Length contraction applies to the distance between any two locations in a given reference frame. It's a measured condition. And, there doesn't seem to be any intrinsic difference between a 'moving' frame and a 'stationary' frame. Each frame is 'moving' according to the other. So how do you tell which measurement is 'real' and which is 'just perception'?
I wasn't attempting to, I was explaining why \(\beta\) is a nice parameter to use. The derivation of the Lorentz transforms is found in any introductory book on special relativity, they follow from the requirement the Minkowski space-time metric is invariant. Like I said before, open a bloody book. You're giving short one line answers as an attempt to provide some retort. It only serves to make it more and more apparent you're aware of your ignorance, you just don't want to admit it. You both misrepresent what relativity says and you display your intellectually dishonesty by making assertions about things you know nothing about. Relativity doesn't say there's more than one reality, only that the length of rulers and the tick of clocks are not frame independent quantities. This is all experimentally verified, which you'd know if only you opened a book.
I work slowly and I prepared a response but you edited so I stopped posting. I agree. To understand my position. My "reference frame " is:There exists a unique Reality. If two observers perceive this Reality differently then at least one perceived wrong.
To mathematicians: Do you realize where led the Theory of Special Relativity? If the light is needed 499.2 seconds to reach Earth from the Sun, and I affirm: then an object which has half the speed of light, need 998.4 seconds to reach Earth from the Sun, I am accused of "intellectually dishonesty" Please Register or Log in to view the hidden image!, since I do not take into account the "length contraction". I wonder how is the space in terms of photon that has the speed of lights and we take into account the "length contraction".
The distance to the Sun, from the point of view of us sitting on the Earth, is about 150,000,000 km. Light moves at about 300,000 km/s. Thus, from our point of view sitting on the Earth, it takes light from the Sun about 500 seconds to reach us. Suppose one of us gets on a spaceship and instantly jumps to v = 0.5c. From his point of view the distance to the Sun is then \(\frac{1}{\gamma}150,000,000\) km. For v = 0.5 \(\gamma = \frac{2}{\sqrt{3}} \approx 1.15\), thus that person sees the distance as about 130 million km. If he's travelling at 0.5c = 150,000 km/s that'll mean he'll get to the Sun after about 870 seconds, according to his watch, not the 998 seconds you claim. The 998 seconds will be what we on Earth see him experience. This is the very essence of time dilation. This is not just some mathematically constructed supposition. It is a measurable fact. Cosmic rays produce muons in the upper atmosphere and they have a very short half life. Thus if we know their decay rate, the height a collection of them are produced and the number that are produced we can predict how many should reach the surface of the Earth. If you do the calculation in the manner you did and then compare to experimental observations you find that your predictions underestimate the number of muons, many more reach the Earth's surface. If you take into account the relativistic dilation effect then you get the correct prediction!! The muons experience less time (from our point of view) and thus more of them live all the way to the Earth's surface. From their point of view they live the normal amount of time but the distance dilation makes the Earth's surface seem a lot closer. It's completely consistent, one frame sees less time but also less distance, thus meaning everyone agrees on speeds, which they must. You don't understand the notion of distance and time dependency on frames. You speak about "Mathematicians, do you know where relativity leads?" but you don't know where relativity leads, you don't know what experiments say. Special relativity underpins both general relativity and quantum field theory, the two most tested and accurate models of nature ever created. These aren't just hypothetical concepts no one has considered, they are the bread and butter stuff first years learn about. The mistake you just made is something a first year would feel embarrassed to make, a misunderstanding that would be corrected by the time they finished their first term. You're utterly ignorant of relativity and you're also delusional enough to think you do understand it, despite it being painfully clear you've never even opened an introductory book on it. Well done, your level of understanding is below a high school leaver, your parents must be so proud.
