to the OP!.

 

[origin]

Suffice to say, I think I might have finally got the message through to the OP!.

You did an outstanding job of patiently and thoroughly explaining the OP's misconceptions. I was really wondering how he was going to come back and disagree with your analysis - I am still not convinced that he won't pop up again but hey you never know.