Essentially because it has a longer path, correct? The local speed of light in anyone's own FoR is always " c" correct?
But is that the question? Are we talking about the relative experience of the observers or the actual mechanics of the physical event in reality? Isn't the question if that ball or that photon behaves differently without an observer and that any apparent associated time of duration is an emergent phenomenon for each observer, depending on their POV?
There is no "actual mechanics..... in reality" distinct from a frame-dependent view. Any description must be from the point of view of some frame of reference or other. The whole point about relativity is there is no preferred frame of reference that has any more validity than any other. This has nothing to do with observed vs unobserved events. That is a concept borrowed from a misunderstood feature of quantum theory.
But it does not have a longer path! The photon's path does not curve it is always straight (from wall to wall), it is the elevator that moves, which creates the illusion in the observer that the path of the photon curves. I think my illustration on page #32 clearly demonstrates the relativistic effect. But what is the reality? Question: Is time compression and elongation a result of the Doppler effect? Does time have a wave function?
Thank you for clarifying. I still have a problem what happens when there is no observer. Question: Doesn't the universe itself have a preferred frame of reference? Is spacetime a variable, where space is self-referential (its own observer) but time emerges as a variable quantity locally?
No. Let's put it this way: Space-time is the background against which we measure events. But space-time by itself places no distinction between space and time. This distinction is supplied by the reference frame against which are measured. As an analogy, imagine space-time as a 2 dimensional plane on which is printed a map. On this map, you have placed grid lines like this: Please Register or Log in to view the hidden image! Here the lines run North-South and East-West. For our example North-South will represent time and East-West, space. The cities would be events that occur in space and time. (in the image above, Springfield and Bend are on the same horizontal line and thus represent events the happen at different points in space at the same time. ) Now the old model of time and space held that these space and time relationships were absolute. They held no matter how you orientated the map. Thus if you rotate the map you get this: Please Register or Log in to view the hidden image! Springfield and Bend maintain the same relation with respect to the grid that defines time and space. However with Relativity this changes. Under relativity, the grid lines are not affixed to the map, but to the view. Thus if you reorient the map, the grid lines defining time and space measurement retain their relationship to the view point, like this: Please Register or Log in to view the hidden image! Here the vertical direction still denotes time and the horizontal space. Now Springfield and Bend appear as events that happen at different points in time rather than simultaneously as they did before. You will also note that while in the first two images Bend and Springfield were a bit over two grids apart along the space direction, in this image they are less than two grids part in the space direction, and thus the spatial separation between these two events is less than it for the previous map orientation. The one thing both orientations agree on is the "straight-line" distance or the combined space and time displacement between Springfield and Bend. This is the "space-time" interval. So what it comes down to is that while both perspectives agree on the magnitude of the space-time interval, they disagree on the magnitudes of the time components and space components it is constructed from. In addition, there is no preferred orientation for looking at the map, every orientation is just as valid as any other. So, if you are asking what the underlying "reality" is, you could say that it is represented by the space-time interval. However we can't directly measure the interval, and have to determine it by measuring its time and space components, which individually depend on the reference frame.
Let's consider the following scenario: Two identical elevators accelerating in the same direction, one behind the other, and under the same acceleraion. A beam of light enters each and crosses to the opposite wall. Each observer has a clock which his uses to measure the time it takes for the beam to across the elevator. Since conditions in both elevators are identical, they should both register the same time: Please Register or Log in to view the hidden image! But, as I noted in the earlier post, according to the lower elevator, the clock in the upper elevator runs fast, and according to the upper elevator the clock in the lower elevator runs slow. Each will measure the light crossing his elevator as moving at c*. Each also sees the path of both light curves as being equal in length. Each elevator would have to see the light cross the other elevator in the same amount of time as the clock in that elevator measured. So for instance, if both clocks measured that their light beam crossed the elevator in 1/150,000,000 of a sec, then the lower elevator would have to say that the upper elevator's light crossed in the time it took the upper elevator's clock to tick off 1/150,000,000 of a sec. But since the lower clock measures the upper clock as running fast, this means that the upper light crosses in less than 1/150,000,000 of a sec as measured by the lower clock. The upper elevator's light has to cross in less time than the lower elevator says its light took to cross. Since the path lengths are equal, the lower elevator as to conclude that the light crossing the the upper elevator was traveling faster than c. ( even though locally measured in the upper elevator an answer of c was arrived at. * Technically, the speed of the light as measured by our observer would change over the course of the curved path, being faster at the top of the curve than at the bottom. But we will assume that our observer is positioned such that according to him, it averages out to c over the length of the path.
