Chapter 1. Simulation of Vertical Arm End-to-End Response Time
Good afternoon A, are you rested and ready for my Phi Mode story? As you will recall from our Part I discussion of the Simulation of Signal Transmission in SR Mode, there is general agreement in the predictions of SR theory and the M/M/+M® Model’s SR Mode predictions even though the equations used in the M/M/+M Model are very different. The M/M/+M Model is based upon the Relative Response Time (RRT) Hypothesis that has been derived from the M/M/1 queuing equation that is ubiquitous in models used for predicting the performance of communications platforms. Now, I would like to discuss the M/M/+M® Model’s SR Mode equations that were introduced in the RRT Hypothesis. The M/M/+M® Model’s SR Mode response time equation (5) RTb‘= RTbd’ + RTdb’ = RTbd/(l.sec/sec’) + RTdb/( l.sec/sec’) = 1.0 sec/( l.sec/sec’) + 1.0 sec/( l.sec/sec’) = 0.5 sec’ + 0.5 sec’ = 1.0 sec’ and the Phi Mode equation (5b) RTb’ = RTbd’ + RTdb’ = STbd*(PLo/PLbd.sec/sec’) + STdb*(PLo/PLdb.sec/sec’) = 0.5 sec*(150,000 / 150,000.sec/sec’) + 0.5 sec*(150,000 / 150,000.sec/sec’) = 1.0 sec’ are in agreement. However, they are in agreement only when the signal path is pointed perpendicular to its direction of motion. For more details on simulation of vertical arm end-to-end response time in Phi mode you may review the Part I discussions for figures 1, 2, 5, 6, & 7 and substitute Phi mode for SR Mode all places. A, being the preeminent mainstream physicists that you are, could you elucidate what you as the Observer at point ‘a’ will see and what you would think that B at point ‘b’ will see in the reflections from her satellite as a review of Figure 7 and to give the reader a clearer understanding of the physics of moving mirrors? Then A thought pensively for a moment and made the statements in the following paragraph.
“In figure 7, the Observer will believe that B will always see her satellite at point x’ = 0 km’ and y’ = 150,000 km’ at a 90º angle to her direction of motion regardless of her relative motion because it is stationary wrt her inertial frame. As the Observer at point ‘a’, I will see that the return signal coming from her satellite radiates outward from her satellite in the shape of the Greek letter Phi (f) where the region within both the upstream send reflection and downstream send reflection circles is bisected by a line perpendicular to the direction of motion as shown in figure 7. The bisecting line connecting the positive and negative apogees is the translated remote y-axis of her satellite and it is always perpendicular to her direction of motion. The line connecting the positive and negative perigees in figure 7 is the translated remote x-axis at her satellite that is always pointing parallel to her direction of motion. The Observer always sees the center of a remote f region at point 'j' travel in lock step with and parallel to point 'b' that is the center of B’s local f region as shown in figure 2. All f regions will be called a Phi-light Zones. A transmission from a remote point such as B’s satellite is a Phi-light zone and her local f region with a center at point ‘b’ is a Phi-light zone but it is called her Bi-convex Inertial Frame (BIF) to distinguish it from other Phi-light zones. B should always see her remote Phi-light Zone as a sphere, or as a circle in two dimensions, that is within her BIF moving in lock-stop with her at the center of her BIF just as if they were not moving. B should see her point image located on the intersection of the solid blue circle and the dash red circle that represents the continuation of her upstream send signal and the downstream send reflection respectively. Her point image should lie on the periphery of the remote Phi-light Zone of her satellite and she should see an image of the brown eye at 'a' beside the point image of her blue eye as they were at time = 0. When these conditions are met she will see the mirror attached to her satellite at a distance that is one-half the distance to her point image. In the case where the satellite is always 150,000 km’ directly above her she will see an image of the brown and blue eyes as they were 1 sec’ in the past at a distance of 300,000 km’ directly above her and she will see her satellite as it was 0.5 sec’ in the past at a distance of 150,000 km’ directly above her. Finally, she will calculate that her vertical arm end-to-end response time will also be 1 sec’ or the same as the time required for light to travel from her point image to her eye.”
