#### Noa Drake

Hello, i am new here.
I have been studying SR en GR for a while on a hobby level,
and i keep pondering on the following :

Consider the following situation :

A train with a person on it leaves the station.

SR says that while moving with constant velocity, the trainguy cannot tell the difference between him
riding out of the station or the station leaving him, relatively to each other. ok.

It is also understood that no experiment can be used to distinguish between these two possibilities.
By extention, no current technology can make the distiction. ok.

I am trainguy (and i also drive the train), and i have to figure it out :

I know that i had to startup the train from 0 km/h to start leaving the station.
For this i had to accellarate for a while first, and then gradually lower the power again to approach a constant speed, until indeed i have reached a constant speed. then maintaining the same level of power.

How can i now distinguish between the station leaving me and the train, or me and the train leaving the station ?
('Now' = while going at constant speed, after the accellaration has terminated.)

> I simply consult my memory , and if i don't suffer any rare medical condition such as instant Altzheimer
from the moment on where accellaration turned into constant speed,

then i can safely conclude that :

-It was definately me starting up the train and performing the necessary handlings to get to a constant speed.
-It was definately not the station that was 'started up' in any way.

-And so it was definately me and the train moving away from the station,
the station that was set in motion in any way.

I don't experience it, i know it.

>>>>

So me and the train are moving away from the station, not vice versa.
I know this by consulting my memory ,
although i may not experience the difference, or detect the difference with a device.

So i simply know the situation is not symmetric, i doesn't matter anymore wether or not i can distinguish between the two by experience, observation, or device detection.

Is this a valid thought experiment ?

Related Special and General Relativity News on Phys.org

#### phinds

Gold Member
Accelerating frames are not inertial. By inserting a non-inertial frame and making it part of the experiment, you have left SR. It is well understood that acceleration is NOT relative and can be determined, thus your experiment adds nothing to SR/GR.

EDIT: by the way, welcome to the forum

#### DiracPool

SR says that while moving with constant velocity, the trainguy cannot tell the difference between him
riding out of the station or the station leaving him, relatively to each other. ok...

I am trainguy (and i also drive the train), and i have to figure it out :

I know that i had to startup the train from 0 km/h to start leaving the station.
For this i had to accellarate for a while first, and then gradually lower the power again to approach a constant speed, until indeed i have reached a constant speed. then maintaining the same level of power.
You start off OK by talking about constant velocity, and then all of a sudden you're accelerating from 0 to whatever. Not only that, but you're driving the car! How are you supposed be objective when you're driving the car? Of course you're going to know that it's you leaving the station.

So, as phinds pointed out, the thought experiment ends right there. The "train" analogy/example goes back to the early 20th century mentality before we started using rocket ships as the relative vehicles, simply because at that time everyone was familiar with trains. Even if you weren't driving the train, you'd have to take into account the psychophysiological effects on your vestibular semicircular canals of the influences of gravitation, inertial acceleration of the train car, and friction of the tracks into your thought experiment. That's why most of the SR thought experiements are done in intergalactic space these days.

#### Noa Drake

@ phinds and DiracPool

Ok, i understand that accellaration is not relative and can be determined, whereas moving with constant speed in the above context is not.

But SR does not stipulate how this constant speed has to be achieved, it does not stipulate that the constant motion cannot be predecessed by an accellaration.

Hence why would the above experiment be unusable ?

If the original SR thought experiment limits the picture to the constant speed, then it has left out an important part of reality : You can never obtain any constant speed without prior accellaration.
Hence predictions made from the limited experiment , must stay confined to this limited thought experiment situation.

In other words, logically speaking, the predictions cannot consist of extrapolations to reality.

No ?

#### DiracPool

No.

But SR does not stipulate how this constant speed has to be achieved, it does not stipulate that the constant motion cannot be predecessed by an accellaration.
Exactly, and it makes no pretensions otherwise. That's why it's called the "special" theory of relativity.

Hence why would the above experiment be unusable ?
It would be unusable mostly because your thesis that, "I simply consult my memory...", etc. is not a factor that plays into the equation. SR is not influenced by your memory.

In other words, logically speaking, the predictions cannot consist of extrapolations to reality.
I don't know what that means.

#### Kyle.Nemeth

I understand why you are confused. It seems like this is a matter of interpreting correctly what SR is "trying to say."

You are absolutely correct when you say that since you refer to your own memory and you do not suffer from any mental illnesses, you can conclude that it was indeed you and the train that left the train station and not the station itself (of course, you make this conclusion once you've finally reached a constant speed at which point you are in a valid inertial frame). This is true!

However, SR says that you could also claim that the station is moving AWAY from you. This claim is also true and completely valid.

Why is the latter true also? Because Albert Einstein postulates in SR that the laws of physics are the SAME in ALL inertial frames of reference. Since you are moving away from the station at a constant speed (after you have accelerated to that speed), yes you are in a valid inertial frame of reference. Now, since you can't feel any type of acceleration or changes in your motion (the reason why constant velocity is required for an inertial frame), you could also imagine that it is the train that is stationary and that the train station is moving away from YOU at that same constant velocity (since you can't feel any type of acceleration). Since the station is also moving away from you at a constant velocity, this is ALSO an inertial frame of reference for you. And since the laws of physics are the same in all inertial reference frames, this must be a completely valid perspective.

