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We should not that “time is ticking off more slowly” is not defined. All we we observe is that the rates of the clocks differ. The clocks tick slower or faster. We can of course define time to mean “rate of ticking of clocks” but then it is simply an abbreviation. There is no intrinsic physical meaning other than clock rates that run faster or slower.
We should not that “time is ticking off more slowly” is not defined. All we we observe is that the rates of the clocks differ. The clocks tick slower or faster. We can of course define time to mean “rate of ticking of clocks” but then it is simply an abbreviation. There is no intrinsic physical meaning other than clock rates that run faster or slower.
We should not that “time is ticking off more slowly” is not defined. All we we observe is that the rates of the clocks differ. The clocks tick slower or faster. We can of course define time to mean “rate of ticking of clocks” but then it is simply an abbreviation. There is no intrinsic physical meaning other than clock rates that run faster or slower.
We should not that “time is ticking off more slowly” is not defined. All we we observe is that the rates of the clocks differ. The clocks tick slower or faster. We can of course define time to mean “rate of ticking of clocks” but then it is simply an abbreviation. There is no intrinsic physical meaning other than clock rates that run faster or slower. Also the “passage of time’ is simply another way of saying “the rate at which the clocks tick”.
Relative theory only states, as far as I can make out, that observers will observe clocks that tick at the same rate when moving at the same speed with respect to the observer will be observed to tick at different rates when moving at different speeds with respect to the observer. The rate observed being slower the faster the clock moves with respect to the observer. Whilst speed is relative because it is defined in terms of speed with respect to other objects/observers rates are not. I do not need another clock to define what a rate is. I can, of course, see if one clock has a faster rate than another clock if I put them side by side (and they move at the same speed). A basic assumption of special relativity is that clocks can be synchronised and can be made to run at the same rate. In special relativity “time” (if we want to define it as a concept) is simply the rate of ticking clocks. With this definition we can say that “time slows down” however there is no fundamental underlying physical concept to this expression it is simply shorthand for saying “we observe that the rate of some ticking clock to be slower”. In special relativity, “time exists” means “clocks tick at a particular rate”, no more and no less.
We can get a feel for the numbers without having to use a calculator. Say v is just 1 meter less than the speed of light so = c-1 (or 299792457 m/s). Here c is in m/s. The formula Lv / (c^2 – v^2) becomes L(c-1) / (c^2 – (c-1)^2) = L(c-1)/ (2c-1) = L/(2 + 1/(c-1) ). 1/(c-1) is very small so the time difference is very close to L/2. For a 10000m train this is very close to 5000 seconds which is about 83 minutes. The video states that this value (83 minutes) is gotten with 299792457.999999999 m/s. This is wrong. The calculation in the video was using c-1 or 299792457 m/s which is 99.999986% of the speed of light.
You are treating the photon as a sort of very small golfball and that is where the analogy breaks down. The energy transfer is not governed by a momentum conservation (which would indeed have infinite speed for a particle with no mass) but should be more considered like plucking a guitar string. The speed of the wave on the string is governed by the tension of the string not by the plucking force. It is the “tension” of space that determines the speed of the photon wave.
That the speed of light is the same for all observers is actually, in a real sense, the simplest theory about nature that we can come up with:
Imagine you are floating in space and there is absolutely nothing else. Are you moving or not? You have no idea – in fact the concept of moving really has no meaning in this context. The question is ill defined. And so is the concept of direction. Am I rotating or not? If I felt a centrifugal force then I would know but there is a real discussion, starting with Newton and carried on by Leibniz and Mach among others, as to whether I would feel a centrifugal force in an otherwise empty universe (https://mathshistory.st-andrews.ac.uk/HistTopics/Newton_bucket/). If I don’t feel any force then the concept of rotating loses its meaning here too.
Lets shine a light and measure its speed (by, for example, holding a clock at arms length and starting the clock at the same moment I shine the light). The clock stops when the light beam hits it. The very simplest assumption is that I always measure the same value. Also, if a beam of light is coming to me the simplest assumption is to assume that the speed is also the same.
In short, the theory in which we make the least amount of assumptions about the nature of space or the speed of light with no concept of movement or direction except movement of light with respect to me and no differences in the speed of light inbound or outbound – implies a constant speed of light outbound or inbound – with respect to me. Of course, the same argument applies to you. My outbound light travels with a certain speed and your inbound light travels with the same speed in this simplest theory. The fact that my outbound light beam may be your inbound light beam really has no bearing on the theory. I measure a speed c on the outbound beam, you happen to measure the same speed c on the same beam inbound.
What is important to note is that the concepts of an object having speed or direction are constructs having nothing to do with space itself but only define interrelationships between objects in space. Except for the speed of light, space doesn’t “care” how or even whether you define speed or direction for objects. From its point of view these are merely artificial constructs that have nothing to do with “real” space. All space (or nature) cares about is to keep nature as simple as possible with as few assumptions as possible and that is by giving light the same speed coming or going. If that creates weird effects when making use of your definitions of object movement or direction then that is your problem not nature’s. Those weird effects are due to your artificial constructs (definitions) and have nothing to do with the nature of space.
Obviously different units (or to be perhaps more pedantic different metrics) will give different numerical values for light’s speed. However, I believe the relevant question is: Why isn’t the speed of light (as observed by an observer) in space twice (or 10 times) faster – or slower – than the value currently measured (using any metric you care to specify)? Any answer is independent of the units discussion.