5 ms·

Thank you for a clear explanation. I'm a total layman here, so forgive my questions if they don't make sense: > One of the deep insights of special relativity

Thank you for a clear explanation. I'm a total layman here, so forgive my questions if they don't make sense: > One of the deep insights of special relativity is that these scalar and vector quantities are actually unified into a single, new entity called a "four-vector" On which basis was this pairing between position and time "decided"? > But the really weird thing about this particular four-vector is that it always has a magnitude of exactly the speed of light Why is that? Is it by definition? > it's actually the change in coordinate time per change in proper time How does this translate to what we call "time" in our daily lives?

jiggawatts 6y ago
It's a tautology. You cannot observe time slowing down, because anything that would affect the "speed of time" affects your brain also in the same proportion. Hollywood movies are not how physics works. The plucky protagonist can never look down at their hand and see a stopwatch run slower or faster! There is no such thing. If some sort of science-fiction field existed that would affect a clock, it would affect the protagonist also. If the clock runs at half speed, your brain runs at half speed, so you see it ticking forward at twice the rate, and 2.0 * 0.5 = 1. Now, of course, I tell a small lie: There can be differences in the tick rate over some distance. But these differences are necessarily small. Big differences in the rate of temporal flow create gravity, as per Einstein's General Relativity. To get an observable difference in time flow over the space of, say, a meter would require a fantastically huge gravitational field that would instantly crush the poor scientists into a pancake. Conversely, in the gentle field of Earth's gravitational field, if you hold an atomic clock in your hand a meter from you head, and an atomic clock in line with your head, then yes, you can see a tiny difference in the tick rates, on the order of nanoseconds per century or somesuch (I'm too lazy to work it out). However, as the distance decreases between the clock and the observer, the difference gets smaller. Extrapolating down to atoms and the like the conclusion is inevitable: time locally always ticks forward at one second per second.
- rl3 6y ago
  >If the clock runs at half speed, your brain runs at half speed, so you see it ticking forward at twice the rate, and 2.0 * 0.5 = 1.0 Consider changes in gravity affect cognition. Likewise, if the brain has any quantum mechanisms, then that 1.0 might not be exactly 1.0.
  - jiggawatts 6y ago
    > Consider changes in gravity affect cognition. That is literally what it does. It slows down cognition. In the exact same way that it slows down clocks. The "clock in your brain" and the "watch in your hand" are all operating on the same physical and chemical principles. It's all just atoms and electromagnetic interactions at the lowest levels. > Likewise, if the brain has any quantum mechanisms Again, this is a pop-science misunderstanding of all of physics, not just Quantum Mechanics (QM). The rules of QM either apply to everything or nothing. The laws of the universe do not begin or end at the edge of the laboratory bench top. Similarly, there are no special rules that apply to just the human brain. The rules that govern galaxies, particle beams, atomic clocks, mechanical watches, and human observers are the same. They all tick along at the same rate. One second per second, locally at least.
    - tsimionescu 6y ago
      > The rules of QM either apply to everything or nothing. The laws of the universe do not begin or end at the edge of the laboratory bench top. Similarly, there are no special rules that apply to just the human brain. Well, for now we don't really know how the rules of QM apply to macroscopic objects. The exact physical interpretation of wave-function collapse (if any) is still a matter of speculation, with all options still being on the table - maybe there is no collapse (e.g. many worlds theory), maybe there exists a collapse when interacting with large enough systems (measurement - the Copenhagen interpretation), maybe collapse is a physical process that happens at precise scales (Roger Penrose seems to believe something like this), maybe the wave function is a physical wave (pilot wave theory) and there is no collapse in another way.
