Experimental validity is relative
James R,
Closeness is not the only relevant criterion for accessibility ...Galaxies are much more massive than the sun, which means they can bend light more
Of course it is not the only criterion that can be taken into consideration. But if it is measurable in our vicinity, then bent light data from within our solar system is a much better realm for study. If we can study all of the phenomenon in our local frame and understand all the variables which affect measurements we can more honestly evaluate distant phenomenon. This can be looked at as an opinion, but I think it is sound. In America, I can continue to receive reports on Aboriginal practices as a basis for my study of the 'primitive' mind, but the indigineous populations in the America's are much more available for first hand study. A loose analogy, but good enough for illustration.
No. We can calculate this exactly, using standard mathematical techniques. No approximation is required.
Are you saying that n-1/n eventually becomes n/n? If you are talking about using elipses to erase the infinite steps then I contend you are wrong given the parameters of the 'halvseys' mathematical setup. If you mean there is a distance between particles where the halving begins to involve an interaction of forces, then you are not talking mathematics, you are in the realm of physical reality.
Such testing is not necessary, because the conclusion that time dilation happens is not derived with reference to any particular physical process.
To state that 'Testing is not necessary' is anti-scientific. This is to say that theories should not be tested. I reject this contention. A theory in physics that is made without any reference to physical processes may or may not be valid, but the theory is meaningless if study and analysis of physical process and the predictions made by the theory do not need to be tested and validated.
When you do a fundamental test of an effect, you look for simple examples with few variables, not an incredibly complicated system where the effect you're looking for is swamped by many other effects
Which is why I contend that local study of relativistic phenomenon is more important. The complexities of the information we receive via light and EM interstellar phenomenon filtered through a multitude of variable interactions is incredibly complex system, wouldn't you agree? I hope someone is willing to get into the light tube gravity experiment..oh yes..yes indeed.
Relativity is an amazing, counter-intuitive theory. Which happens to be right (for all tests so far).
It is counterintuitive in some of its explanations, yes. Its 'rightness' in its various parts are the nature of many people's constant study.
That is incorrect. You're downplaying the insights relativity gives us into the nature of space and time.
To state that this is about measurements is to understand relativity[SR for now]as measurement issues. Here are some folks and their thoughts:
*Pauli, W., Theory of Relativity (1921), Dover 198112-13]:It therefore follows that the Lorentz contraction is not a property of a single rod taken by itself, but a reciprocal relation between two such rods moving relatively to each other, and this relation is in principle observable.
*Eddington, A. S., The Nature of the Physical World , 1928, CUP / MacMillan (NY)33-34]:
"The shortening of the moving rod is true , but it is not really true."
*Taylor, E.F., & Wheeler, J.A., Spacetime Physics: Introduction to Special Relativity, 2nd ed., W.H. Freeman, New York, 1992.]Does something about a clock really change when it moves, resulting in the observed change in the tick rate? Absolutely not! Here is why: Whether a clock is at rest or in motion ... is controlled by the observer. You want the clock to be at rest? Move along with it. ... How can your change of motion affect the inner mechanism of a distant clock? It cannot and it does not. [CRISP-Thanks for the complete reference of this book]
*McCrea, W.H., Relativity Physics, 4th ed., Methuen, London, 195415-16]:The apparent length is reduced. Time intervals appear to be lengthened; clocks appear to go slow.
Minkowski, H., "Space and Time" (1908), in H.A. Lorentz et al., The Principle of Relativity, Dover, 1952,75-91. ][The] contraction is not to be looked upon as a consequence of resistances in the ether, or anything of that kind, but simply as a gift from above, - as an accompanying circumstance of the circumstance of motion.
The range of approaches is astounding. If you claim I am incorrect on the assertion that SR is more about measurements of time, then do you discount Taylor & Wheeler. I will read them in complete context, but their statement appears to clearly state it is an appearance of dilation, no? Should I follow Eddinton's logic: it is true and not true? McCrea's focus on appearances must be downplaying the insights as well. There are more, but that will be for another time.
