Relativity Geometry Inquiry

[arkain101]

This is the typical geometric expression of special relativity (<--click text). It demonstrates how two frames differ on the velocity of light (a photon). One frame experiences the photon move back and forth as normal, while the other frame observes the photon travel the same time it ticks back and forth.

 

I follow this logic and it makes sense. It explains that this effect will cause 'time' to be 'observed' run slower because of this geometric expression. However, when the frames are experiencing inertial motion relative to eachother it is said that each frame experiences the same dilation in time. That is, each clock slows down the same. Right?

 

I've found that using this description it makes an assumption that is not possible. That is, by assuming what occurs in another frame, it is not possible, because as SR states, and logic would agree, your frame is restricted to observe only where it resides.

 

So I have continued to have issues with this geometric description/illustration.

 

I've included a hard worked at animation :( that offers what I tend to look at as the alternative explaination in geometric illustration of a fast moving observation. In this expression, there is no intruding into a frame you are not allowed to intrude into. There is also no time dilation caused from geometric change. Instead, there would be doppler change.

 

I am not sure if this is workable and that is why I am posting about it.

 

I only bother to work with this because some observation principles lean towards it.

-any inertial frame (one that assumes it is at rest) that shines a laser will observe the laser to shoot out in a strait line at velocity C away.

-Any inertial observer, observing an inertial moving frame, observes light travel towards itself in a strait line, and also at velocity C towards.

-Any inertial observer, observing an inertial moving frame that is seperated by a given distance, observes information that is of the 'past' in respect to the source, and the delay is a perportion to the distance of the source. -furthermore, also, the velocity of that source forms a perportional change to the observed position and the actual position, for the observer in respect to a given photon.

 

So from that, I am pretty sure we end up with a geometric expression that is attatched (it may not work at first, so bare with me I will get it to work).

 

The dimensions are not to scale. We should assume that each observer of each frame (the red and green dot's) witnesses the blue photon (blue dot) travel at C, with respect to each observer's perspective. (this should mean that each blue path is of equal distance even though my animation does not display this correctly, oops)

 

Note: when the red observer recieves the photon it reports the source at the location where it originated. That is, the red observer reports that the source (green dot) is at a location further back, than is the actual position.

 

added image: Science Forums

[LaurieAG]

I've found that using this description it makes an assumption that is not possible. That is, by assuming what occurs in another frame, it is not possible, because as SR states, and logic would agree, your frame is restricted to observe only where it resides..... So I have continued to have issues with this geometric description/illustration....-Any inertial observer, observing an inertial moving frame that is seperated by a given distance, observes information that is of the 'past' in respect to the source, and the delay is a perportion to the distance of the source. -furthermore, also, the velocity of that source forms a perportional change to the observed position and the actual position, for the observer in respect to a given photon. So from that, I am pretty sure we end up with a geometric expression that is attatched (it may not work at first, so bare with me I will get it to work)..... Note: when the red observer recieves the photon it reports the source at the location where it originated. That is, the red observer reports that the source (green dot) is at a location further back, than is the actual position.

 

Hello Arkain, good points,

 

Just to extend your logic. The observer doesn't actually have to be stationary (with respect to the point being observed), it only has to be stationary for the discrete instance when the observations are made. This means that the effect will be symetric for observers at both locations that are collecting photons from a wide field and are travelling in the same relative direction (i.e. relative to each other they are stationary).

 

In the past I created an image of this type of distortion as it would appear from one solar system being observed from another identical solar system where both systems have the same radius and speed of rotation around their respective galactic centers and the distance between them in light years equals one rotation period or greater. I found the image. The image is an extension of your simple example to two bodies that are rotating (in phase or out of phase) and it produces light paths from point sources that produce identical patterns to objects that are presently perceived as spiral galaxies.

 

The latest astronomical observations indicate that one side of a solar system (i.e. what appears to be a spiral galaxy due to the cumulation of the distortions you describe) has red shift while the other side has blue shift.

 

This distortion, IMHO, can also explain away anti matter if we are really looking at the same object rotating in a circle/oval (whose diameter is completely within our field of view) instead of something that we perceive as a much larger conglomeration of matter, because of the distortion (reinforced by the observed doppler effects) described in your previous post.

[arkain101]

 

I think i see what you were attempting to illustrate in those images.

 

A kind of wavey spray of light, like the view we see of water when you wiggle a spraying garden hose back and forth? The water would give information of a spiral, but it's source, is just an accelerating hose.. as I think you dispalyed..

 

Onward.

 

I was thinking about an equation that would relate to what this concept is after. It would simply have to do with velocity and angles.