So it is not that SR is trying to tell you that you aren't moving away from the train station. You ARE moving away from the train station! But SR is telling you that it is ALSO true that the station is moving away from you.

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#### PhysicistMike

A train with a person on it leaves the station.

SR says that while moving with constant velocity, the trainguy cannot tell the difference between him
riding out of the station or the station leaving him, relatively to each other. ok.
While even Einstein thought that was true when he wrote the special theory of relativity (SR). How SR applies to inertial frames and thus to situations in the absence of gravity. I tried this myself and found it to be true. What happens is that there is a cross term in the metric of the form dtdx which causes particles falling down to be deflected. Therefore you can tell which is moving. However if instead of using train stations we used space stations and thus inertial frames then we're back to SR again and what you said is true again.

#### ghwellsjr

Gold Member
Hello, i am new here.
I have been studying SR en GR for a while on a hobby level,
and i keep pondering on the following :

Consider the following situation :

A train with a person on it leaves the station.

SR says that while moving with constant velocity, the trainguy cannot tell the difference between him
riding out of the station or the station leaving him, relatively to each other. ok.

It is also understood that no experiment can be used to distinguish between these two possibilities.
By extention, no current technology can make the distiction. ok.

I am trainguy (and i also drive the train), and i have to figure it out :

I know that i had to startup the train from 0 km/h to start leaving the station.
For this i had to accellarate for a while first, and then gradually lower the power again to approach a constant speed, until indeed i have reached a constant speed. then maintaining the same level of power.

How can i now distinguish between the station leaving me and the train, or me and the train leaving the station ?
('Now' = while going at constant speed, after the accellaration has terminated.)

> I simply consult my memory , and if i don't suffer any rare medical condition such as instant Altzheimer
from the moment on where accellaration turned into constant speed,

then i can safely conclude that :

-It was definately me starting up the train and performing the necessary handlings to get to a constant speed.
-It was definately not the station that was 'started up' in any way.

-And so it was definately me and the train moving away from the station,
the station that was set in motion in any way.

I don't experience it, i know it.

>>>>

So me and the train are moving away from the station, not vice versa.
I know this by consulting my memory ,
although i may not experience the difference, or detect the difference with a device.

So i simply know the situation is not symmetric, i doesn't matter anymore wether or not i can distinguish between the two by experience, observation, or device detection.

Is this a valid thought experiment ?
You are considering two Inertial Reference Frames (IRF's):

1) The rest frame of the station in which the trainguy starts out at rest.

2) The rest frame of the trainguy after he accelerates.

Both of these IRF's are equivalent (as well as a million others) but you have to include the same things in all of them.

In IRF 1, the station remains at rest while the trainguy accelerates to a final velocity.

In IRF 2, both the station and the trainguy start off traveling at some negative speed but the trainguy decelerates to a stop while the station continues moving.

#### nearlynothing

Hello, i am new here.
I have been studying SR en GR for a while on a hobby level,
and i keep pondering on the following :

Consider the following situation :

A train with a person on it leaves the station.

SR says that while moving with constant velocity, the trainguy cannot tell the difference between him
riding out of the station or the station leaving him, relatively to each other. ok.

It is also understood that no experiment can be used to distinguish between these two possibilities.
By extention, no current technology can make the distiction. ok.

I am trainguy (and i also drive the train), and i have to figure it out :

I know that i had to startup the train from 0 km/h to start leaving the station.
For this i had to accellarate for a while first, and then gradually lower the power again to approach a constant speed, until indeed i have reached a constant speed. then maintaining the same level of power.

How can i now distinguish between the station leaving me and the train, or me and the train leaving the station ?
('Now' = while going at constant speed, after the accellaration has terminated.)

> I simply consult my memory , and if i don't suffer any rare medical condition such as instant Altzheimer
from the moment on where accellaration turned into constant speed,

then i can safely conclude that :

-It was definately me starting up the train and performing the necessary handlings to get to a constant speed.
-It was definately not the station that was 'started up' in any way.

-And so it was definately me and the train moving away from the station,
the station that was set in motion in any way.

I don't experience it, i know it.

>>>>

So me and the train are moving away from the station, not vice versa.
I know this by consulting my memory ,
although i may not experience the difference, or detect the difference with a device.

So i simply know the situation is not symmetric, i doesn't matter anymore wether or not i can distinguish between the two by experience, observation, or device detection.

Is this a valid thought experiment ?
You could also conclude that while your engines were accelerating you, you remained stationary in space, and that there was an interaccion deviating you from geodesic motion, while it was the station that failed to remain stationary in space.

So even though you remember you started off the engine yourself you cant tell just which is moving away from which in an absolute manner. These are frame dependent notions.

#### phinds

Gold Member
You could also conclude that while your engines were accelerating you, you remained stationary in space, and that there was an interaccion deviating you from geodesic motion, while it was the station that failed to remain stationary in space.

