I Relativity's "time dilation" or clock accuracy alteration

[Crowxe]

Mr. Dale , i can't understand exactly, and it's not your fault , it's me with my scientific degree just high school physics education 26 years ago . but since i was 10 years old i heard about time dilation and accepted it for 34 years until i watched the light clock experiment, it made me reject what i believed . if you explain to me in language that i can't understand then i won't argue and just take your word for granted but i can understand the light clock experiment and i can argue with it (not argue with the relativity theory itself) . anyway thanks to the link you gave me, it doesn't only have the Muons measure but the Doppler experiment too along with others but those two were enough . so i believe in the relativity and apologies to Ernestine for thinking he's reckless . my only problems are :
1. the light clock is an experiment that is loosely designed (maybe it was explained wrong, so i hope you can provide me with link that you approve)
2. there's chaos of not only point of views but also understanding relativity, and that's even clear here if you read the comments

Ps: is there any existing/ongoing experiment that ends the argument of our actual speed and direction of movement

 

[Herman Trivilino]

i'm getting more confused than when i first asked my question (although i found the answer in the Muons)

I think your misunderstanding is in the way you are thinking about moving clocks. When you move with them they behave the same as they do when you're at rest with them. When they're in motion relative to you they behave differently in your rest frame.

A muon's lifetime, as measured in the muon's rest frame, is not increased simply because it's moving relative to you. But in your rest frame its lifetime is increased.

If you are misled by the light clock analysis you'd do well to understand why. The fault does not lie with the light clock.

 

[PeterDonis]

is there any existing/ongoing experiment that ends the argument of our actual speed and direction of movement

How would you test this experimentally?

 

[Crowxe]

I think your misunderstanding is in the way you are thinking about moving clocks. When you move with them they behave the same as they do when you're at rest with them. When they're in motion relative to you they behave differently in your rest frame.

A muon's lifetime, as measured in the muon's rest frame, is not increased simply because it's moving relative to you. But in your rest frame its lifetime is increased.

If you are misled by the light clock analysis you'd do well to understand why. The fault does not lie with the light clock.

i think I'm getting closer and i understand that my clock will always tick at the same intervals that mind is used to. but still have couple of basic questions to clear misconception in my mind caused by the light clock .

in the light clock, the experiment display a change in the light beam direction leaning towards the direction of movement instead of staying perpendicular to the mirror. There's a difference between the track it should take to meet the mirror and the actual track it should take according to light behavior unless the experiment states that light will behave as ping pong ball bouncing up and down between train's floor and sealing because it gained horizontal speed from the train. to my understanding, the light shouldn't behave like that and it doesn't gain speed from its source's speed

 

[PeroK]

i think I'm getting closer and i understand that my clock will always tick at the same intervals that mind is used to. but still have couple of basic questions to clear misconception in my mind caused by the light clock .

in the light clock, the experiment display a change in the light beam direction leaning towards the direction of movement instead of staying perpendicular to the mirror. There's a difference between the track it should take to meet the mirror and the actual track it should take according to light behavior unless the experiment states that light will behave as ping pong ball bouncing up and down between train's floor and sealing because it gained horizontal speed from the train. to my understanding, the light shouldn't behave like that and it doesn't gain speed from its source's speed

It's interesting that this question seems to come up a lot. The beam of light can only do one thing. If it bounces up and down between the mirrors, it bounces up and down between the mirrors. That is a physical fact. If you are at rest with respect to the mirrors, then you see that as vertical motion. But, if you moving with respect to the mirrors, you see that as a zig-zag motion.

The light beam can't be vertical in your frame and vertical in its rest frame at the same time.

 

[PeroK]

PS The key to why the constant speed of light, independent of the motion of the source leads to SR is contained in this fact. If the source is moving and you see the light go at a diagonal, then the vertical component of its velocity must be less than the speed of light. But, for someone at rest wrt to light clock, the vertical component must be the full speed of light.

The two observers will, therefore, measure different values for the vertical speed of the beam - and that leads to time dilation.

In contrast, if the speed of light depended on its source, like a ball being thrown up, the ball would be moving faster to the observer watching the train go by. In fact, in this case, if you don't throw the ball, the observer with the ball measures its speed to be 0, while the observer watching the ball go past measures the speed of the ball as the same as that of the train.

