Why Adding Velocities Does Not Work in Special Relativity
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- čas přidán 8. 08. 2020
- Special relativity is counter-intuitive in a lot of ways. But perhaps the result which is the most confusing for people seeing it for the first time is that nothing can travel faster than the speed of light in a vacuum. It seems straightforward that this can't be true, right? I someone is travelling at 0.5c relative to you and they throw a ball at 0.6c relative to them, clearly you see that same ball travel at 1.1c, and it is going faster than the speed of light! If this is the case, then special relativity has contradicted itself! So, we have to dive deeper into the assumptions we make and the framework we are working in when we assume that velocities simply add together like this. What we find is that there is a surprising rule for the addition of velocities in relativity!
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Partially inspired by xkcd.com/675/
Amazing quality
Amazing video
Keep it up
@Raaghav thank you! I'm glad you enjoyed! (And I will certainly try to keep it going!)
Nice summary! Sometimes the math was kinda fast, but that's what the play/pause button is for ^^
I just left a relativity lecture with this exact question in mind, you just cleared it all up for me wow thank you.
My brain wasn’t taking into account the time dilation that each moving part experiences. Which is what causes them to not just be totally additive right?
The video is awesome. Actually, the whole series is awesome. I love them, and hope you could keep it going.
In general,
is it possible for someone to travel a distance 'd'
(i measure) in time 't' (according to them) such that
d/t > 'c' ?
Meaning:can they reach that point (not moving wrt their starting point) & see the light that was emitted before they left?
U can also use general relativity.
Trying to understand why something is wrong. I might be doing the fallacy explained in this video, but I'm not sure. And I'd like to figure out how it relates to the idea of "now slices".
If you are in a spaceship 1 lightyear away from Earth and traveling towards Earth at .25 the speed of light (no acceleration), a light shined from your ship towards Earth would travel from you at 1 lightyear per year away from your reference frame. Since, in your reference frame, the Earth is traveling towards you at .25 C, it would intersect with the light beam before the beam traveled 1 lightyear away from your ship. But from the point of view of the Earth, the beam would take 1 year to travel 1 lightyear from its starting point.
So 1 year for them would be less than 1 year for you.
I think this would mean that you would see the Earth spin faster as you moved towards it and slower as you moved away.
Time would move slower for you, on the ship, relative to on the Earth. And from the Earth, the ship would appear to be viewing the year-long event as less than a year, so the things going on inside the spaceship would look slowed down.
But from what I gather, this is not right, and I've seen people say that the velocity toward or away from some other object is not related to time distortion. But then how is the 'now-slice' idea a thing?
It says that direction matters, in a Brian Green video on youtube called "The illusion of time".
That video says there is an idea that as you are moving towards something, you see its future as "now," and away, you have their past as "now", but I do not know if this has to do with the type of distortion discussed in this video.
I also don't know how seeing an object's future as now would relate to seeing it spin faster. But either way, does this video say that direction doesn't matter? The video on now-slices does not say it is due to acceleration, but he says it's due to their clocks not agreeing.
But in my scenario, what if no light is being shown? Which side would have time slowed down then? Hmmm. . (And if an object is moving towards me, seeing now as my future, doesn't that mean I see now as its future?)
If a ship is flying towards a planet, and the planet shoots a light out when it is 1 lightyear away, the planet would say the light hit the ship as it intersects (less than year). The ship would see the light coming from 1 lightyear at the speed of light. If the ship can't make the light move faster than C in relation to its reference frame, then would that event still take 1 year, magically forcing the planet to speed up? It seems like a weak point, that the ship would run into the light sooner because of the same decrease of distance, but, from view of the ship, you are standing still while the planet is moving and just shining a light, trying to add velocity to it.
Same situation, different light source, different side slowed down.
@Wade Gruber this is a fantastic question. Hopefully I can give a satisfactory answer. As far as I can tell, everything you said is correct. As the ship flies towards the earth and they shine a light toward the earth, the time it takes the light to reach earth is less from the ship's point of view than the earth's point of view. And of course the opposite is true when the ship is moving away. Again, as you said, if the light was instead shone from the earth, everything would be reversed. And to make everything more confusing, time dilation certainly does not depend on direction of motion: if I see someone moving relative to me, I think their clock should run slower no matter what. So how does all of this get resolved?
There are two key things to remember here: 1.) there are no "correct" reference frames which always move at constant velocities in special relativity and 2.) space and time mix together as we go from reference frame to reference frame.
Let's start with 1.). Since the speed of light is always the same in all reference frames, no single one can be called correct. The only thing that matters is that they are moving (with constant velocity) relative to each other. If this is the case, then it isn't really a problem if they disagree on whose clock is running slower. The reason why this is is that there is only one point in spacetime where the two observers can accurately compare clocks: when their paths cross. To see why this is, let's say that we have two identical clocks and we put one on earth and one on a distant spaceship. These clocks work by sending out light with a designated frequency which determines how fast the clock ticks. When the spaceship travels toward the earth, the earth sees light "blue-shifted" (meaning they see higher frequency light coming from the ship), so they say that clock is running faster than theirs. However, the ship sees the earth's light as blue-shifted, so they say the same thing. Similarly, when the two observers are moving away from each other, they see each other's light as "red-shifted" and say that the other's clock is running slower. This is not a problem because there is only a single point in spacetime (the point where the two observers are at the same point in spacetime) where they can accurately compare clocks. However, one point is not enough to actually determine whose clock is really slower; you need at least two (since you need a time difference). So as long as the paths cross only once (i.e. they always travel at the same constant velocity relative to each other), it is not a problem that they both say that the other's time is slower/faster than their own.