From a point of view, distance is not measured (or effected) by velocity. You seem to believe that velocity effects distance. For velocity requires time, and distance does NOT! It doesn't matter how fast you are traveling, when you state a distance, it is timeless, meaning, distance doesn't have a time factor. Distance is not effected by your velocity because a velocity occurs over a time interval, a distance does not, it is a measure of instantaneous distance, of which velocity is irrelevant because there is no elapsed time! Where do you see a unit of time in the expression "10 feet?" How many ways do I have to say it for you to understand? How fast do you have to go to travel 1 mile instantaneously? You're delusional if you think there is a velocity that can travel that distance instantaneously. Change occurs over time! There is no velocity that can travel ANY distance instantaneously!
I think everyone understands perfectly what you are trying to say. The problem is that you are wrong so the understanding part is moot. Lets assume that you are traveling at 99% the speed of light. As you approach earth you would see the earth as having a diameter of about 12,756 km as you passed the earth and measured its diameter along your direction of travel you would measure it's diameter at about 1800 km. Newton assumed distance and time were invariant. Einsein discovered that they are not. You can deny this all you want, however that does not make it so. All experimentation says Einsein is right and you are wrong. I think I will stick with Einstein and not you. Revel in your ignorance....Please Register or Log in to view the hidden image!
The Lorentz Transformations refer to an object having mass in motion. If real distances were to be contracted relative to the motion of an object moving between two points, all observers should agree on the changing distances. First outside of a thought experiment how would you measure changes in distance relative to an objects velocity? All objects in relative motion with each other will observe the other as length contracted. This whole length contraction discussion can be viewed as a rehashing of the twin paradox. To know which of two objects, in relative motion with one another is actually length contracted you have to know which one is actually in motion. This is most often addressed, by either some method of synchronizing and later comparing clocks or establishing which object experienced acceleration. What frame of reference would you choose to describe motion and acceleration of space? If distance were contracted by the velocity of an object moving in space, neutrinos moving at near c would play havack with our ability to measure the distance between any two points.
Yeah, and the moon has a diameter of about 12" at night from my point of view Please Register or Log in to view the hidden image!, but we both know the distance from the center of the moon to the surface of the moon is more than 6" correct? 12" is an illusion created by distance. I'm not concerned with illusions, like you are. I'm interested in the facts. The fact is, the moon has a greater diameter than 12". The fact is, at any point in time the moon is a specific distance away from the earth, regardless of what disillusioned observers in the universe say. The moon is a specific distance away from the earth at any point in time, period! That distance is not dependent on observer's illusions.
Lets assume that the photon has 100% trhe speed of light. Now what space has it? I think you'll be very surprised. ....................................................................................Theory of relativity,Scope What is your evidence that the Lorentz transformation describes quantitatively correct?
Relativity is not an illusion. You can choose to believe whatever you want. The illusion is that time and distance is invariant. I have seen several of your conjectures that are in conflict with science, and all I can sa is, you can live in your own little reality, but I don't think there will be many that will join you...
Sorry but I have no idea what you ate trying to ask.:shrug: :shrug: How about this discussion on muons?
It's not an illusion that the moon is 12" in diameter??? The moon has a specific diameter, and it is not 12". You can choose to live in your world of illusions, but the fact is, the moon is not 12" in diameter. You can choose your reality based on your velocity, but just so you know, your velocity doesn't change the size of the moon. The moon couldn't care less how fast you are going. The moon has the same diameter whether you have a .1c velocity or a 2.99c velocity.