 

[Crowxe]

How would you test this experimentally?

i was asking if there's any but since you asked then i'll share my naive idea if the following are true facts
1. if light speed is constant in a medium regardless to the source speed
2. if that speed varies between one medium and a nother

so it could be done as follows:

if light speed in vacuum is 300,000 km/s and is 151,000 km/s in another medium . we can emit light through both mediums at same moment and have two detectors at same distance say 300,000 km away from the source (that distance is measured by time from our own perception , so I'm still within relativity point of view).

if we measure the time difference and then rotate the whole setting 180 degrees in x plan or 90 degrees in y plan , then maybe get different time shift (because the experiment is moving but we just don't know to what direction).

i did the calculation for that example based on the system at absolute rest then at speed 150,000 km/s. first time shift was 0.5 seconds and the second shift was 148 seconds (without taking time dilation in consideration) or 172 seconds with time dilation but i think we should count on our perception at that speed and say 148 seconds

 

[Crowxe]

It's interesting that this question seems to come up a lot. The beam of light can only do one thing. If it bounces up and down between the mirrors, it bounces up and down between the mirrors. That is a physical fact. If you are at rest with respect to the mirrors, then you see that as vertical motion. But, if you moving with respect to the mirrors, you see that as a zig-zag motion.

The light beam can't be vertical in your frame and vertical in its rest frame at the same time.

i understand what you're saying, the two observers , time dilation and constant speed of light but i need one point addressed . the ping pong ball bouncing in a train adopts the train horizontal velocity , that's why it's vertical to the man on board and diagonal to the observer. but light aimed vertically will continue travel vertically (every segment of it travel vertically but the over all path should be diagonally backward in respect to the moving ship) we can't add horizontal or any speed to the light by moving the source

 

[Crowxe]

i must declare that i had doubts in time dilation but now i fully understand it and it even makes sense . the continuation of this thread is only related to the light behavior in the light clock

 

[PeroK]

i understand what you're saying, the two observers , time dilation and constant speed of light but i need one point addressed . the ping pong ball bouncing in a train adopts the train horizontal velocity , that's why it's vertical to the man on board and diagonal to the observer. but light aimed vertically will continue travel vertically (every segment of it travel vertically but the over all path should be diagonally backward in respect to the moving ship) we can't add horizontal or any speed to the light by moving the source

In that case, the light would have to go in two different (physical) directions at the same time. Imagine the man on board aims the light at a target. It either hits the target or it doesn't. It can't hit the target according to one observer and miss according to another. The light must follow the same physical path in both cases. You could define the path to be a series of hoops that the light passes through. It either passes through each physical hoop or it doesn't.

The "direction" of the motion of the light must be different in the two different frames, as the definition of "vertical" motion depends on the frame.

Forget the source for a moment. Just imagine a beam of light and two observers, standing together. Let's say the beam is moving vertically away from the two. One observer starts to move to the right. Now he is in a different frame and, as he moves, the light no longer moves vertically to him. From his new reference frame it is moving vertically and to the left.

The second observer still sees the light take the same physical path - and pass through the same physical hoops. But, now, to him the hoops are moving and the path is diagonal.

Finally, you have made an interesting and quite common misinterpretation of the constancy of the speed of light. That somehow the light can be "vertical" to two different observers, whose definition of vertical motion is different! Even light can't do that.

 

[stevendaryl]

in the light clock, the experiment display a change in the light beam direction leaning towards the direction of movement instead of staying perpendicular to the mirror. There's a difference between the track it should take to meet the mirror and the actual track it should take according to light behavior unless the experiment states that light will behave as ping pong ball bouncing up and down between train's floor and sealing because it gained horizontal speed from the train. to my understanding, the light shouldn't behave like that and it doesn't gain speed from its source's speed

If you're on a train moving at a constant speed, and you start bouncing a basketball up and down, then to you, it is traveling a path that is perpendicular to the floor. To someone outside the train, the basketball travels a diagonal path. Light is no different in this respect. So the conclusion is that the angle that the bouncing object follows is relative to the rest frame of the observer. Special Relativity is no different from pre-relativistic physics in this regard.

I understand the intuition: In the light clock, when the clock is moving, it appears that the light must be "aimed" ahead of the mirror. But the same thing is true of the person bouncing a basketball inside a moving train: From the perspective of someone at rest looking at the train move past, it seems that the person with the basketball must "aim" it slightly ahead of the point on the floor where he wants it to hit. But the person aboard the train isn't doing anything differently than if the train were at rest.

