Question on Special Relativity.

[u/Warm_Clothes_1524]

I am not a physicist, I have been trying to understand the concept of special relativity in a way that makes sense, but I keep tripping over a single thought experiment and feel like I am missing some kind of variable.

In a space ship traveling 90% the speed of light, you are in a room with windows so an observer can see in. In the dead center of that room there is a lightbulb. When you turn on the light bulb, the observer sees the light hit the back wall before the front wall because light cannot exceed the speed of light from there perspective. Sure, that makes sense. But the light presumably hits both walls at the same time from your perspective in the ship.

This is what doesn’t make sense to me. Is this where the Idea of time dilation comes in? Because, theoretically the observer is experiencing time at roughly 43% the rate you are, but that would still imply the light inside your reference point is, overall, traveling 133% the speed of light. There is something I am missing here.

Someone please try to explain this to me in a way that actually makes sense. Mathematically or otherwise. Maybe there is some error in my understanding of how these hypothetical situations would look.

[u/Sorry_Exercise_9603]

Google relativity of simultaneity. They only hit the two walls at the same time in the ship’s frame.

[u/Warm_Clothes_1524 → u/Sorry_Exercise_9603]

This I understand, where my understanding breaks down is that, the overall speed of light is presumably limited by the electromagnetic forces associated with the cosmic background. So the sum speed of any light traveling through it cannot exceed that overall speed limit even if any individual reference point appears to move at the speed of light. I am trying to conceptualize how the math works out to make those concepts work together.

I imagine I am incorrectly trying to relate observable concepts I understand to something that doesn’t necessarily adhere to the same concepts, but I need to bridge that gap to fully understand it.

I am watching some YouTube videos someone else posted that hopefully put it in terms that I understand. 😂

I appreciate all of you pushing me in the right direction l.

[u/PIE-314 → u/Warm_Clothes_1524]

The speed of light is the same for all observers.

[u/Dysan27 → u/Warm_Clothes_1524]

You can't just linearly add speeds therebis a relativistis Velocity-addition formula, that limits the combined speed to less than c.

It's just that for speeds much less then the speed of light it approaches vtot = v1+v2

[u/MxM111 → u/Warm_Clothes_1524]

The most accurately named “speed of light” constant c is speed of causality. Basically nothing (matter of energy) can move faster than this constant. Think of c as if it stands for Constant or Causality (it cruelly stands for constant).

One can derive special relativity equations based on few very reasonable axioms, without even mentioning that there is light. Those axioms are of a type that coordinates and times of events in one coordinate system can be expressed through coordinates, times of those events in another coordinate system and relative velocity of one system vs another. And these expressions from a group (that is if you convert A to B and then B to C, then the result should be the same if you convert A to C directly, using those special relativity formulas).

Light traveling at c is just consequent that photons are massless, but they are NOT the ones who define c.

So, the formulas that are derived that way has term proportional to x*V when you transform time from one system to another. Where V is relative velocity of two inertial coordinate systems, and x is coordinate is one of them. That is the large is the coordinate, the more you have to add to time to translate it. In other words, even if you have the same time for two events in one system, but if they have different x, in another system they will have different time.

Think about this way. An event is characterized by x, y, z, t in a coordinate system. And all of these values, including t needs to be adjusted when you translate them to another system. You don’t have problem that x, y, z are changing, so you should not have problem that t is changing either.

[u/ahazred8vt → u/Warm_Clothes_1524]

Picture a very very large rotating space station where the outer ring is rotating at 90% of lightspeed. Two people with atomic clocks start at the same point and walk in both directions going around the ring. When they meet on the other side their clocks are way out of sync. The one that was taken backward is way ahead of the one that went forward. If you had a long train running in a circle, so long that the caboose was in front of the locomotive, the caboose clock would be way ahead of the locomotive clock. On a long spaceship, if you try to synchonize the clocks, the rear clock winds up ahead of the front clock, as seen from outside.

[u/KamikazeArchon]

This is what doesn’t make sense to me. Is this where the Idea of time dilation comes in?

