W4U; [Gravity forms stars and configurations of stars and other objects. If the effect on an object is measured, the scientist interprets the force as an inverse square law. That does not make gravity mathematical. It is more of a redirecting effect of object motion by more dominant masses. I see no basis for the scientist to attribute (better than impose) his math onto inanimate matter.] [When particles lose their maximum energy, they are considered in a 'ground state'. Isn't strange that when people die, they too reach a 'ground state'. When a system of particles has all its available energy removed, it is in a dormant inactive state. Maybe science has it backwards. Complexity is fundamental and simplicity is degenerate. I think there are universal laws, but not universal mathematics.] [Until the new family of particles were discovered, and physics at that level became more complex. Does that sound familiar! [You have the correct order, experience it, and record it. The simplest instance of timekeeping is a diary.]
Einstein DID specify that the perpetually-inertial twin can determine, at each instant of her life, what the age of the accelerating twin is then ... she needs only the famous time dilation equation to determine that. So she can always draw an "age correspondence diagram" (ACD) that plots his age as a function of her age, according to her, no matter how he is accelerating. But as far as I know, Einstein never had anything to say about the ACD that gives her age as a function of his age, according to him. It seems to me to be unreasonable to contend that there exists an ACD for the perpetually-inertial twin's conclusion about simultaneity at a distance, but there does not exist an ACD for the accelerating twin's conclusion about simultaneity at a distance.
Mike; [Read the PDF 'reciprocal slow time' for inertially moving frames first. The graphic is based on that, but the calibration curves are replaced with straight lines, since there are only two cases of td. If B changes speed at Ut=1.00, the axis of simultaneity (green) also changes. It would be parallel to the mathematical Bx axis resulting from clock synchronization. If B decelerates (-) his return signal is earlier, and the At=1.00 event is assigned an earlier B-time, A-clock rate is faster. If B accelerates (+) his return signal is later, and the At=1.00 event is assigned a later B-time, A-clock rate is slower. Since the A-clock rate is constant, it's B's perception of the A-clock frequency that has changed, i.e. doppler effect, not aging. Clock synchronization is conditional on maintaining uniform velocity.] [The coordinate transformations depend on having (x, t) coordinates for the other frame, and that requires measurements. In the simple case of clock A with inertial motion vs clock B with accelerated motion, it can be shown, for any motion that departs from the inertial motion, the B clock will lose time relative to the A clock. My question is, why bother with all that observation. The clocks accumulate the time correctly, so wait for them to pass each other and compare.] Please Register or Log in to view the hidden image!
That is not how I interpret it. IMO, it's the universe that imposes its universal math onto humans , who symbolize it in human language. Let me ask if the universe displays some mathematical properties. i.e.value input --> (algebraic) function --> value output ? As I understand science, most scientist attribute at least some mathematical properties to the universal geometry. I'll ask the question that if the Universe has some mathematical properties, what prevents it from having only mathematical properties, regardless of human symbolic maths.? When we speak about time, is that not an additive quantity, a mathematical function? Function space Main articles: Function space and Functional analysis https://en.wikipedia.org/wiki/Function_(mathematics)#Function_space
Let's cut to the chase. What do you say the age correspondence diagram (ACD) is, according to the accelerating twin, for the standard twin paradox scenario? I.e., what does the accelerating twin (he) say the age of the perpetually-inertial twin (she) is, at each instant of his own life during his trip? The ACD according to HER is well-known: She says his age increases linearly, with a slope of 1/gamma, for the entire trip. So for speed v = 0.866, gamma = 2.0, and the ACD according to her is just a straight line of slope +1/2. But what is the ACD according to HIM in that case? I.e., what is her age, according to him, at each instant of his life? I don't think Einstein ever gave an answer to that question. What is your answer?
Time is movement from one place to another, also a specific location in space time.,geometrically. At any time you are within and a part of the grand union of the motions of space time. Because of that, one would have difficulty in 'time' travel, i.e. you would have to duplicate the geometry of your location and all the locations that you are a part of. However, since all of the locations are geometrical, then a common geometry might suffice. Now it it is not just geometry, it is also its' corresponding total densities. So duplicate the geometry and duplicate the density. As that happens you will find that you will be "floating' along with the 'environmental space-time" though not even leaving your location. Duplicate Nature and Nature will reward you.