 

[Crowxe]

In that case, the light would have to go in two different (physical) directions at the same time. Imagine the man on board aims the light at a target. It either hits the target or it doesn't. It can't hit the target according to one observer and miss according to another. The light must follow the same physical path in both cases. You could define the path to be a series of hoops that the light passes through. It either passes through each physical hoop or it doesn't.

The "direction" of the motion of the light must be different in the two different frames, as the definition of "vertical" motion depends on the frame.

Forget the source for a moment. Just imagine a beam of light and two observers, standing together. Let's say the beam is moving vertically away from the two. One observer starts to move to the right. Now he is in a different frame and, as he moves, the light no longer moves vertically to him. From his new reference frame it is moving vertically and to the left.

The second observer still sees the light take the same physical path - and pass through the same physical hoops. But, now, to him the hoops are moving and the path is diagonal.

Finally, you have made an interesting and quite common misinterpretation of the constancy of the speed of light. That somehow the light can be "vertical" to two different observers, whose definition of vertical motion is different! Even light can't do that.

thanks for the effort and explaining , it cleared a lot of the confusing things to me . if you still have energy left , i would like to tweak a bit the example that you put here.

lets say it's one observer with light beaming vertically to the plan he's standing on and then him along with the light source gained speed horizontally , he and the light source gained horizontal speed but did the light gain that horizontal speed?

 

[Crowxe]

If you're on a train moving at a constant speed, and you start bouncing a basketball up and down, then to you, it is traveling a path that is perpendicular to the floor. To someone outside the train, the basketball travels a diagonal path. Light is no different in this respect. So the conclusion is that the angle that the bouncing object follows is relative to the rest frame of the observer. Special Relativity is no different from pre-relativistic physics in this regard.

I understand the intuition: In the light clock, when the clock is moving, it appears that the light must be "aimed" ahead of the mirror. But the same thing is true of the person bouncing a basketball inside a moving train: From the perspective of someone at rest looking at the train move past, it seems that the person with the basketball must "aim" it slightly ahead of the point on the floor where he wants it to hit. But the person aboard the train isn't doing anything differently than if the train were at rest.

there's one significant difference comparing the bouncing ball and the bouncing beam regarding the direction (according to the person in the same reference frame) . the ball can gain the train's horizontal speed but light can't gain speed

 

[stevendaryl]

there's one significant difference comparing the bouncing ball and the bouncing beam regarding the direction (according to the person in the same reference frame) . the ball can gain the train's horizontal speed but light can't gain speed

Well, there is the speed in the horizontal direction, and there is the speed in the vertical direction. The total speed (which is defined by: (total speed)² = (horizontal speed)² + (vertical speed)²) is constant, but light can change its horizontal speed.

 

[Crowxe]

Well, there is the speed in the horizontal direction, and there is the speed in the vertical direction. The total speed (which is defined by: (total speed)² = (horizontal speed)² + (vertical speed)²) is constant, but light can change its horizontal speed.

thats a simple language i can understand , so the horizontal speed is through aiming the beam forward or gained by the horizontal source movement ? (i believe in both cases time dilation will take place and relativity should still hold)

 

[PeroK]

thanks for the effort and explaining , it cleared a lot of the confusing things to me . if you still have energy left , i would like to tweak a bit the example that you put here.

lets say it's one observer with light beaming vertically to the plan he's standing on and then him along with the light source gained speed horizontally , he and the light source gained horizontal speed but did the light gain that horizontal speed?

Yes, because it's all about reference frames. If the light (or anything) is moving vertically in his frame of reference, then it must be moving vertically and horizontally in another frame of reference in which he and the light source are moving horizontally. That's essentially a physical/geometric reality - and, in fact, has to do with all physics, not just relativity.

It's better not to think about the light source or light "gaining" horizontal speed, but to see that it has a horizontal component to its motion in one frame. If its horizontal speed in frame A is 0, then in a frame B moving horizontally at speed $v$ with respect to frame A, its horizontal speed must be $v$.

This was standard, classical physics from Netwon's time at least. In classical physics, you can then take the vertical speed $w$, say. which is the same in both frames and then:

The speed of the object is $w$ in frame A.

The speed of the object is $\sqrt{w^2 + v^2}$ in frame B.

However, there was experimental evidence that if the "object" was a beam of light, then this did not apply. In particular:

The speed of the light is $c$ in frame A.

The speed of the light is $c$ in frame B. It is not $\sqrt{c^2 + v^2}$.