The aim to express how the distance and angle of approach would change for a photon to arrive at an observer from an inertial moving source, while it travles at C for each observer.

 

For the photon to travel at C for each observer, and arrive at the observers frame:

 

A faster moving source would create;

-a smaller origin point angle. But the angle would be limited to reduce to a specific size which I beleive is in the range of a minimum 33 degrees.?

-greater change in position displacement

 

A slower moving source would create;

- a larger angle.

-less change in position

 

 

This would be the basis diagram to work with.

[arkain101]

Using example attatched below, I kindly ask for some mathmatical assistance.

 

Equations of use:

 

Lorentz Factor [math]\gamma = \frac {c}{\sqrt {c^2 - v^2}}[/math]

 

 

Pythagoras Theorom: [math]a^2 + b^2 = c^2[/math]

 

On the diagram below a,b,c are paths. path c is photon @ velocity c (relative to observer green) at 1 second distance. Length C is 299,792,458 meters. Or 1 for simplicity basics.

 

Further:

a = velocity source. distance @ 1sec

 

b = velocity photon @ unknown distance and time

 

c = source photon @ velocity c for 1sec

 

work:

 

[math]a^2 + b^2 = c^2[/math]

then into conversion for diagram:

[math]c^2 + a^2 = b^2[/math]

 

[math]1^2 + 0.5^2 = b^2[/math]

 

[math] b = \sqrt {c^2 + v^2}[/math]

 

[math] b = \sqrt {1^2 + 0.5^2}[/math]

 

[math] b = \sqrt {1.25}[/math]

 

[math] b = 1.118 [/math]

 

Note:

 

Or simply, path B of photon is a ratio of [math]\sqrt {2}[/math] = 1.4142

 

This is because: If the source (green) is at velocity C for 1sec distance. The lenght of both source path and photon path are equal. Thus, path observer photon (B), would become pythagoras constant 1.4142 (for other two lengths at 1).

 

However, since velocity is not achievable for C, the photon path (b) for observer is a ratio of 1.4142 (a ratio of a constant)

 

The ratio being between 1 to 1.4142

for 1sec time

 

path b=1 means source is at rest.

 

path b=1.4142 means source is at 'c'

 

velocity resides inside that value for time @ 1 sec

 

Question: What is the angle of [math]\theta[/math] ?

 

Conclusion:

 

We end up with two options:

 

1)

Did the photon travel path b and c in 1 sec simutaniously... That is, path b relative to red observer @ 1 sec, and path c relative to green observer @ 1 sec.

 

"supporting time dilation"

-supporting time dilation by requiring time to alter in others frames for simutanious arrivals.

 

Or:

 

2)

Did the photon travel path b and path c at different values of time. That is, in this example, 1 sec for path c, and 1.118 secs for path b.

 

Yet, arrive at those locations at the same time, over different distances both at C.

 

"supporting quantum mechanics and no time dilation?" (for intertial moving frames)

-supporting quantum mechanics, by allowing in this case one photon to be considered in more than one place at the same time.

[arkain101]

So technically the dilations can be derived from these equations?

where a,b,c are the paths in the above example.

 

[math]tan \theta = \frac {C}{A}[/math]

 

[math]sin \theta = \frac {C}{B}[/math]

 

[math]cos \theta = \frac {A}{C}[/math]

 

 

Path C is velocity of light 'c'

 

The angle for [math]\theta[/math] should be in the range from 90(rest) to 45.111...(near speed of light) -depending on the velocity of the inertial source-

 

So as the velocity increases towards c

we observe that length 'a' will increase (angle will decrease), and misposition of actual object will be equal to a.

 

 

and as we graph these values of [math]\theta[/math] we should end up with things similar to this for the wavelenghts(?)

 

 

The trigonometric functions are periodic, with a period of 360 degrees or 2[math]\pi[/math] radians.

[arkain101]

Rough example:

 

-based off same illustration(s) earlier. Traveling left.

 

-The grey circle is where observer reports from the photon where the moving frame is located.

 

-The Green circle is where the object is actually located.

 

-The red cirlce is where the observer is at rest

 

-The "Photon observer ratio # value" is the (length of the hypotenuse), which is the ratio of the photon path for the observer at rest, relative to the observer in motion (which remains at c @ 1 sec) let it be 1

 

 

 

 

See Animation Here

 

It plays slow, so patience is required.

[arkain101]

Updated Graph.

 

This forms a graph of curvature of the Aberration of light from velocity rest to c(light) for the moment perpendicular relative motion. For c @ 1sec

 

By these results, this also forms a theoretical prediction of an alternative geometry to dilations.

 

Although this is theory, it can be tested. I doubt it to be correct. It is an alternative in that there is no length contraction. It also states that any one photon has the capability to be in two places at the same time, yet arrive on target simutaniously.