Mike; [Fig.1 is the simplified case with each moving at a constant velocity. The A-clock ticks at a constant rate so A ages accordingly. The B speed profile, 0-8 and 8-16, is not possible for one observer. Replacing B with two observers B1 and B2 already moving, B1 sets his clock to the A-clock as he passes, B2 sets his clock to the B1 clock as he passes. If A sends signals for each unit of time, to poll the B-clocks for a reading, the readings will be uniform but the B2-clock rate will be .80 of the A-clock. Fig.2 is the comparison of B-clock rate to the A-clock rate. The black line indicates .80.] [If each just records signals received from the other sent for each unit of time: A receives 8 in her 16, and 8 in her 4, totaling 16 in her 20. B receives 4 in his 8 and 16 in his 8, totaling 20 in his 16. The perception is not reciprocal. Both agree B is younger.] [In fig.3, there is a curve to transition from outbound to inbound, with no significant change in the B-clock. This results in the axis of simultaneity rotating with one observer B, avoiding the 'time jump' experienced in fig.1.] [In fig.4, B sends uniformly spaced signals to poll the A-clock. B's perception of the A-clock is initial rate of .80 his rate, then increasing to the reversal, then decreasing to the reunion. During the reversal, B experiences an equivalent g-field which he perceives as the cause of A returning to him. During the reversal, the A-clock rate is approx. 2x the B rate, which also occurs in fig.1. He is observing doppler effects.] [A general rule for SR: The high speed of an observer cannot affect distant objects or processes, but can affect the observers perception of those things.] [I would guess the subject you present wasn't a priority on Einstein's list, which included forming the General Theory.] Please Register or Log in to view the hidden image!
W4U; [Gravity directs objects toward the center of mass of Earth. No one knows how the energy is transferred from source to object. Science measures g-force in terms of object acceleration using math. Where in the sequence, source to field to object, would math be used?] [We agreed time is an artificial event, and the clock is designed to count them. Once a time is assigned to an event of interest, we can't use it again. It becomes a unique identifier.] [Abstract math can be applied sometimes to describe the physical world.]
AFAIK the equation of gravity is a mathematical constant, which means it is a property of spacetime. The universe does not know this. It just behaves in a mathematical manner which humans have been able to symbolize. I agree. Each durable object or changeable condition acquires its own unique timeline within the larger universal timeline. That is what I view as proof of abstract universal mathematics. I have read several cosmologist describe that when they test an equation and they do the math correctly, the universe rewards them with a confirmation of the maths and they get the impression those maths were always there to begin with but in an abstract natural form One scientist even went as far as to describe: "If you ask the universe a question and you use the correct mathematics, the universe will reward you with an answer", which is of course meant in the abstract sense of mathematical communication. Hence Tegmark's proposition that instead of possessing some mathematical properties, the universe possesses only mathematical properties, which IMO is an entirely reasonable and logical proposition. It certainly explains all the regularities we observe. Someone mentioned that the recognition and symbolization of the mathematical structure and functions in the universe are man's greatest discovery and achievement. The mathematical "Language of the Universe". As ex-bookkeeper that expression sounds so elegant and useful, I cannot possibly conceive of a more efficient accounting system of natural phenomena. An interesting factoid is that many animals and plants have inherent mathematical abilities, albeit in rudimentary form, refined by natural selection for efficiency and utility. http://www.bbc.com/earth/story/20150826-the-animals-that-can-count https://en.wikipedia.org/wiki/Plant_arithmetic https://en.wikipedia.org/wiki/Patterns_in_nature If we posed the counterfactual that the universe is not mathematical in essence, we'd end up with an eternally chaotic universe without any individual chronologies (timelines) within it...Chaos Theory would not hold......Please Register or Log in to view the hidden image!
Write4U; What about young animals learning survival skills from the adults? That does not seem mathematical.
Of course it is. All deliberate action in nature is based on fundamental mathematics. The difference is that humans are able to symbolize the learned maths into numbers and functions. Animals just use the maths from observing elder experienced parents. How did you acquire your math skills? From elders, no? The examples are abundant, just a few ; Lemurs can tell the difference between more and less just as fast as humans. Rudimentary counting. Spiders weave webs with mathematical precision. Rudimentary architecture. Bat's and Whales use sonar (echo-location). Rudimentary wireless measurement Daisies, Sunflowers, Pine-cones use the Fibonacci Sequence in their petal and seed arrangement. Rudimentary section for most efficient energy gathering and storage. Basically, every evolved survival mechanism and behavior in nature is mathematically efficient. Natural selection selects for efficiency and that always involves a mathematical equation. The organism or object doesn't know this, it has become hard-wired behavioral skills and/or learned from observation of elders. Or it is influenced by external forces and attains an emergent mathematical pattern such as wave frequencies and other natural mathematical constants. The more you look, the more you see the mathematical nature of things. Only humans have need for representative symbolic maths to use for their convenience over and above survival skills. As to time; all living organism seem to acquire some form of circadian rhythm. https://en.wikipedia.org › wiki › Circadian_rhythm This behavior starts at very basic levels of slime molds; Which is eerily reminiscent of neural networks in higher evolved organisms!