      - jiggawatts 6y ago
- dreamcompiler 6y ago
  > Conversely, in the gentle field of Earth's gravitational field, if you hold an atomic clock in your hand a meter from you head, and an atomic clock in line with your head, then yes, you can see a tiny difference in the tick rates, on the order of nanoseconds per century or somesuch (I'm too lazy to work it out). This is why GPS satellites need time correction. GPS satellites contain atomic clocks, and they are further from the center of the Earth than you are. Therefore they experience slightly less gravity than you do. Therefore their clocks run slightly faster than atomic clocks on Earth's surface. That's the General Relativity correction. But GPS satellites also move a lot faster than you do, because they are in orbit. That makes their clocks run slower than clocks on the ground. That's the Special Relativity correction. Both corrections have different signs but they do not cancel each other out.
dkersten 6y ago
I find using the speed of light confusing as it has little to do with light other than that light happens to travel at that speed [1], but rather the speed of propagation of cause and effect. If you stay absolutely still, cause and effect still propagate at the same speed and so time ticks forward at this speed. If you physically move (have velocity), cause and effect still ticks forward at the same speed, but some of it appears to tick into moving you physically. You can still only propagate at the speed of propagation, but some of that propagation is happening on the physical position axis, so less happens on the time axis. [1] because light is massless, so in a vacuum there is nothing slowing it down
gus_massa 6y ago
> On which basis was this pairing between position and time "decided"? Three partially correct answers of the same question: 1) Nobody decided it. It is just how the universe is. 2) You have the formulas where the space-something appear, and you randomly try propose to replace something with things you know, like mass, time, color, ... It is actually more easy, because using the units you know that something must be measured in seconds, so it discards a lot of possibilities. 3) You have the "classic" formulas where space appears https://en.wikipedia.org/wiki/Lorentz_transformation https://en.wikipedia.org/wiki/Lorentz_transformation that were actually discovered almost 20 years before the work of Einstein. And you rewrite them in the equivalent of the "vectorial" notation. In the usual space it is like replacing (x,y,z) with a big X and never looking inside X. If you try it, the only way you can success is if you group (ct,x,y,z). The trick is to look carefully at the calculation and try to think what you can arrange it to be able to rewrite the calculation in the correct form. For example with momentum, you look carefully and realize you must add energy as the fourth component. If you choose to group space and time, and you choose to group momentum and energy, then you must use the same choose in all the formulas. You can not choose a different grouping for each formula. But sometimes it is not so easy. With speed you realize that it is too bad to be fixed, and you must define another speed-like-thing and then give another formula that transform the "real speed that you measure in a lab" and the "abstract speed-like-thing that you use in the calculation". With the electric field, ... well you can't put it in a 4-vector, you must use something more weird that is a 4x4-matrix.
im3w1l 6y ago
The reason for creating these pairings is that they make calculations easier. Maxwells laws of electromagnetism in particular become very beautiful when defined in terms of these 4-vectors.