[arkain101]

-Total geometry of dilation

-Both observers views

-Near C left, near C right, and Rest.

[Jay-qu]

I cant see what you are trying to prove/point out - relativity is consistant when you look at it from all angles..

[arkain101]

updated.

I cant see what you are trying to prove/point out - relativity is consistant when you look at it from all angles..

 

Here is a great interactive tool for the doppler effect. Classical and Relativistic modes: Physlets Home Page

 

My thesis is that SR appears to contradict itself.

 

For example:

 

A slow relativistic moving source will have a so called light clock appear in this kind of geometric observation: ///////////......

 

As it gets faster of course the path resembles / / / / / / /

 

Where as nearly C it would resmeble nearly a line:-------------

 

The condradiction is that as it nears C, light can not escape from the source.

 

This is, the angle at which the light would be capable to attempt perpendicular travel would be so little light could not reach an observer unless from a very great distance away.

 

For example. Imagine the photon in the photon clock. As the frame nears C the photon is very slowly bouncing to either side. The photon is apparently drifting with the frame (drifting, keeping the same pace as source). Now if we suddenly removed one of the mirrors (the one on our observing side), the photon would slowly leave the frame containing the same drift velocity of its source, and it would cover so little distance towards the observer (due to its angle) that it may never reach us. SR, instead, claims that once a photon is able to get out of the frame, it loses all drift velocity, and travels directly towards the observer.

What causes one photon to travel with the frame, and the other to not?

 

My point is that the moving source in their frame has the same laws of physics as the observing frame. However, because an observer is limitted by probability and principles of observation it can not observe the moving frame directly, so instead it observes the source's past, and locations of its position relative the sources velocity.

 

This does not claim that SR will have incorrect predictions. Instead it means that the dilations are only observations, not physical actions in the sources present moment. Also, that the source itself remains by all means the same as any frame in respect that the probabilty to observe the source at its present moment and location (certainty), reduces in specific perportions to velocity, direction, and location.

 

Our probabilty of observing location and present moment has everything to do with how many signals per sec an observer recieves. The geometry of a fast moving source creates a situation where the probabilty for certain predictions reduces.

 

For example. If you snap a picture of a fast moving frame that is 5 light seconds distance away. The location the picture displays is not where the object is. Also, the distance the light traveled for the observer in comparison to the source reference frame is different.

 

Where as, if you take a longer picture such as a video, you recieve several signals during a period of time (t). In this way you define if the frame is inertial and predict a high level of certainty of its location, but you still can not observe the frame itself, thus, the observer can only experience, probable certainty. High or Low relative to the situation.

[arkain101]

Please note this is work at a legitamit paper and thesis. There is no attempt to be right or wrong or call scientists and current physics wrong. It is variation of SR interpratation that can be proved or disproved.

 

As expected, in a scientific method, do not argue with me. If you wish to argue against the data brought forward, do so with the support of other data to compare where it is wrong.

 

I am not sure if its right or wrong, it is a sound, testible, peice of research that creates predictions.

 

However, I do feel confident the data is correct, or that is, worth investigating.

 

It is at this point I think the last argument I have for current physics. :naughty:

[Jay-qu]

It can all be worked out with length contraction and time dilation, like I said it is completely self consistant. There have been scientists picking over it for the last 100 years - Im not trying to be rude, but do you really think you would be the first to notice an inconsistancy?

[arkain101]

Im not trying to be rude, but do you really think you would be the first to notice an inconsistancy?

I really do not think that.

 

Think of this as a students thesis paper. I am no physicist. I am just bringing forward my understandings after picking at it many ways.

 

Accidently, through this it appears it has derived and generated the equations of light aberration, but it also goes further.

 

I am rude to myself just the same, I would not claim this is right, just as no theory should ever claim it is right. I just wanted to investigate it.

 

The kind of response I am most interested in getting is a data supported counter argument to specific points. Though, I do not request anyone to invest their time to do so.

[arkain101]

Uses of system. Diagram @ 1 sec of time:

 

 

 

1)Gamma:

 

[math]\frac {hypotenuse}{velocity}[/math] works out dilations for gamma.

 

 

 

2)Aberation of position:

 

Where as, the [math] side (a)^2 + side (b)^2 = hypotenuse^2[/math]

which is:

 

[math] \left( \sqrt{v*t^2 + c*t^2}\right) = x [/math]

 

this works the aberration of position aberration (x).

