For all you believers in Relativity BEWARE. There is more consequences to the concept than just being "Counter Intuitive". Follow the consequences to the logical (mathematical) conclusion. You are aware that the theory precludes travel faster than light (FTL). You are aware that it claims spatial contraction as a funtion of relative velocity. For those of you familiar with the mathematics you can prove the following to yourself. For those of you not familiar trust me or seek confirmation from those that do . FACT: Given a cosmic body at rest to earth but located a mere 3 B LYr away. Given you are in your standard USA made Ford or Chevy on a flat straight roadway in line between yourself and the cosmic object in consideration. Given your car accelerates from 0 - 60Mph in 6 seconds towards the object (very typical performance and certainly not in the realm of relavistic fantasy), the distance to the remote cosmic object IN ACCORDANCE WITH SPECIAL RELATIVITY is contracting at a rate of 10,502c!!!!! That is right at these velocities and acceleration rates of which we all experience every day of our lives, SR predicts a closure rate to remote spatial bodies that is FTL at MANY times c!!!!!!. A theory that prohibits FTL travel actually creates it. The closure rate between you and the cosmic object IS MANY FTL c's. What is even more pointed is if you accelerated away from this object you got closer at FTL also. BEWARE BELIEVERS.
I think you misunderstand the meaning of ''everything is relative.'' But yes... we need some equations here.
yes, and one more comment. It is not about believing in relativity. So far, SR and GR are well tested experimentally, so it is having confidence in the theory, not faith.
Wrong. ONLY one way gamma functions have ever been tested. SR is based on the claim of "Relative Velocity" and the inherent reciprocity has never been observed nor any attempt to test or prove it. Oh and by the way Spatial Contraction has not been tested nor observed either. If you retain the fact of clock dialtion after acceleration then the traveling clocks accumulated time fully accounts for the trip with NO spatial contraction possible. Spatial contraction ONLY occurs mathematically because you erroneously change time tick rate standards and then treat them as equal - Shhhhsh.
My pleasure. However, I suspect I will have to spend just a little time educating you mathematically. But before doing that I just want to laugh at how fast this was shoved into pseudoscience. I have correctly stated conditions created by SR and it is labled pseudoscience. I happen to agree SR IS pseudoscience. So. I am very familiar with the formulas of SR and how to use them. I hope you are aware that it is virtually impossible to apply those formulas to our everyday experiences(relative velocities) because the changes are 30+ decimal places out and calculators and computers just don't retain that data but rounds such fractional number to 1.0000n30 instead of 0.99999n31. That being pointed out there are approximation methods to evaluate such low relative velocities. It is a mathematical convergence series. To prove the series is applicable I'll first apply them to known SR calculations and results. i.e. - GPS. It is known that GPS orbiting satellites gain tick rate due to GR affects and lose time according to relative velocity (note I did not say SR - nor relative to what). The time loss due to GPS orbit velocity is 7.2useconds/day. Given: The GPS orbit velocity is 3,874.5m/s The surface velocity at the equator is 463.8m/s The differential velocity would be 3,410.7m/s To use the series: Result = Range * [(V/c)^2]/2 Range in this case is the number of seconds per day = 3,600 * 24 = 86,400 seconds. Result = 86,400 s/day * [(3,874.5 m/s/3E8m/s)^2]/2 = : 7.206us/day Hmmm seems to work. While here I'll just add another note: The differential between the surface and orbit at maximum velocity at the equator results in only a loss of 5.584us/day and GPS only works because it uses an absolute local common preferred frame of rest reference (center of the earth) and not velocity differential or relative velocity. The only place relative velocity of the surface and orbit compute correctly is when the surface is at the pole and v = 0. Further using such common preferred frame is Lorentz Relativity which precludes reciprocity and not Einstein Special Relativity which mandates it. Now given the ability to evaluate low velocities lets look at the situation I proposed. Range in this case is the number of meters in 3Blyr. c = 3E8m/s s/d = 86,400 s d/yr = 365 (excluding leap year) distance = 3Bly Range = 3E8 * 86,400 * 365 * 3E9yr = 2.838E25m 60Mph = 88fps = 26.83m/s in 6 seconds = a a = 4.47m/s^2 So the velocity (V) change in 1 second = 4.47m/s: Result = 2.838E25m * [4.47m/s/3E8m/s)^2]/2 = 3.15E9m/s Result/c = 10.502c or FTL. Seems I slipped a decimal point (hit "," instead of ".") in my original post but it doesn't change the facts. Now Velocity is a fact of rate of change in distance to an object. And the fact is SR causes unacceptable destruction of basic physics because distance to objects is changing as a rate proportional to the distance of the object the reality is any time you accelerate you are achieving an infinite different number of velocities. While I may claim I am going from 0-60mph in 6 seconds relative to the stop sign I just left, I'm going FTL to remote objects in the universe. I am getting closer to objects when I have accelerated away from them, etc. Don't just jump up and down objecting, do the math and think. Nothing here detracts from the fact that SR is very useful and produces precise predictions for limited purposes but its consequences cannnot be ignored and they mandate that it is nothing more than a handy mathematical tool and has no meaning in terms of physical reality. I should add that you don't have to work in the subluminal ranges and use approximations. Go ahead calculate some changes for particles in particle accelerators using conventional relavistic formulas. Your results are even more FTL in shorter ranges.