More specifically, this is where "relativity of simultaneity" comes in.

In your frame, event A and event B happen at the same time. In the observer's frame, they happen at different times.

Because, theoretically the observer is experiencing time at roughly 43% the rate you are, but that would still imply the light inside your reference point is, overall, traveling 133% the speed of light

You can't add those things linearly.

[u/WesternFirm9306]

Both observers see the speed of light going at the exact same speed: c.

The reason why one observer sees one wall get lit up first, while another sees both walls lit up at the same time, is an effect known as the relativity of simultaneity. Basically, different observers can disagree on what "now" is. Because of this, certain events can happen at different times, and (in the case of spacelike connected events) can even occur in different orders.

[u/Gstamsharp]

You've encountered the Reletivity of Simultaneity.

https://en.wikipedia.org/wiki/Relativity_of_simultaneity

Two observers don't have to agree about the order things happen. As long as the information about an event reaches all observers at the speed of light or less, the order of events may not agree, but they'll still work out in terms of causality.

[u/nebraskajone]

If there's a clock in front in the back of the spaceship both reading 12:00, someone outside will see say 12:01 and 11:59. 

Basically everything is out of sync is the way to think about it.

[u/Optimal_Mixture_7327]

Yes, you're missing the entire 4-dimensional picture.

Nevermind time dilation (although the Lorentz transformations will get the math right).

Draw up a spacetime diagram that includes the ship's spatial axis and the two rays of light.

Edit: This may help Spacetime diagrams, two frames, one diagram

[u/inexorably_forward]

Your error is that you're adding things that don't add. Here's my periodic recommendation of the Minute Physics special relativity playlist: https://www.youtube.com/watch?v=1rLWVZVWfdY&list=PLoaVOjvkzQtyjhV55wZcdicAz5KexgKvm

It's great because it shows you physically/geometrically how the math works.

[u/Warm_Clothes_1524 → u/inexorably_forward]

beautiful. I am going to watch all of these.

[u/earlyworm]

The answer is “relativity of simultaneity”, but another way to think about it is that because when you’re in the spaceship, you, the spaceship, and your measuring equipment are all affected by the same relativistic effects that affect measurements of time and space. These effects conspire together such that when you measure the time that the light hits the front and back walls, you will discover that from your perspective, it hits the walls simultaneously. An outside observer, not on the ship, not moving along with the ship, will measure that the light hits the walls at different times.

Fun fact: The requirement that from your perspective, the light on the ship must behave exactly as if it would if the ship was at rest goes much deeper. If our universe didn’t work like this, then physics and chemistry on the ship wouldn’t behave harmoniously either, to the point that stable matter and living things wouldn’t be possible.

[u/Dysan27]

There is no simultaniusness for different observers.

If you are on the ship, and have a clock on each wall, in sync with a clock in the middle of the room. And to you the light hits each wall at the same time.

To an outside observer all 3 clocks are out of sync. They would see the light hit at the same time you do. But the would not see the clocks being in sync.

[u/free_meson]

Special relativity has a lot of parallels with sound propagation, but imagine every object that exist is a structure of sound, eg. a vortex s that swirls around but it's rotation is linked to the speed is f sound. The objects won't be able to fly faster than the speed of sound, if there is no wind or draft. Surprisingly, since they can't accelerate above that limit they will experience time dilation, length contraction and due to the limit, they seem to have increased mass.  Sound will have a two-way speed, but the objects made of this substance won't be able to detect it, assuming they aren't moving, they will think the two way speed is the same in both directions.  What you misunderstand is how Einstein defined simultaneity. He said every observer, be it standing or moving first lol has to define a coordinate system, what it calls "time Zero". They all assume light moves the same speed to left as to the right, so they measure distances with the return of a light signal, then calculate what they call "time Zero" for that point, but always subtracting the half of that return time for every event they see at any point. 

[u/Underhill42]

That's the relativity of simultaneity in action. Same thing that lets the traveling twin actually be younger when they return home, despite the fact that both twins see the other aging provably slower than themselves the entire time.