Where x is the hypotenuse.

where c=1

 

 

3)The speed of light in a medium:

 

The speed of light in a medium is equal to the [math]cos \theta = \frac {c}{(vn)} [/math]

 

where: [math]n = \frac {c}{a}[/math]

 

Where n is the index of refraction

and v is the velocity of a particle

where a is the speed of light in the medium

 

 

 

 

 

 

(examples using attatched image)

 

 

 

 

 

 

Calculating [math]\gamma[/math]:

 

1second diagram:

let the hypotenuse be 1=c(light)

let "side a" be velocity length (<1)

 

[math]\gamma = \frac{c}{\sqrt {c^2 - a^2}} = \frac{1}{\sqrt {1^2 - a^2}} = \frac{1}{\sqrt {1^2 - 0.5^2}}[/math]

 

[math]\gamma = \frac{1}{\sqrt {1^2 - 0.5^2}[/math]

 

[math]\gamma = \frac{1}{\sqrt {0.75}[/math]

 

[math]\gamma = \frac{1}{0.866}[/math]

 

[math]\gamma = 1.1547344[/math]

 

 

 

worked out list in this manner:

 

(%c) - gamma

0.010 - 1.000

0.100 - 1.005

0.200 - 1.021

0.300 - 1.048

0.400 - 1.091

0.500 - 1.155

0.600 - 1.250

0.700 - 1.400

0.800 - 1.667

0.866 - 2.000

0.900 - 2.294

0.990 - 7.089

0.999 - 22.366

 

 

There might be some math errors but I am too tired to go through this at the time.

[Qfwfq]

The condradiction is that as it nears C, light can not escape from the source.

 

This is, the angle at which the light would be capable to attempt perpendicular travel would be so little light could not reach an observer unless from a very great distance away.

On what grounds? I didn't see anything helpful to clarify this on the page you linked to.

 

SR, instead, claims that once a photon is able to get out of the frame, it loses all drift velocity, and travels directly towards the observer.

How does SR make this claim?

[IDMclean]

Something that I remembered from my physical science class in fifth grade.

 

The speed of light is a geometric definition. c, is actually the hypoteneus of a triangular relationship in the wave form of a propagating electromagnetic ?charge/field?.

 

If you where to draw a line from the mean point under the crest of the wave form (the the zero point along all axises) to the crest of the wave form (highest point on the y or z axises) then draw a line from the top and bottom of this line to the trouphe of the wave form, you would naturally get a triangle. c is defined as the square root of the distance of the hypoteneus of this triangle.

 

That is, it is the line. It's the result of the relationship of [math]E/B = c[/math]. Which is essentially [math]\sqrt{a^2 + b^2} = c[/math].

 

I am trying to find source for this, but I am reasonably certain of it's validity.

 

Just thought I would note this because of the last post on page 1

[arkain101]

I think I see what you mean Clown.

 

Using this model, in a geometric sense we can show a the relationship that SR uses for dilations.

 

I am using 1 second, one photon, for perpendicular moment.

 

Let the Hypotenuse remain constant = 1 = C

 

Let The top side be Velocity value and represent the distance the source moves in 1 sec.

 

Let the vertical side be the ratio of change relative to Hypotenuse.

[math]b^2[math]

 

The "system" is the triangle. The values are the squares. We see how the changes occur at rates of which they do.

 

All values in this system are sides and all sides are squared.

 

[math]a^2 + b^2 = c^2[/math]

 

Notice, Initially.. the increase of length is greater in the velocity side(a) than the dilation side(b). That is,

0.2 gain in velocity is, 0.04 length loss in dilation.

0.4 gain in velocity length is, 0.16 loss in length in dilation..

 

When the sides are equal, and that is the hypotenus has two 45 degree angels. That is, the velicocity side and dilation side are equal. At this point the greater change switches from the velocity's side(a) to the dilations side(b).

Effectively, each small change in velocity creates large changes in dilation.

 

I have an example. By taking a pencil and standing it up against a wall.

 

Let the Pencil be the hypotenuse

 

Pull the bottom out from the wall and keep the top of the pencil against the wall.

 

At first the bottom of the pencil is doing most of the motion. Eventually, in a curvature rate of change the top of the pencil and the bottom change at about the same rate at 45 degrees. Now, the top of the pencil takes over in the curved rate of change. A small movement in the bottom creates a large drop/movement at the top of the pencil.

 

The system being essentially enclosed in 90 degree singularities. Where (0 degrees) Vertical = Rest, and (90*)Horizontal is equal to C. Everywhere In between is relative motion. I am attatching an animation that may be the expression of this model.

 

Animation: Relativistic Geometry

 

 

The curvature of that change should be equal to the curvature of the curvature in SR that Calculations map out. This is, when you focus on the rate of change on the dilation tip of the line (the top of the pencil in the wall/pencial experiment example).