🎓 Doc Freemo 🇳🇱 @freemo@qoto.org

@QOTO @Gargron @arteteco @Sphinx @khird @freemo
Kind of cancels the whole "moderation" thing if mods can be blocked.

AHHHHHH I finally understand quaternions!! XDD :DD

I always thought they were neat fun thing in abstract algebra and a neat but arbitrary way of representing rotations with unnecessarily extra numbers.

If someone had just said to me this sentence I would have seen how insanely perfect they are!! :D

As rotations, the i/j/k coefficients are the x/y/z components of the axis-of-rotation vector, and the fourth lone number is the amount of the rotation in radians!

#Math #Geometry #Quaternions

@Zest

Its actually not that surprising you see this happen every day with other things, you just never see it happen at such short distances (which is only possible due to the high speeds)...

Imagine sound instead of light, which travels slow enough you can actually see the delays and therefore is easier to conceptualize. if you are right in the middle of two lightening strikes then you would hear them at the exact same moment, assuming you only used your hearing and not sight you would assume they were simultanious.

Likewise imagine you are much closer to one than the other, you would hear that one almost immediately and might not hear the other for a few seconds. Even if they happened at the same time it would seem to you, with your different frame of reference, as if they happened at significantly different points in time.

That's all that is happening here, just in a more confusing way because it isnt due to you being in a physically different location but because time and space itself is warped. But in principle its the same thing.

@Science

@freemo @Science woah! but why though? that's actually really perplexing, I don't know of any reason why it would happen that way

@Zest

The idea is called simultaneity. What that means is that two events that appear simultaneously to one observer (in one frame of reference) is not necessarily simultaneous in another frame of reference.

In this case the two events are the closing and re-opening of each of the barn doors. While that occurs simultaneously from the perspective of the barn and the person doing it, from the perspective of the ship they are not. So while the ship's perspective looks like it cant fit into the barn, and in reality it cant fit in the barn from its perspective, it doesnt have to. From the ships perspective the doors are never closed at the same time. one door closes, then opens, then the other door closes and opens, all at the right time to ensure the ship passes through without crashing through a door.

So while from the ships perspective the ship was never enclosed (both doors shut with it inside) in the too-small-to-fit barn, from the barns perspective where it is more than big enough the ship was, in fact, enclosed inside for a moment.

@Science

@Zest

This moment right here is what I live for...

Give it time though you will start to have questions againa nd feel like it stops making sense. Dont let that win, you got the idea, it does make sense, and when you realize the "gotchas" it doesnt mean you dont really understand, it just means there are some unusual scenarios that require one other piece of the puzzle to understand and incorperate...

I dont want to break up your tears of joy but take this curve ball (again don't think it means your thinking about it wrong, i promise you aren't), i will give you the answer if you'd like but its kinda the only time piece you haven't considered so worth exploring...

Remember that ship looks short to you and the universe looks short to the ship... so take this class paradox of that scenario and consider how you might resolve it logically... You have a barn that normally is more than large enough to hold the ship. The barn has two huge doors on opposite sides. Normally the ship is small enough to fit inside. Now as a ship flying at 98% the speed of light flys past you and flys through the barn (the doors are initial open) you very quickly in the instant it is inside the barn close both the doors, containing it inside, then open them again before the ship crashes intot he door, and it flys away.

Now because the ship is going 98% the speed of light it is 19.9% its normal length. This isnt a problem because the ship could fit inside at full size anyway. However from the ships perspective the universe is 19.9% shorter and the ship is normal size. So that means from the perspective of the people on the ship the barn is 19.9% its normal length and they should not be able to fit inside it and have both doors closed at the same time. Yet somehow from their perspective it all works out.. how is this possible?

You can also flip this around and presume that at normal lengtht he ship is too big to fit in the barn but when it is traveling at speeds and is 19.9% its normal length it can fit inside just fine, therefore to the stationary person they can still close the doors safely when it is at speed, but couldnt otherwise, and to the ship there is still an apparent paradox (it isnt really but there is something you need to realize to understand why)...

Let me know if you have any ideas as to how this is answered, or if you just want me to answer it for you I Can do that too.

@Science

@freemo @Science oh my god! it all makes sense now I'm actually literally crying thank you so much for explaining all this!

@Zest @Science

> would those objects that are moving apart from each other anyways not still be moving apart from each other at rather high speed

from all observers the distance between the earth and original ship will appear to be increasing, though not at the same rate.