Thanks for clarifying the physics of moving mirrors A; you have concisely concluded this chapter.
Chapter 2: Simulation of Non-Vertical Arm End-to-End Response Time.
Computer performance analysts not only need to be able to use their models to see problems in observed or hypothetical systems, they must also be able to test potential solutions by using their models to simulate "What If" assumptions. Unexplained paradoxes are apparent in the MM+M Model’s SR Mode simulation of reflections for all arms except the vertical arm. A model that can uncover potential problems but cannot be part of the solution may as well be viewed as part of the problem because it is a tool that limits your range of vision. Therefore, the usefulness of the M/M/+M Model depends upon its ability to facilitate the discovery of a potentially more accurate predictor of relativistic phenomena instead of its ability to find fault with the assumptions of Special Relativity.
Therefore, A let’s see what happens with the simulation of reflections if we ask: "What If" we change the length contraction equation? Figure 11 shows B with her satellite configured at point’d’ that is now directly ahead of her in her direction of travel as she passes over your solarium. In this configuration, she resets her stopwatch to t’ = 0 when your camera broadcasts its snapshot. This time her satellite is 40,192.3789 km directly in front of her by your space coordinates while your satellite is still 150,000 km directly above you. The distance PLbd = 40,192.3789 km is a Phi Mode calculation for the horizontal arm assuming no significant gravitational forces. This value for the contracted horizontal arm length PLbd is derived from the RRT hypothesis equation (1e) PLbd = RTbd*(c-v) where (1d) RTbd = (Lo*l)/c. At the extreme velocity of 259,807.6211 km/sec, Pbd = ((150,000 km * 2) / 300,000 km/sec) * (300,000 km/sec - 259,807.6211 km/sec) = 40,192.3789 km. Therefore, there is a difference of over 46% between the predicted arm lengths of the SR equation L = Lo (1 - (v/c)2)1/2 = 75,000 km for the horizontal arm and the Phi Mode "What If" assumption of 40,192.3789 km at this extreme velocity. However, at an orbital velocity of 8 km/sec PLbd = 0.50000001777 sec * (300,000 km/sec - 8 km/sec) = 149,996.0053 km and L = 150,000 km * (1 – (8 km/sec / 300,000 km/sec)2)1/2 = 149,999.9999 km for a difference of only 0.0027%.
Now let’s take a look at the MM+M Model’s Phi Mode output in Figure 12 and compare that output to SR Mode results for the same network configuration. Phi Mode gets its name from the Greek letter Phi because in this mode, the Observer calculates that the Traveler’s transmission spreads out in a shape that is similar to the letter Phi as the region within both the upstream send and downstream send circles is bisected by a line perpendicular to the direction of motion as shown in figure 12. The bisecting line connecting the positive and negative apogees is the Traveler’s translated y’-axis and is always perpendicular to the Traveler’s direction of motion and has a length = 2Lo. The line connecting the positive and negative perigees in figure 12 is the Traveler’s translated x’-axis that is always pointing in the Traveler’s direction of motion and has a length = 2L. In Phi Mode, the downstream send signal that is not also within the upstream send circle can not be seen directly by the Traveler and the upstream send signal that is not also within the downstream send circle can not be seen directly by the Traveler because outside this area the transmissions are traveling faster than the speed of light wrt the Traveler’s moving space-time coordinates. The transmissions that are moving at a velocity = c wrt the Traveler are within the Traveler’s BIF. The M/M/+M Model is a hybrid time step and queuing simulation model that uses a convergence methodology to derive the value of PLbd for any non-vertical arm when the path length at rest, PLbd’ = Lo, is given in addition to velocity and direction information. After the value of PLbd is derived it can be input to the model for "What If" simulations to determine performance data such as response time and throughput. Also, an observed value for PLbd can be input to the model in addition to velocity and direction information to perform the "What If" simulations that will determine performance data.