For 2.) it is helpful to proceed by analogy. Imagine that we are standing next to each other, but facing different directions. Now, you draw an arrow in the "forward" direction according to you. Since I am rotated relative to you, the arrow that you drew is not perfectly forward for me. If I were to measure the amount of that arrow that is in MY "forward" direction, it will always be less than the total length of the arrow, no matter what direction I am rotated in or how much I am rotated by (since only a piece of the total arrow will lay along my forward/backward direction). This is analogous to time dilation, where we replace "forward" by "time" and the rotation with a relative velocity. No matter how fast or which direction I see a frame travel relative to me, their clocks should run slower than mine. Time is just another coordinate which we can "rotate in" (all the Lorentz transformations shown in this video really are are just "rotations" between space and time). But in the case of the problem that you give, the arrow would not be only pointing "forward" for you since things are moving in both space and time. So, some of the arrow is in your forward/backward direction and some of it is in your left/right direction. If I now want to figure out how much of THIS arrow is in my forward/backward direction, I absolutely need to know how much I am rotated relative to you and in what direction, since my forward/backward direction is a mixture of both your forward/backward AND left/right directions. The same goes for the thought experiment you gave. Since things are evolving in both space and time, I have to take into account that space and time mix (given by the Lorentz transformation) as I change reference frames. The amount of mixing definitely depends on the direction of the velocity.
This is definitely not an easy concept to wrap your head around and I had to give it some serious thought to try to come up with a good explanation, so hopefully that makes sense and clears things up a little!
@@zapphysics Thank you for your answer. This is really helpful. There is a lot in there that helps me understand the idea better.
I was looking for an intuitive answer not algebra. Can somebody tell me in a sentence with actuall words why it isn't working and why the accelaration slows down close to the speed of light?
Like "speed generates mass somehow and as your speed incrases you need to put more effort to move yourself and the speed of light is the natural limit for anything in our universe, in a universe where the mass of the higgs bosont is different the speed of light would be different too."
Or something like this. I just made it up.
tbh for me it's unclear what you want please rewrite it into one simple question
@@dasvanalo3504 how?
just rephrase it i dont know what your question is
@@dasvanalo3504 how would you explain to someone phisically what is happening, without math?
@Mile Dávid perhaps an answer to your question has to do with symmetry. By symmetry, I mean that, if I have a physical system and I try to change it in a certain way, but it doesn't end up changing. If this is the case, then I would say that that "change" I tried to make is a symmetry of the system. So for example, if you are holding a perfect sphere and you tried to rotate it, it will always look the same. Then, you would say that the sphere has a symmetry of rotation. "Built-into" our universe are a certain set of symmetries. One of these is shifts by constant velocity. We know from observation that just changing your velocity by a constant doesn't actually alter the physics you see (whereas, say, acceleration would). There are a couple of ways that this "velocity-shift" symmetry could come about. One is much more intuitive (Galilean relativity), where one of the results is that velocities just add together like you might expect. The other is more complicated (special relativity), where velocities don't just simply add, but this velocity-shift symmetry still can exist. Two of the consequences of this more complicated way of realizing the symmetry are that the speed of massless things (e.g. light) in a vacuum is a constant (everyone sees light travel the same speed no matter how fast they are travelling relative to each other) and nothing travels faster than this speed (the speed of light in a vacuum is a universal "speed limit"). So really, at the end of the day, these "laws" are just consequences of the symmetries that are inherent to our universe. Hopefully that helps!
I don't get it, and I don't think I have the motivation to put my head down to understand this, can I just imagine that spacetime gets warped because of the speed and that's the reason it would look like that to an observer?
@Toxodos so since we are dealing with special relativity, everything is always flat: so spacetime is never warped in this discussion. The better way to think about it is that when we change observers, space and time mix together in a non-trivial way.
This may see surprising, but it's actually a concept you are probably already familiar with. So say you and I are standing next to each other, but facing different directions. What you call forward is not going to be what I call forward. In a sense, your forward direction will be a mix of my forward/backward and left/right directions. Nothing mysterious is happening, though because our disagreement is resolved by simply rotating me to face the same direction as you.
In the same way, space and time mix together in special relativity, only now, instead of using a rotation, you have to use this Lorentz transformation to relate the observers.
Not sure who this video is for. I have had a pretty hard time trying to understand all the math you are throwing at me. Maybe I'm the dumass, but I feel like you wanted this to be an ELI5 type of content and ended up making something way too complicated
@K. Péter This is a totally legitimate and understandable criticism, and I appreciate it! I don't think you're dumb at all for thinking it. My thought process was to make this video for people who have been exposed to some special relativity, but still want to gain a functional understanding of it. In my personal opinion, I really don't like when people try just give a result without any explanation and so I try to hold myself to that same standard. Sometimes to do this, I really have no option but to dive into the math, which can understandably be a turn-off for people. I suppose my goal is to include enough math in the video so that those who want to follow it can, but also explain the results so that the people who don't care so much about the math can have an idea of what the result means. But perhaps I did not succeed with that goal in this video. I will keep your comment in mind for the future!