> if all three objects stopped moving relative to each other then, how would that effect the distance between them?

You have actually just hit on the third component of special relativity, you already knew about time dilation as you mentioned it, and we already discussed velocity dilation (that velocity is relative to the observer just like time is), now you are basically realizing the third aspect of special relativity, that is, length dilation (formally called length constriction). the length of a thing is just as relative as the rate of time or the speed of the thing.

Depends on who out of the group is doing the decelerating in order to create a relative velocity of 0 between them.. If you are standing in between two spaceships each going 98% the speed of light in opposite directions away from you, and they both decelerated equally until velocity was 0, then the distance between you and teh ships and between the two ships from your perspective would not change (however the length of the ships themselves would). When the ships are moving at high speed they would be much short in the direction they were moving, specifically 19.9% of their normal length, as if they were "compressed" in that one direction. As they come to a stop their length would expand to their normal length again.

However the perspective from the moving ship is much more interesting, assuming the ship is the one that did the accelerating the entire universe, along the direction that it is moving, would be 19.9% shorter than it appears to you, so a star that would normally had been 1 light year away is now only 0.199 light years away and from the perspective of the person on the ship would take 1/5th the time to get there that it would have taken light to do the journey.

Similarly if we had two ships moving away from you at 98% the speed of light the distance from the perspective of the ship is 19.9% less from the ship to you or the ship to the other ship than it appears to you. However the moment the ship accelerates and becomes stationary to you the universe will expand to its normal length again and the distances seen from the people on the ship would agree entirely with your own measurement of distance.

@freemo @Science
My hobbies include, watching time go by. Said no #photon ever.

we need a technological advance in the field of whiteboard markers

@Zest

> because intuitively if one thing is moving away from you and another thing is moving in the same direction, if you accelerate fast so that your relative speed is equal to the speed of light, is it possible to travel away from both of them at the same speed?

So this is your first mistake, the phrase "speed is equal to the speed of light" makes no sense. You can never have anything moving relative to you at the speed or light or faster (other than light of course or another massless particle).. You would have to rephrase this to say "near the speed of light" to make any sense.

If you and the object are moving at the same speed and direction and are moving at near the speed of light relative to the earth the earth would appear to be receding away from you at near the speed of light, lets say 98% of C.

Now if you left the object that is moving with you behind and now accelerated to 98% the speed of light relative to that object what you would see is that even though you increased your speed by 98% C relative to the object that was moving with you, relative to earth you only appear to have accelerated by 1.98% the speed of light. In other words after accelerating the object that was moving with you would now be receding away at 98% the speed of light and the earth would now be receding away at 99.98% the speed of light.

> is this a time dilation thing?

Well, no it isnt a time dilation thing exactly, though time dilation is occurring it isnt really relevant to the people in the ship (who would be unaware of any time dilation presumably. but not completely unrelated either (if they had a telescope and looked at earth thigns would appear to be moving slower in terms of the people and clocks the faster they go). With special relativity you cant really ignore any one aspect wholly.

> and would that only be from your perspective

Well not only from your perspective exactly, but only from certain perspectives. Obviously if a second ship were traveling along side you at the same speed and direction as you and accelerated along side you then they would see all the things you see from their perspective.

But yes that perspective is not shared by other observers necessarily. From your perspective (since you're not accelerating) it feels and looks like you are stationary and it is the object and the earth that are moving instead. So to you on the ship the object is moving 98% the speed of light and the earth is moving 99.98% the speed of light. From the perspective of the object the object is stationary and you are moving away from it in one direction at 98% the speed of light and the earth is moving away from it in the other direction at 98% the speed of light. Likewise from earth the object appear to be moving at 98% and you appear to be moving at 99.98%

> the relative speed by an observer who was traveling even faster than the other object you could be moving slower relative to all three things from their perspective because time would be going differently to them?

Direction matters here, but yes. If there was another object in the mix that was another ship and basically flew along side you and accelerated when you did, but lets say they stopped accelerating just a few moments before you stopped, so they are almost at the same speed and direction as you but not quite. From their perspective the object and earth would be moving marginally slower than from your perspective. However this new ship would appear to be moving very slowly away from you and in the direction you came from (towards the earth) while to the new ship you would appear to be moving very slowly away from them and in the direction away from earth.

@Science

6 reasons the #Fediverse is better than regular Social Media

https://slashdev.space/posts/2021-01-18-reasons-the-fediverse-is-better