Well, then either use software with arbitrary precision numbers, or just set the precision of your data to "enough" bits, say 256 (To demonstrate just how much precision this actually is, consider the following: 256 bits is enough to represent a distance on the order of 10^51 light years in ångström.) Arbitrary precision numbers is a very common feature of scientific computing software (Mathematica, Matlab, Maple etc.) and library functions are available in pretty much any mainstream language to support it as well. Or, if you want something cheaper (and easier), bc is freely available for all your abitrary precision computing needs. Hardly "virtually impossible", then.
Please note: So using a different non-SR formula does not address the core issue here. We were in fact addressing the issue of being able to demonstrate mathematically here, not using some remote precision software.
No. You said you couldn't use the formula's because calculators didn't keep the fractional numbers and instead rounded. He said, "yes, you can use the formula's, and here's how". There were no "non-SR equations in the conversation at all. Maple is perfect to do this, I used it in college to do some standard SR stuff that every advanced physics class goes through.
OK no big deal. Just show me how you propose to employ Maple here in my proof. Go ahead. That was the issue. And speaking of issues maybe we should stick to it.
I see the replies have subsided and none seem to address the issue. Hmmm. For information to others, at the 0-60Mph acceleration in 6 seconds condition SR predicts objects have a closure rate v = c at a mere 5% of the universe radial distance. Any object further distant will be closing >FTL, even if you initially vector away from the object you are getting closer to it.
MacM: I can't see where this formula comes from and I don't understand what quantity it is calculating. Please explain, and provide a derivation. And is this supposed to be a formula from special relativity, or general relativity?
WellI do forget the actual name of the series but it is a series used here before by others and it is very useful. What it is calculating is rather obvious. in that I gave the example step by step computing the daily time loss of a GPS satellite. The seond case is based on the number of meters in 3 Blyr rather than the number of seconds in a day. Same process. Had you read the presentation you would have known this is NOT an SR nor a GR formula and it is rather obvious it is not. IT IS a convergence series which approximates the result of the SR formula for time dilation or lorentz contraction. Now let me suggest you concentrate on the issue and not try to deflect the result by attacking the use of a series to provide easy to follow processes. 1 - Do you assert that acceleration, even at subluminal ranges does not shorten the distance between object? 2 - Do you claim that the changing distance (closure rate) to an object is NOT the relative velocity? 3 - Do you claim somehow that the lorentz contracted distance isn't the only measurable distance by which one must compute travel time and velocity? These are the issues you must address, not the use of the approximation convergence series. This sereies only makes it easy for any here to follow and compute for themseleves (WITHOUT PURCHASING "MA[PLE" OR SOME OTHER PRECISION SOFTWARE PACKAGE.
MacM: At this stage, I don't understand your argument, but maybe it will become clear in time. I will try to answer your questions as best I can in the meantime. 1 - Do you assert that acceleration, even at subluminal ranges does not shorten the distance between object? Acceleration of an observer changes his or her reference frame. When the reference frame changes, so do distances measured by that observer between objects that are not co-moving with that observer. Of course, it makes no sense at all to talk about the "real" distance between two objects. The only quantity that can be talked about is the distance measured by one or another observer. There is no "real" distance, distinguishable from any other measurement. The closest thing we have is distance in the rest frame. 2 - Do you claim that the changing distance (closure rate) to an object is NOT the relative velocity? The relative velocity of two objects, A and B is the velocity of object A minus the velocity of object B. Of course, as you know, to compare the relative velocity of A as seen by B to, say, the velocity of A as seen by C, requires a relativistic velocity addition unless B and C are stationary relative to one another. I'm not too sure about relative velocities measured from non-inertial (accelerating) reference frames, but I suspect they are somewhat complicated. 3 - Do you claim somehow that the lorentz contracted distance isn't the only measurable distance by which one must compute travel time and velocity? If you want to compute average velocity, then you need to measure both distance and time in the same reference frame. That is all that is necessary. Does that help?
by the way everyone, MacM or not....in May 2008 the results of the gravity B probe will be published, the ones testing Einsteins general relativity equations. http://einstein.stanford.edu/
From: Yuriy being a physicist. Does that help? Certainly and the measured distance at any instant (even durring accelertion) is based on the insdtantaneous veloicty. It cannot be otherwise. Hence the changing perception of distance with time equal the basis for computed velocity. Without saying so you have just confirmed my claims. instantaneous distances are changing with instantaneous velicty even during acceleration and such distance changes computed by SR creates FTL changes for remote objects even a t sub-sub luminal veloicties due to the affect of asserted lorentz spatial contraction. Yes or No. Don't worry about my use of the Taylor first approximation formulas. Use any appropriate and valid mathematical formulas you wish to rebutt my assertions. No need to try and complicate matters using (3) observers and velocity addition. We have only discussed relative velocity between A & B. Also relative velocity during acceleration is NOT complicated both distance and velocity are based on the instantaneous data. As you go from 0 - 60 Mph you must instantaneously go thorough every increment of veloicty and at that veloicty SR predicts the affect on distance. The only reason to claim otherwise is to trry and avoid confronting the simple truth. Please indicate where in my presentation I have even once said compute "Average Velocity". The function of distance and velocity being discussed is and must be the instantaneous corresponding values. Now please use whatever mathematics you feel appropriate (that is valid) and post the instaneous distance changes from 0 m/s to 4.4m/s in 1 sec to an object 3Blyr distant from the accelerating observer. Now using sub-sub-luminal velocity here your time shift argument just went out the door. There is virtually no measureable time differential in the distance change measurement. Any time differential from the stated 1 second will not substantially alter the connclusion of the FTL distance change. But go ahead now prove me wrong. If YOU need help doing the math just ask.