jiggawatts 6y ago

It's a tautology. You cannot observe time slowing down, because anything that would affect the "speed of time" affects your brain also in the same proportion. Hollywood movies are not how physics works. The plucky protagonist can never look down at their hand and see a stopwatch run slower or faster! There is no such thing. If some sort of science-fiction field existed that would affect a clock, it would affect the protagonist also. If the clock runs at half speed, your brain runs at half speed, so you see it ticking forward at twice the rate, and 2.0 * 0.5 = 1. Now, of course, I tell a small lie: There can be differences in the tick rate over some distance. But these differences are necessarily small. Big differences in the rate of temporal flow create gravity, as per Einstein's General Relativity. To get an observable difference in time flow over the space of, say, a meter would require a fantastically huge gravitational field that would instantly crush the poor scientists into a pancake. Conversely, in the gentle field of Earth's gravitational field, if you hold an atomic clock in your hand a meter from you head, and an atomic clock in line with your head, then yes, you can see a tiny difference in the tick rates, on the order of nanoseconds per century or somesuch (I'm too lazy to work it out). However, as the distance decreases between the clock and the observer, the difference gets smaller. Extrapolating down to atoms and the like the conclusion is inevitable: time locally always ticks forward at one second per second.

rl3 6y ago
>If the clock runs at half speed, your brain runs at half speed, so you see it ticking forward at twice the rate, and 2.0 * 0.5 = 1.0 Consider changes in gravity affect cognition. Likewise, if the brain has any quantum mechanisms, then that 1.0 might not be exactly 1.0.
- jiggawatts 6y ago
  > Consider changes in gravity affect cognition. That is literally what it does. It slows down cognition. In the exact same way that it slows down clocks. The "clock in your brain" and the "watch in your hand" are all operating on the same physical and chemical principles. It's all just atoms and electromagnetic interactions at the lowest levels. > Likewise, if the brain has any quantum mechanisms Again, this is a pop-science misunderstanding of all of physics, not just Quantum Mechanics (QM). The rules of QM either apply to everything or nothing. The laws of the universe do not begin or end at the edge of the laboratory bench top. Similarly, there are no special rules that apply to just the human brain. The rules that govern galaxies, particle beams, atomic clocks, mechanical watches, and human observers are the same. They all tick along at the same rate. One second per second, locally at least.
  - tsimionescu 6y ago
    > The rules of QM either apply to everything or nothing. The laws of the universe do not begin or end at the edge of the laboratory bench top. Similarly, there are no special rules that apply to just the human brain. Well, for now we don't really know how the rules of QM apply to macroscopic objects. The exact physical interpretation of wave-function collapse (if any) is still a matter of speculation, with all options still being on the table - maybe there is no collapse (e.g. many worlds theory), maybe there exists a collapse when interacting with large enough systems (measurement - the Copenhagen interpretation), maybe collapse is a physical process that happens at precise scales (Roger Penrose seems to believe something like this), maybe the wave function is a physical wave (pilot wave theory) and there is no collapse in another way.
    - jiggawatts 6y ago
dreamcompiler 6y ago
> Conversely, in the gentle field of Earth's gravitational field, if you hold an atomic clock in your hand a meter from you head, and an atomic clock in line with your head, then yes, you can see a tiny difference in the tick rates, on the order of nanoseconds per century or somesuch (I'm too lazy to work it out). This is why GPS satellites need time correction. GPS satellites contain atomic clocks, and they are further from the center of the Earth than you are. Therefore they experience slightly less gravity than you do. Therefore their clocks run slightly faster than atomic clocks on Earth's surface. That's the General Relativity correction. But GPS satellites also move a lot faster than you do, because they are in orbit. That makes their clocks run slower than clocks on the ground. That's the Special Relativity correction. Both corrections have different signs but they do not cancel each other out.

dkersten 6y ago

I find using the speed of light confusing as it has little to do with light other than that light happens to travel at that speed [1], but rather the speed of propagation of cause and effect. If you stay absolutely still, cause and effect still propagate at the same speed and so time ticks forward at this speed. If you physically move (have velocity), cause and effect still ticks forward at the same speed, but some of it appears to tick into moving you physically. You can still only propagate at the speed of propagation, but some of that propagation is happening on the physical position axis, so less happens on the time axis. [1] because light is massless, so in a vacuum there is nothing slowing it down

gus_massa 6y ago

> On which basis was this pairing between position and time "decided"? Three partially correct answers of the same question: 1) Nobody decided it. It is just how the universe is. 2) You have the formulas where the space-something appear, and you randomly try propose to replace something with things you know, like mass, time, color, ... It is actually more easy, because using the units you know that something must be measured in seconds, so it discards a lot of possibilities. 3) You have the "classic" formulas where space appears https://en.wikipedia.org/wiki/Lorentz_transformation https://en.wikipedia.org/wiki/Lorentz_transformation that were actually discovered almost 20 years before the work of Einstein. And you rewrite them in the equivalent of the "vectorial" notation. In the usual space it is like replacing (x,y,z) with a big X and never looking inside X. If you try it, the only way you can success is if you group (ct,x,y,z). The trick is to look carefully at the calculation and try to think what you can arrange it to be able to rewrite the calculation in the correct form. For example with momentum, you look carefully and realize you must add energy as the fourth component. If you choose to group space and time, and you choose to group momentum and energy, then you must use the same choose in all the formulas. You can not choose a different grouping for each formula. But sometimes it is not so easy. With speed you realize that it is too bad to be fixed, and you must define another speed-like-thing and then give another formula that transform the "real speed that you measure in a lab" and the "abstract speed-like-thing that you use in the calculation". With the electric field, ... well you can't put it in a 4-vector, you must use something more weird that is a 4x4-matrix.

im3w1l 6y ago

The reason for creating these pairings is that they make calculations easier. Maxwells laws of electromagnetism in particular become very beautiful when defined in terms of these 4-vectors.