Figure 12 is the M/M/+M Model’s Phi Mode output for a simulation of a send signal to B’s satellite that is assumed to be shortened to a distance of (1e) RTbd*(c-v) ahead of her at point 'b' as measured by you A as the Observer at point 'a'. The Phi Mode equation (5b) RTbd’ = STbd * (PLo/PLbd.sec/sec’) = 0.1340 sec * (150,000 / 40,192.3789.sec/sec’) = 0.5 sec’ yields the correct value for the Traveler’s Response Time RTbd’ when the path is pointed in the direction of its motion. The SR equation (5) RTbd’ = RTbd /l.sec/sec’) must be calibrated by the Out-of-sync factor +(v*Lo/c2) when the path’s slope is 0º wrt its direction of motion. Also, an Out-of-sync factor must be used to calibrate equation (5) for a path of any slope other than 90º. However, SR theory does not propose an Out-of-sync equation that is expressed as a function of path slope. The Phi Mode equation (5b) does not need to be calibrated because ST and (PLo/PLbd) vary with the slope of the moving path while l and (v*Lo/c2) do not. When B uses Little’s Law to calculate her response time as RTbd’ = (PLbd’ / c) = 150,000 km’/300,000 km’/sec’, she gets the same answer RTbd’ = 0.5 sec’ as equation (5b) for the configuration shown in Figure 12. The Phi Mode calculation for RTbd’ in equation (5b) does not agree with the SR value T’ = To(1 - (v/c)2)1/2 = 1.866 sec * 0.5 sec’/sec = 0.933 sec’ for B’s horizontal path because the length of the horizontal arm in Phi Mode (1e) PLbd = Pbd = RTbd*(c-v) =1.0 sec * (300,000 km/sec - 259,807.6211 km/sec) = 40,192.3789 km is shorter than the SR value L = Lo (1 - v/c)2)1/2 = 75,000 km. Phi Mode calculations for response time do not have the disagreements that SR Mode has due to the greater length contraction; therefore, the Out-of-sync Time adjustment is not needed. The Concept of Simultaneity that is intended to account for the difference (0.5 sec’ + 0.433 sec’ = 0.933 sec’) in SR Mode calculations is unnecessary in Phi Mode simulations.
We have seen that the M/M/+M Model running in SR Mode can simulate the "What If" premise that PLbd shrinks from length Lo at rest to length L in motion as described by the SR equation L = Lo(1 - v/c)2)1/2 and that B’s send response time component is degraded from 1.8660 sec to 0.9330 sec’. However, the M/M/+M Model in Phi Mode does not declare it is degraded because there is a clock at point 'b' that runs out of sync with a clock at 'd'; instead, it asserts that B’s three clocks – her stop watch, the clock at her satellite, and her photon clock that has a blue photon running between her and her satellite all run in-sync with each other and all of her clocks run slower but in-sync with all three of the Observer’s clocks according to the relationship RTb = ETa * (1 - v/c)2)1/2 when there are no significant gravitational changes between point 'a' and point 'b'. Figure 13 shows the Phi Mode configuration after the return signal has been received at point 'b'. The blue photon that is the reflection of the blue send photon has completed its trip from B and back to point 'b'. B calculates her total end-to-end response time as (11) RTb' = RTbd' + RTdb' = (PLbd'/c + (PLdb/c) = 150,000 km'/300,000 km'/sec' = 0.5 sec' ) 0.5sec' = 1.0 sec'. The Observer will calculate B's total end-to-end response time as (5b) RTb' = RTbd' + RTdb' = STbd* (PLo/PLbd.sec/sec') + STdb*(PLo/PLdb.sec/sec' = 0.1340 sec) * (150,000 / 40,192.3789.sec/sec') = 0.5 sec' + 0.5sec' = 1.0 sec'.