This was a terrible puzzle for classical physics. By using this experimental fact and his light-clock thought experiment, Einstein showed that one explanation was that "time itself was suspect" and that with respect to one frame, time in the other frame is dilated by the factor of $\frac{c}{\sqrt{c^2 + v^2}}$.

This time dilation explains why, even thought the observer in frame A sees the light moving only vertically and B sees the light moving vertically and horizontally, they measure the same speed $c$.

There was never any thought that somehow the light was moving vertically in both frames.

 

[PeroK]

there's one significant difference comparing the bouncing ball and the bouncing beam regarding the direction (according to the person in the same reference frame) . the ball can gain the train's horizontal speed but light can't gain speed

It can't increase its speed, but its speed will and must have a horizontal component in some frames! You need to give up this idea that light can only travel vertically!

 

[Crowxe]

Yes, because it's all about reference frames. If the light (or anything) is moving vertically in his frame of reference, then it must be moving vertically and horizontally in another frame of reference in which he and the light source are moving horizontally. That's essentially a physical/geometric reality - and, in fact, has to do with all physics, not just relativity.

It's better not to think about the light source or light "gaining" horizontal speed, but to see that it has a horizontal component to its motion in one frame. If its horizontal speed in frame A is 0, then in a frame B moving horizontally at speed $v$ with respect to frame A, its horizontal speed must be $v$.

This was standard, classical physics from Netwon's time at least. In classical physics, you can then take the vertical speed $w$, say. which is the same in both frames and then:

The speed of the object is $w$ in frame A.

The speed of the object is $\sqrt{w^2 + v^2}$ in frame B.

However, there was experimental evidence that if the "object" was a beam of light, then this did not apply. In particular:

The speed of the light is $c$ in frame A.

The speed of the light is $c$ in frame B. It is not $\sqrt{c^2 + v^2}$.

This was a terrible puzzle for classical physics. By using this experimental fact and his light-clock thought experiment, Einstein showed that one explanation was that "time itself was suspect" and that with respect to one frame, time in the other frame is dilated by the factor of $\frac{c}{\sqrt{c^2 + v^2}}$.

This time dilation explains why, even thought the observer in frame A sees the light moving only vertically and B sees the light moving vertically and horizontally, they measure the same speed $c$.

There was never any thought that somehow the light was moving vertically in both frames.

thanks a lot , you've been great help , i think I'm confusion free for now

 

[stevendaryl]

thats a simple language i can understand , so the horizontal speed is through aiming the beam forward or gained by the horizontal source movement ? (i believe in both cases time dilation will take place and relativity should still hold)

A mirror that is oriented vertically cannot change the light's horizontal speed. So if the light is initially traveling vertically, it'll keep traveling vertically. If it is initially traveling at a diagonal, it will keep traveling diagonally. After bouncing off the mirror, the only change is to the vertical velocity: that switches direction.

So the mirror doesn't need to "aim" for where the light should go.

Now, you could ask the question of how the light gets started traveling diagonally, in the first place. Although it's maybe not intuitive, the fact is that if the person on the train takes an ordinary flashlight, and aims it straight up, the light coming out of the flashlight will travel "diagonally" as seen from someone outside the train.

 

[Crowxe]

A mirror that is oriented vertically cannot change the light's horizontal speed. So if the light is initially traveling vertically, it'll keep traveling vertically. If it is initially traveling at a diagonal, it will keep traveling diagonally. After bouncing off the mirror, the only change is to the vertical velocity: that switches direction.

So the mirror doesn't need to "aim" for where the light should go.

Now, you could ask the question of how the light gets started traveling diagonally, in the first place. Although it's maybe not intuitive, the fact is that if the person on the train takes an ordinary flashlight, and aims it straight up, the light coming out of the flashlight will travel "diagonally" as seen from someone outside the train.

i guess the confusion is almost gone but i'll just state it again in case it wasnt clear. i wasnt talking about 2 farme references , just the one on the train and my prediction was the light beam would appear diagonally backward to him

 

[Dale]

1. the light clock is an experiment that is loosely designed (maybe it was explained wrong, so i hope you can provide me with link that you approve)

I don't have a particular favorite light clock presentation. It is nothing more than a teaching aid, so if it doesn't help you, then I would move on to something else. Personally, learning about four-vectors was what made relativity "click" for me, not any of the usual thought experiments.

there's chaos of not only point of views but also understanding relativity, and that's even clear here if you read the comments

Did you ever read the poem about the descriptions of the elephant? All of the descriptions you have received are correct, they each correctly describe part of the relativity "elephant". It is not "chaos" it is a bunch of pieces of a big picture that you currently haven't seen. For a full and coherent description of relativity you will need a textbook.

is there any existing/ongoing experiment that ends the argument of our actual speed and direction of movement

The experiments are pretty conclusive that there is no such thing as an "actual speed", only "relative speed".