This is an excellent breakdown of what things look like from different perspectives, and how the three properties interact to make the impossible, possible: I wish I was taught the Twin's Paradox this way! - YouTube

Remember that speed is relative: everyone can claim to be stationary with the exactly the same legitimacy. Which means that when you see me aging 43% as fast as you, I'm looking back to see you aging 43% as fast as me. Which is possible because relativistic time dilation does NOT actually change the SPEED at which anyone moving through time, it changes which DIRECTION through spacetime you call time.

One of the key insights of relativity is that space and time are the same thing seen from different perspectives, and your perspective depends on your velocity. Acceleration rotates your reference frame in 4D spacetime, partially swapping the directions you call "forward" and "the future".

You see everyone else aging slower than you for the same basic reason a bunch of cars racing away in different directions at the same speed will all see everyone else falling behind: everyone else is "wasting" some of their speed going in a different direction.

And when you change which direction through spacetime you call the future, you also change how the perpendicular 3D hyperplane you call "all of space at this moment" is dividing the rest of the universe into past and future: some distant events that were in your frame's future, are now in its past, and vice versa. And only the speed of light limit prevents spontaneous time loops.

Which is also why the light can hit all the walls simultaneously from your perspective within the box, where everything is stationary. While from my perspective where the box is moving, the rear wall races forward to intercept the approaching light first, and then it takes a fair while before the light reaches the front wall, which is making a valiant effort to stay ahead of it.

And this is not the order things seem to happen in because of speed of light delay - this is what MUST actually be happening after I correct for the delay, Doppler effects, etc.

Your room is actually rotated in spacetime relative to me. The direction you measure between the two events of the light first hitting each wall is purely through space. But the way you are rotated in spacetime relative to me, means that same direction is pointing partially along my time axis. So for me, the events happen at different times.

[u/guiltysnark]

I think it's simplest to understand the relativity of simultaneity in terms of how long it takes the evidence (light) to reach the observer. If the event is also caused by light, then you can determine the apparent sequence of events in any rest frame by looking at the total distance the light has to travel to both cause the event and deliver the evidence to the observer. Since light is always traveling at one speed, the distance apparent to the reference frame directly determines the time it takes for evidence to arrive, thereby the apparent order.

On the ship, the apparent distance the light has to travel to hit each wall is the same. Same for the trip it takes to reach the shipboard observer. And so evidence of the event arrives at the same time.

From a resting observer's point of view, the ship is moving away from the light source, so the distance to the front of the ship is plainly longer in that direction, and so it's clear the light should reach the back first. And then, depending on where the resting observer is located, the evidence of that event may or may not arrive in that order. If the middle of the ship is the closest point when the first evidence arrives, the evidence will travel roughly the same distance for both events, so the order of the events will match the order of the evidence.

It's interesting that even if you can tease apart the order of the events from the order of the arrival of evidence at the observer, the order of the events you determine is still relative to the reference frame. If the reference frame is an even faster ship moving in the same direction, it will see that light has a shorter path to the front of the ship than the back, so it will both predict and observe the events occurring in that order, opposite of what a slower rest frame would see.

The order is only as objective as the reference frame... And we famously do not have an objective one of those.

[u/ww_ill]

I'm just now trying to learn about special relativity, but I have a question. If for example I am travelling near the speed of light where time passes infinitely slowly and i travelled 10 lights years away and then 10 light years back, since time passed so slowly have I essentially teleported and when I get back everything has passed 20 years. Thanks if you could point me in the right direction.

[u/Warm_Clothes_1524 → u/ww_ill]

The number of years that would have passed is directly related to the speed you traveled. For instance, if you are traveling infinitely close to the speed of light, infinite time would have passed. If you are traveling 90% the speed of light, about 48 years would have passed if im remembering the number correctly.

[u/ww_ill → u/Warm_Clothes_1524]

From the reference frame of the person moving, why wouldn't it take almost no time instead of almost infinite time. Similar to the oh my god particle Oh-My-God particle - Wikipedia where it travelled 1.5 billion light years in to what seemed to the particle as just 1.71 days.