Now, A, take a look at the Send and Receive videos. The videos show her satellite as you see it when it is 150,000 km' ahead of her and inclined at a 75º angle to her direction of motion according to the Observer at point ‘a’. What is the angle of incline according to the Traveler at point b? Also, can you tell me what you and B will see in the mirror attached to her satellite in Figure 14 and how it relates to the receive video? A replied as followings: "I would say that videos are just an artist’s conception of the mechanics of light. It illustrates the path of B's send transmission and her receive transmission that is also the reflected send transmission. In the Send and Receive video’s, the arm is inclined at a 75º angle according to the Observer at point ‘a’: however, the angle that B measures must be an aberration because it is clear in your pictures that the angle of incline is less than 75º according to B at point ‘b’ due to the contraction of B’s Spherical Inertial Frame (SIF) to the shape of a bi-convex lens. It is also easy to visualize that the M/M/+M® equation RT = ST / (1-QU) describes the behavior of both the horizontal arm as well as the vertical arm in the MM Experiment. This simple unifying equation “orders things more easily” and describes a single arm that can be pointed in any direction relative to the direction of motion. I can also see that my reflection and my red photon can travel on the red downstream send reflection and that B’s reflection and her blue photon travel on the blue upstream send reflection. Based upon figure 14, I can see that my reflection and B’s reflection behave the same way as they do in the receive video. Also in figure 14, I can see that all of B's clocks run at precisely half the speed of all of my clocks at all times during the send and receive transmissions; therefore, I do not see any of her clocks running out-of-sync with each other. In figure 14, the Principle of Relativity and all of the laws of physics appear to be upheld including the physics of mirrors. B sees an image of her blue eye beside an image of my brown eye reflected in the mirror as they were 1 sec’ ago at time = 0 and at the point image 150,000 km’ behind the mirror attached to her satellite at point ‘k’ that was 150,000 km’ in front of her when the return signal started 0.5 sec’ ago for the horizontal arm just as she saw in the case of the return signal above her for the vertical arm. Also, she sees the point image on the continuing upstream send signal. Her returning blue photon is on the reflection of her upstream send for the horizontal arm just as in the case of the return signal for the vertical arm and the receive video. I see an image of B’s blue eye beside an image of my brown eye reflected in the mirror as they were 2 seconds ago at time = 0 and at the point image 300,000 km behind the mirror attached to her satellite at point ‘e’. I see the point image on the continuing upstream send signal and my returning red photon is on the downstream send reflection in accordance with the physics of mirrors and there is no clock synchronization or speeding-photon paradox."
Finally, I inquired, now that you have told me what you can see and what you think B can see in the M/M/+M Model's pictures what is your opinion of these pictures? A said with a stern twinkle in his eye, “I am a mainstream physicist and we go by a code of conduct; in order to protect our jobs and ourselves from ridicule within the mainstream we do not agree with any theory that contradicts Einstein. As for your pictures I will only give you a quote from Einstein himself. “True art is characterized by an irresistible urge in the creative artist!”
The "What If" assumptions simulated in Part I were that the vertical arm of the MM Experiment does not contract and that the horizontal arm pointed in the direction of motion contracts to a length L = Lo * (1 - (v/c)2)1/2. The "What If" assumptions simulated in Part II were that the vertical arm of the MM Experiment does not contract and that the horizontal arm pointed in the direction of motion contracts to a length L = ETa * (c - v). Do these stories have a burden of experimental proof? Yes, they most definitely do! Assumptions in theories or models about light transmission in the MM Experiment must be proven experimentally when different sets of assumptions can reliably predict or simulate the observed behavior of the MM experiment. Why were 20th century physicists complacent about exhaustive and thorough experimental investigation of SR assumptions? Did they think such an investigation would be a “huge money burner” and may only prove that Einstein’s SR theory was correct? This is clearly not the case in SR's predictions of starlight aberration. The aberration equations based upon SR theory are not as precise as Phi Mode aberration predictions. Also, starlight aberration equations based upon SR Theory and Phi Mode can be testing very economically. Will the laziness or complacent attitude about learning and using new measurement tools and doing simple cost efficient testing prevail among mainstream physicists in the 21st century?