 

[PAllen]

i guess the confusion is almost gone but i'll just state it again in case it wasnt clear. i wasnt talking about 2 farme references , just the one on the train and my prediction was the light beam would appear diagonally backward to him

And this would be a counterfactual prediction. Any simple optics experiment disproves this because the Earth's motion in one season relative to its motion at a different season is substantial, thus one or the other should see your proposed effect. This is exactly what the many variations of the Michaelson-Morely experiment refute.

 

[stevendaryl]

i guess the confusion is almost gone but i'll just state it again in case it wasnt clear. i wasnt talking about 2 farme references , just the one on the train and my prediction was the light beam would appear diagonally backward to him

Well, that's not the way that light works. If you shine a flashlight, the light comes out traveling straight away from the flashlight, in the frame in which the flashlight is at rest (the frame of the train). (Actually, the light coming from a flashlight is spread out in all directions, so maybe we should talk about a laser pointer, instead of a flashlight.)

 

[Vitro]

@Crowxe, I think you are still holding on, whether consciously or subconsciously, to a notion of some absolute universal "rest" frame relative to which everything has an actual speed (in an absolute sense), and probably trying to figure out ways you can detect or measure this speed, like what's the actual speed of the Earth through space.

Many physicists over many centuries have wondered and tried the same and, at least for mechanics, they have realized since Galileo that there was no such thing, or at least mechanics didn't offer any means for detecting such absolute speed or rest. The laws of mechanics obeyed the Principle of Relativity, they were the same in every inertial reference frame.

But there was one thing that wasn't covered by Galilean relativity and which could potentialy be used to measure this absolute speed, light (electromagnetism), thought to be carried by a medium (luminiferous aether) which determined its speed. Many experiments were performed, first to mesure the speed of light with ever increasing accuracy and then to try to measure the speed of the Earth through this hypothetical aether by detecting variations in the speed of light measured at different times of the day or year and in different directions as the Earth rotated on its axis and orbited the Sun. But the speed of light always turned out to be the same no matter what, all attempts to detect or measure speed relative to the aether were unsuccessful.

Einstein realized that the Principle of Relativity must also apply to the laws of electromagnetism extending the PR to say that all laws of physics are the same in every inertial frame, which also implied that the speed of light must be the same in every inertial frame (the two postulates of Special Relativity). Basically what this means is that if you are in a closed box floating somewhere in empty space (and you cannot see outside to notice stars changing position) there is no experiment whatsoever that you could perform inside the box to determine its absolute speed, so the notion simply doesn't apply. And even if you do look outside and see the stars moving that doesn't mean that the box is moving, or that the stars are moving (in any absolute sense), it just means that they are moving relative to each other. It makes no sense to ask "but which one is really moving?". The answer would be "from who's perspective?". From a star's perspective the box is moving, from the box's perspective the star is moving, from some other perspective both the star and the box are moving, and all those perspectives are equally valid.

As a first step towards understanding relativity you must give up any notion of absolute rest or motion, speed is purely relative, anything can be considered moving or at rest simply by changing one's point of view or perspective.

Regarding the speed of light being constant, you must differentiate between two notions: speed and velocity. Velocity is a vector, it has a direction. Speed represents the magnitude of the velocity vector, and is just a value (has no direction). Speed is the one that's constant and cannot be changed, the velocity is observer dependent. The direction of the same pulse of light can be different for different observers, no physical aiming of the source in different directions is necessary for this.

 

[Crowxe]

@Crowxe, I think you are still holding on, whether consciously or subconsciously, to a notion of some absolute universal "rest" frame relative to which everything has an actual speed (in an absolute sense), and probably trying to figure out ways you can detect or measure this speed, like what's the actual speed of the Earth through space.

Many physicists over many centuries have wondered and tried the same and, at least for mechanics, they have realized since Galileo that there was no such thing, or at least mechanics didn't offer any means for detecting such absolute speed or rest. The laws of mechanics obeyed the Principle of Relativity, they were the same in every inertial reference frame.