That's just the way it turns out
..regarding light as an integral part of the formulas of SR. I know you must be speaking facetiously. If you are being serious, then Einstein just accidentally used the speed of light and it just happens to work out and every one goes home saying we understand space and time.
That's what the formula tells us straight out! You only need to read it correctly. It is not about transmission of information. I've already explained why (twice).
Some of the biggies in relativity would disagree with you; this is not just a random opinion held only by yours truly.
In other words, how would you tell if a clock slowed down but "existence" did not? Please give me an example, if you can come up with one. If you can't, I'm afraid you'll have to accept that the rate of "existence" is measured with clocks.
When the shadow on my sundial says it is three o'clock PM and the sun is at its furthest distance from the earth and my battery powered clock says it is 10 AM. The interactions of systems within local and distant frameworks which have been studied mapped and charted over centuries act as good error correcting devices for fallible human clocks. Human-made devices to slice up the passing of time for the convenience of humanity [or enslavement say some.] are astoundingly important to our era, but the position of the heavenly bodies mapped out time for most of our history. In countries that observe daylight savings time, time/existence is not speeded up in spring because the clocks are set forward one hour. If I create a clock with non-standard gear ratios so that the time measurement is slowed down, have I changed the rate of existence? Is it merely the democracy of a majority of timepieces that ensure that a standard existence is metered out? Modern measuring devices are tools that are supposed to be held to a consistent standard. If a clock is slow compared to a standard, this does not necessarily mean that anything has changed but the clock's synchronization to the standard.
Einstein's own words: After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations. From the very beginning if appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how, otherwise, should the first observer know, i.e., be able to determine, that he is in a state of fast uniform motion?
It may be too easy to visuallize what a water wave would look like at a standstill, but it is an artificial visualizaton...a visualization of what can not exist. There is no such thing as a spatially oscillatory water wave at rest, either. There can be a standing wave, but this is not at rest. So why is this not a valid slowed down parallel to a beam of light? We are dealing with energy in a waveform. If the waveform seems to be at a standstill, it is either a standing wave, and hence an continuing oscillation, or we are moving at the speed of the wave. Notice how Einstein is speaks of the need for one to determine if he is in a state of fast uniform motion. ***I will endeavor into his germinal ideas more another time***
Q,
Yes. Each twin will view their own clock as ticking normal and will view the other twins clock as ticking slower. Each twin will measure their own rods at one meter and the other twin's rod at (.44) meters. Therefore one twin measures differently than the other relative to their own measurements.
So it is merely a matter of appearances, depending upon their respective positions? If you are saying both realities are true, then you are saying both slowed down and both rods were shortened in an equal measurement, net result is zero.
The OTHER frames, relative to your FOR, will be measured to experience the effects of SR, time dilation and length contraction.
Then you are saying that equivalent relativistic effects equally apply to both FORs? That it is irrelevant which FOR is referenced as the rest FOR?
I'm trying not to hold your hand through the entire explanation but am allowing you to put some of the pieces together yourself. Think it through. I calculate one meter to be one meter from my FOR. For the twin moving at .9c, his meter will measure (.44) of a meter. If the twin travels to the nearest star and back, a distance of about 8 lightyears (75.2 trillion miles), he will have traveled about 3.5 lightyears (33 trillion kilometers).
Implying hand-holding is a clever rhetorical device to lessen my attempts to elicit clarity, but it does not erase the contradictions.
If a star is one light year away, and someone goes .9c, then it will take 1.111111111. The at rest FOR may see the shortening of the moving one's measuring rod, but the mover will not. This is by your own statements. How is someone going slower than the speed of light able to move faster than the speed of light? You give a distance of 8 light years, state that a lightyear is a standard in all frames, yet a slower than light speed traveller moves faster than light to return 4.5 lightyears earlier than a beam of light would take?
When he returns to Earth and the twins compare clocks, the Earth bound twin will have aged more than the moving twin. No paradox.
Again, you have stated that either twin measures the other clock as slowing and the other's rod as shortening. So either twin can meet back up with the other and be the aged one. Paradox intact.
Regards,
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