I hate to be difficult, but I think that is a wrong interpretation. How can a photon move faster a the the top of the curve and slower at the bottom and still average out to "c"? Even as experienced by the observer. Something is wrong here. The simple solution is that the light beam always moves @ "c", and never follows a curved path. It is the movement of the observer inside the elevator which creates the subjective relative observation of a "curved path". But it is only the observer inside the elevator who experiences the curved path. The rest of the universe sees the light follow a straight line through a moving object and the light will hit the opposite wall at exactly the same time every time, regardless if the elevator is moving or not. The only difference is that the light will miss the target because the elevator has moved, not because the photon followed a curved trajectory and therefore has a longer path to follow. Example: I shoot a bullet at a target 100 meters away. After I pull the trigger, the target is pulled sideways . Does the bullet hit the target at a different time if the target was moved 6 inches or would it hit the target at the same time if it was left stationary? The observer sitting on top of the target will see the bullet curve away from him as the target is moved. But that is only an relative illusion. Even then, the bullet will always strike the target at the same time. It will miss the bulls-eye, but that is irrelevant.
You are too hung up on the idea that there is one "true" path that the light travels. The curved path measured by the elevator is just as "real" as the straight path measured by an inertial frame (Of which there an infinite number to choose from, each with its own path the light follows.)
Saint; Let's try pictures. In this example, a ball b is thrown vertically from floor to ceiling, a distance h, on a train moving a distance d in time t, as measured by bystander B on the platform. The moving train is length contracted due to its motion in the x direction. That shortens the distance b moves from d to d'. This in turn decreases the angle a slightly. B measures the time of ball contacting ceiling as t. B calculates the speed of b in space as d'/t which is < d/t. Passenger P records a time of t' (due to time dilation (red)). P calculates the speed of b as d/t' which is > d/t. Please Register or Log in to view the hidden image!
Yes I understand this. But that does not change the physics. The light always following a straight path through the elevator. The rest is an effect of relativity from the POV of the observer. IOW, it is a "local" (only inside the elevator) phenomenon. If the observer weighs 200 lbs Earth weight and the upward accelerating elevator will make the man exert a force of 500 lbs on the floor of the elevator, does the man now weigh 500 lbs or is it the upward motion of the elevator that is creating the apparent increase in weight of the man? When the elevator stops the man will weigh 200 lbs again? C'mon, that makes no sense. Of course there is a universal constant somewhere. Relativity is only useful to humans. It is a mathematical phenomenon that allows us to make relational measurements. Just because my house disappears in the distance does not mean it has grown legs and started moving on its own. It only moves in relation to my driving away from my house with my car. In physical reality my house remains firmly attached to its foundation. I find it very confusing that scientists always stress the importance of physical aspects rather than the mathematics. Tegmark's mathematical universe suffers a lot of derision. Yet here the role is reversed and the mathematics is preferred over the physics. Relativity is not a physical phenomeon, it is a mathematical phenomenon. So which POV are we to adopt?
This is wrong. The ball does not bounce at an angle relative to a stationary train. It's the train that moves horizontally relative to the ball. All your arrows are pointing vertically, but should be pointing horizontally. The ball just bounces straight up in its own frame of reference. Time has nothing to do with it.
Write4U, imagine that somewhere in deep space, far from any gravitational bodies, there are two asteroids named P and Q which are coasting past each other at constant speed. Asteroid P can consider itself to be stationary, and then it would consider asteroid Q to be moving with a real physical velocity. Meanwhile, at the same time, asteroid Q can consider itself to be stationary, and then it would consider asteroid P to be moving with a real physical velocity. They are both correct, and neither one is wrong or seeing an illusion. That is real physics, not just mathematics. It is because all inertial reference frames are equally valid. That is just Galilean relativity. Einstein's relativity builds on that, so that each asteroid, taking itself to be stationary, also says that the speed of light is constant relative to itself. This does not lead to the other asteroid saying that the speed of light is c+v or c-v or anything other than c. Instead, it leads to each asteroid saying that time (the rate of ticks of a standard clock) proceeds more slowly on the other asteroid. In other words, asteroid P can consider itself to be stationary, and then it would consider the time on asteroid Q to be proceeding more slowly than asteroid P's own time. And asteroid Q can also consider itself to be stationary, and then it would consider the time on asteroid P to be proceeding more slowly than asteroid Q's own time. Just as with Galilean relativity, they are both correct, and neither one is wrong or seeing an illusion. That is called time dilation, and in addition to that, Einstein's relativity also has length contraction, and relativity of simultaneity. All three of those are the logical results of the speed of light being the same constant in all inertial reference frames (which are all equally valid as each other).