What do these stories intend to do? They intend to suggest as a hypnotist attempts to suggest and often succeeds depending upon the persuasiveness of his “hook” and the suggestibility of his subjects. Are these stories science or fiction? No one can really know whether the SR story or the Phi Mode story is science or fiction. Some will believe one is all science if they are suggestible enough. Only personal and exhaustive examination of experimental proof of the reliability of predictions that follow from a story (or model) will be good enough for the doubting Thomas. No amount of emperical proof will be good enough for the mainstream physicists who must obey a code of conduct that is a survival defense mechanism to protect their income or to protect themselves from ridicule within the mainstream.
In the future, performance analysts will eventually be faced with a problem of measuring response time components, throughput, and signal aberration between platforms moving at high speeds. When this time comes, they must be able to draw their own conclusions about the credibility and reliability of competing models. Can private industry be trusted to produce reliable measurement tools or will private industry rubber stamp SR models to appease the mainstream physicists? The National Bureau of Standards regulates standards for tools that measure lengths and weights. Why shouldn't such an unbiased Government Agency with measurement expertise play a role in the regulation and standardization of tools that measure RF signal transmission delays, signal aberration and other parameters where standardization and/or guidelines will be needed by performance analysts in the future?
There is much more to learn about what the M/M/+M® Model can simulate. Video tutorials and/or video-conferences will describe current capabilities and future derivatives of M/M/+M® Models. A Video Tutorial is currently available at this web site that will provide a detailed description of what the Traveler will see according to the M/M/+M® Model’s Phi Mode simulations [see "M/M/+M® Model, Version 1, Tutorial" at the Tutorials page]. Proof of the M/M/+M® Model’s ability to accurately predict stellar aberration as viewed by astronomers on Earth and details concerning what an intra-galactic space Traveler will observe measure or calculate wrt distant stars will be described on this web site [see “Relativistic Stellar Aberration & Bearing estimator (Best) Equations” at the Stellar Aberration page]. The M/M/+M® Model can simulate aberration or contraction of the space (or distances) in the Observer’s inertial frame from the Traveler's point of view as well as the aberration or contraction of distances in the Traveler's inertial frame according to the Observer. The M/M/+M® Model is a reliable predictor of starlight aberration, it can resolve SR paradoxes such as the twins' paradox and issues related to preferred inertial frames or absolute inertial reference points vs. relative inertial frames, it can also clarify clock synchronization issues. Also, a Video Tutorial will describe the simulation of the aberration of starlight coming from the star y-Draconis [see "M/M/+M® Model, Version 2, Tutorial" at the Video Tutorials page]. More research, development and testing should be done to exploit and validate this promising alternative to SR Theory. More research can break us out of the SR box and more development can result in many derivative discoveries and products that can have immense commercial value.
Those who believe we will eventually need a Galactic Positioning System (GPS) for space travelers as well as models that will accurately predict performance metrics and signal aberration for systems moving at relativistic speeds should be proactive and play an active role in research, development and testing in the dialectic process of selecting a preferred method or best practice for predicting relative response time, throughput, signal aberration and other performance metrics or relativistic phenomena. The Version 1 Release 0 (V1R0) Beta Release (R0) and the Version 2 Release 0 (V2R0) Beta Release (R0) of the M/M/+M® Model are user friendly R&D test beds that are currently available and can be demonstrated to interested parties. Arrangements for a free video-conference and demonstration may be arranged at no cost to representatives of a university or legal entity (corporation, LLC, etc.) by e-mailing a request to