To be precise, our best evidence is that Lorentz transformation describes a symmetry of nature more quantitatively correct than any similar idea by Aristotle, Galileo, Newton, or Maxwell, even though it was Maxwell's equations describing nature which were first discovered to have this symmetry. What about this 1859 measurement of the speed of light in moving water? http://www.sciforums.com/showthread.php?p=2039656#post2039656 What about Thomas Precession, which was discovered hiding in special relativity as late as 1927. http://www.mathpages.com/rr/s2-11/2-11.htm What about (as origin points out) that muon (called mesotrons in the first years after discovery) decay at high speeds relative to the laboratory is described consistently by using the Lorentz transformations? http://web.mit.edu/8.13/www/JLExperiments/JLExp14.pdf http://prola.aps.org/abstract/PR/v59/i3/p223_1 (similar relations are discovered in the laboratory when we can produce the muon and its heavier cousin the tau lepton, and various other particles which decay) What about the operation of the GPS system which exhibits both SR and GR effects. http://relativity.livingreviews.org/Articles/lrr-2003-1/ What about the success of General Relativity which is predicated on Special Relativity being locally correct. http://relativity.livingreviews.org/Articles/lrr-2006-3/ http://relativity.livingreviews.org/Articles/lrr-2005-5/ What about the success of Quantum Electrodynamics which builds on the work of Maxwell, Schrodinger, Einstein and Dirac to produce a fully relativistic and fully quantum descriptions of electrons and photons which just happens to be 1) Dead simple to express, and 2) extremely precise: \(\mathcal{L} = \mathcal{L}_{\textrm{electrons}} + \mathcal{L}_{\textrm{photons}} + \mathcal{L}_{\textrm{interaction}} = \left( i \bar\psi \gamma^\mu \partial_\mu \psi -m \bar{\psi} \psi \right) - \frac{1}{4}F_{\mu\nu}F^{\mu\nu} - e\bar{\psi}\gamma_\mu A^\mu \psi \) where \(F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu\) http://en.wikipedia.org/wiki/Anomalous_magnetic_moment#Anomalous_magnetic_moment_of_the_electron "The QED prediction agrees with the experimentally measured value to more than 10 significant figures, making the magnetic moment of the electron the most accurately verified prediction in the history of physics." Because we have mastered the math of space-time, we can master the math of things in space-time. http://en.wikipedia.org/wiki/Precision_tests_of_QED
You are a lost ball in high weeds my friend... You really think the visual diameter of the moon has anything at all to do with relativity? Well this is a useless discussion - enjoy your "science". It seems that I would have a better chance of my cat understanding this than you...
You seem to be misunderstanding what I mean, and what SR says. Length contraction means that if a measurement is made of the distance between two points, that measurement will be longest if the measuring system is at rest relative to the points. If the points are moving past to the measuring system, or the measuring system is moving past the points, then a contracted length will be measured. Resolving the twin 'paradox' doesn't rely on knowing which is "really" at rest, it just requires proper analysis. For example, say that the Earth is always moving, the spaceship first leaves Earth and waits for some time while Earth moves on, then catches up. This is a physically identical scenario to having the Earth stay still while the spaceship travels away and returns. I wouldn't describe motion and acceleration of space. The terms don't apply.
Apply the Lorentz transformation on the space when the photon velocity is C. I'm not sure if you understand the Theory of Special Relativity. I have my time or space unaltered. That is my "reality". Lorentz transformation is applied to the others, from my point of view. But I can not duplicate myself, so my reality is always the same. You argued: Yes, this is your reality, but I have my own reality, because the Lorentz transformation. And everyone has their own reality based on relative speed. Some of us declare that we have a unique shared Reality, and we make efforts to push the boundaries of knowledge of this unique Reality. We live together in this unique Reality, while you live each in your own reality based on relative speed of each.So who lives in his own dream and who lives in a common dream that they called Reality.
@rpenner, In astronomy, a .01% error can be significant due to large distances. It can mean whether or not a meteorite collision with the Earth or another celestial body.Do you have any knowledge of that astronomers to calculate the trajectory in space and time, of a celestial body they apply the Lorentz transformation?
Of course not. I told you, Einstein wins. Your inability to understand relativity is not a very good reason to abandon science. Twisting words and obfuscating is typical of your pseudo science crowd but in reality it is a very silly way to have any sort of meaningful discussion.