This is wrong. Relativity is nothing to do with human perception. Consider the famous example of atmospheric muons, generated by cosmic ray bombardment in the upper atmosphere and which travel towards the surface of the earth at relativistic speeds. We know from lab experiments what the half life of these muons should be. According to that, very few of them should survive the journey to ground level, because most of them should have decayed before they arrive. And yet we find a lot of them do survive. This is because they experience time dilation, from the perspective of the frame of reference of the earth. From the perspective of their own frame of reference, they have a normal lifetime but, instead, the distance they travel is contracted. Both length contraction, according to one frame of reference, and time dilation, according to the other, lead to an identical result, which is the result observed. So both are equally right and the effect is nothing to do with anybody observing what is going on. The muons do what they do, just as they did for millions of years before Man existed. The same thing (time dilation) happens in particle accelerators. To give a different example, the colour of gold is due to the effect of relativity on the effective mass of electrons in the orbitals of the gold atom, which travel at relativistic speeds due to the high charge on the nucleus. The effect is to pull down the absorption band from the UV into the blue, causing the metal to look yellow. Nobody is watching the electrons going round and round.
Of course it does. It's an entirely subjective experience from a "frame of reference". It's a mathematical equation, a relational measurement. I understand the concept of relativity. The Doppler effect is a perfect example of relativity based on the POV of the observer (instrument). But it always takes two or more observers. Individual measurements can only account for a relationship from their own local frame of reference. (obs. A) ----------------------------->train(whistling @ "f#") with (obs.C)-------------------------------------> (obs.B) Observer A hears the note "f". Observer B hears the note "g". Both are relative measurements against observer C, who hears the true physical wavelength of the note "f#". It's a perfect mathematical equation, but only C hears the true physical wavelength emitted by the train whistle. Can we say that C 's measurement of the train whistle is relative to A or B? It's the moving train whistle which is causal to wave lenghtening @A, and wave compression @B. The train whistle does not move in relation to @C and C measures (observes) the true wavelength of "f#". I cited my house build on its foundation disappearing in the distance because I am driving my car away from it. In my car I see my house disappear into the distance along with every object I pass. I know I am the one who is moving relative to the house. And so does the observer by my house know that it is the car which is moving relative the house which is stationary. My house is not physically changing location, time dilation or not. It is stationary on the foundation. An observer at my house sees the car disappear into the distance, but unlike the driver in the car, this observer has no movement of the house in relation to its own environment. The observer can only conclude that the house is stationary in relation to its direct environment (frame of reference) and only relative to the moving car, a local event. Can I say that my houses's foundation is moving. The dirt underneath my house anchors the foundation . Can I say that the dirt is moving? The dirt is part of the earth. Can I say that the earth is moving away from the car? In the end we find that the universe basically records relative change of spacetime coordinates. But that is a mathematical function (an equation) not true physical mechanics. Inside the universe everything happens from the POV of the universe itself. The universe has no relative partner by which to compare its movement. At some point relativity stops as there is nothing to relate to. Does the universe move within a greater nothingness. Is there a measurable relationship of spacetime with nothingness. What happens to relativity when there is nothing to relate to. Is time an emergent property based on infinitely number of events which are relative to each other or relative to spacetime itself from the Universe's POV ? The question is, if you remove the related observer (in the most general term), does the phenomenon of time dilation still exist at all ? According to Einstein, time stands perfectly still for a photon travelling @ "c". Talking about time dilation, @ "c" time does not exist at all. But as soon as you slow down, time emerges relative to "c", no? Question; if time dilates for a local event, does all of spacetime change, or is that time dilation an emergent local phenomenon?
And I cited two asteroids moving past each other somewhere in deep space. Each one considers itself stationary. Can you to tell me which one is really stationary and which one is really moving? You can, but only in relation to some reference frame that you choose. If you were on one of the asteroids, what experiment would you perform to prove whether it is stationary or moving at constant velocity? Yes. In the reference frame in which the sun is considered to be stationary, the earth moves at 67,000 mph (107,000 km/h) along its orbit, and your house moves also. Likewise, in the reference frame of your car, the whole earth moves, if you consider yourself to be stationary. Get with the times, you are arguing with the ideas of Galileo and Einstein. Hint: It's not because you're smarter than them, or because you know something that they didn't. It's because you've apparently never even thought about this until today, and you are letting your "intuition" be your guide.
Thank you for your patience. I am just familiar enough with relativity to play "devil's advocate". They're just loose ends I am trying to tie up. My posits are more probative than declarative. I try never to argue against mainstream science, which has withstood much better scrutiny than I can give....Please Register or Log in to view the hidden image!
Just highlighting a key part for those having problems. Think hard about this... If speed is a ratio of distance and time, and different frames of reference measure different distances but still measure the same speed. I think you see where this is going...