But there was one thing that wasn't covered by Galilean relativity and which could potentialy be used to measure this absolute speed, light (electromagnetism), thought to be carried by a medium (luminiferous aether) which determined its speed. Many experiments were performed, first to mesure the speed of light with ever increasing accuracy and then to try to measure the speed of the Earth through this hypothetical aether by detecting variations in the speed of light measured at different times of the day or year and in different directions as the Earth rotated on its axis and orbited the Sun. But the speed of light always turned out to be the same no matter what, all attempts to detect or measure speed relative to the aether were unsuccessful.

Einstein realized that the Principle of Relativity must also apply to the laws of electromagnetism extending the PR to say that all laws of physics are the same in every inertial frame, which also implied that the speed of light must be the same in every inertial frame (the two postulates of Special Relativity). Basically what this means is that if you are in a closed box floating somewhere in empty space (and you cannot see outside to notice stars changing position) there is no experiment whatsoever that you could perform inside the box to determine its absolute speed, so the notion simply doesn't apply. And even if you do look outside and see the stars moving that doesn't mean that the box is moving, or that the stars are moving (in any absolute sense), it just means that they are moving relative to each other. It makes no sense to ask "but which one is really moving?". The answer would be "from who's perspective?". From a star's perspective the box is moving, from the box's perspective the star is moving, from some other perspective both the star and the box are moving, and all those perspectives are equally valid.

As a first step towards understanding relativity you must give up any notion of absolute rest or motion, speed is purely relative, anything can be considered moving or at rest simply by changing one's point of view or perspective.

Regarding the speed of light being constant, you must differentiate between two notions: speed and velocity. Velocity is a vector, it has a direction. Speed represents the magnitude of the velocity vector, and is just a value (has no direction). Speed is the one that's constant and cannot be changed, the velocity is observer dependent. The direction of the same pulse of light can be different for different observers, no physical aiming of the source in different directions is necessary for this.

i've been talking 2 points lately :
1. the light direction / path if beamed perpendicularly to the platform line of motion and that is from the observer in same frame reference not another observer stationary nor any other reference frame.
2. we all presume things and examples to reach conclusions , so i think it's valid to assume we are stationary in an example or presumed test just to simplify it and then later apply it to our situation of not knowing what is our actual speed. i think that question is valid even if it can't be answered until now

 

[PAllen]

i've been talking 2 points lately :
1. the light direction / path if beamed perpendicularly to the platform line of motion and that is from the observer in same frame reference not another observer stationary nor any other reference frame.
2. we all presume things and examples to reach conclusions , so i think it's valid to assume we are stationary in an example or presumed test just to simplify it and then later apply it to our situation of not knowing what is our actual speed. i think that question is valid even if it can't be answered until now

This exact question has been answered numerous times in this thread. As I mentioned, you could test it yourself with any beam source you like. Just do the experiment in winter and also in summer. Further, the experiment has been done to great precision for many decades because many types of precision optical devices would need continual adjustment if your hypothesis were true. In fact your garage door opener safety beam would need regular adjustment due to Earth's changing state of motion, if your hypothesis were true. This is, in fact, a moderately precise implementation of your question.

 

[Herman Trivilino]

we all presume things and examples to reach conclusions , so i think it's valid to assume we are stationary in an example or presumed test just to simplify it and then later apply it to our situation of not knowing what is our actual speed. i think that question is valid even if it can't be answered until now

There is no experiment that has ever been done, or observation ever recorded, that distinguishes between a state of rest and a state of steady motion. Any distinction that you make is therefore unsupported.

The present state of physics includes the assumption that no such distinction can be made.

there's one significant difference comparing the bouncing ball and the bouncing beam regarding the direction (according to the person in the same reference frame) . the ball can gain the train's horizontal speed but light can't gain speed

The very notion that the ball "gains" the train's horizontal speed implies, to my way of thinking, that the ball's inertia is somehow a property of the ball. It's not. It appears simply because of an observation made in a frame of reference that is in motion relative to the ball.

Likewise, the claim that the train is in motion is just a result of the train being observed from a frame of reference that is not at rest relative to the train.

 

[Dale]

it's valid to assume we are stationary in an example or presumed test ... not knowing what is our actual speed

The reason that it is valid to make the assumption that we are stationary is precisely because there is no such thing as "our actual speed".

 

[Vitro]

As a first step towards understanding relativity you must give up any notion of absolute rest or motion, speed is purely relative, anything can be considered moving or at rest simply by changing one's point of view or perspective.

Except for light and other massless things which always move at $c$, so not really anything.

 

[Drakkith]

Thread locked pending possible moderation.