So even though you remember you started off the engine yourself you cant tell just which is moving away from which in an absolute manner. These are frame dependent notions.
"stationary in space" is a meaningless concept. All motion is relative. "stationary" is a form of motion and is only meaningful when stated as being relative to something. "space" is not something in that sense.

#### phinds

Gold Member
... However if instead of using train stations we used space stations and thus inertial frames then we're back to SR again and what you said is true again.
HUH? What difference does it make if you use train stations or space stations? If one of them accelerates, the passengers/driver/whatever can TELL that they are the ones accelerating. As I have already pointed out, the error in his logic was not in using a train instead of something in space, it was in using something that accelerates and expecting SR to be applicable.

#### nearlynothing

"stationary in space" is a meaningless concept. All motion is relative. "stationary" is a form of motion and is only meaningful when stated as being relative to something. "space" is not something in that sense.
I didnt refer to a coordinate system, but of course there would have to be a coordinate system, either one in which the train is at rest or where the station is at rest.

So my statement would be that they're stationary in the space of one of these frames, defined according to some simultaneity convention.

#### nearlynothing

HUH? What difference does it make if you use train stations or space stations? If one of them accelerates, the passengers/driver/whatever can TELL that they are the ones accelerating. As I have already pointed out, the error in his logic was not in using a train instead of something in space, it was in using something that accelerates and expecting SR to be applicable.
SR is perfectly applicable for accelerated motion.

#### phinds

Gold Member
I didnt refer to a coordinate system, but of course there would have to be a coordinate system, either one in which the train is at rest or where the station is at rest.

So my statement would be that they're stationary in the space of one of these frames, defined according to some simultaneity convention.
Exactly. And if they then move apart there is some acceleration going on, which is my point.

#### phinds

Gold Member
SR is perfectly applicable for accelerated motion.
And does that lead you to the conclusion that the OPs original logic is sound?

#### Noa Drake

@Kyle.Nemeth (post 6) :

I see that you understood what i intended with the thought experiment, thank you .

Then you said this :
"However, SR says that you could also claim that the station is moving AWAY from you. This claim is also true and completely valid.
Why is the latter true also? Because Albert Einstein postulates in SR that the laws of physics are the SAME in ALL inertial frames of reference."

> Using the postulate as a defense against an argument that tries to illustrate that we cannot extrapolate things about THE laws of physics from a very limited thought experiment (were essential parts of reality are not allowed to exist), is not very fair.

You could never obtain the constant speed without at some point in the past having accellarated to some degree.
It is like saying let us imagine an experiment were a guy is hanging in the air, and exclude the rest of reality.
Being that he must have been jumping first, or perhaps have fallen out of a plane etc.
It is cutting a shorter clip from the entire scene.

>What validity does the original SR thought experiment have if you deliberately handicap the observer (trainguy is not allowed to use his memory) and omit essential information ? How could any predictions about the laws of physics in general be correct, when derived from this limited and unreal situation ?

(I understand now that maybe i had better posted this under phylosophy.)

#### nearlynothing

Exactly. And if they then move apart there is some acceleration going on, which is my point.
This acceleration brings nothing new into play, i think maybe you're not getting my point.

The passenger in the train can define a frame in which he is at rest, regardless of his acceleration.
This frame cant be inertial if he is accelerating, but that doesnt matter here.
His acceleration can be measured locally, with accelerometers, so this can be defined in absolute terms, with no reference to coordinates. Now in this frame he sees the station failing to remain stationary, he interprets his own acceleration as a means to remain stationary in that frame.

If looked at from the point of view of someone in the station, this person can also define a frame in which he is at rest, this frame can be inertial. Now he interprets the acceleration of the train as causing a change in velocity of the train in this frame of reference.

Both points of view are valid and so you cant say which is moving in a frame-independent manner even though the passenger would clearly remember the engines being working and accelerating the train.

The only thing you can say absolutely is that there is an interaction deviating the particles composing the train from geodesic motion.

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#### nearlynothing

And does that lead you to the conclusion that the OPs original logic is sound?
Well i dont see a logic flaw there, the point is he doesnt know yet how to interpret the tought eperiment in the context of relativity.

#### ChrisVer

Gold Member
You could never obtain the constant speed without at some point in the past having accellarated to some degree.
It is like saying let us imagine an experiment were a guy is hanging in the air, and exclude the rest of reality.
Being that he must have been jumping first, or perhaps have fallen out of a plane etc.
It is cutting a shorter clip from the entire scene.
That's actually wrong. You can forget about the "past" and care about the present in order to determine the future.

#### Kyle.Nemeth

@Kyle.Nemeth (post 6) :

I see that you understood what i intended with the thought experiment, thank you .

Then you said this :
"However, SR says that you could also claim that the station is moving AWAY from you. This claim is also true and completely valid.
Why is the latter true also? Because Albert Einstein postulates in SR that the laws of physics are the SAME in ALL inertial frames of reference."

> Using the postulate as a defense against an argument that tries to illustrate that we cannot extrapolate things about THE laws of physics from a very limited thought experiment (were essential parts of reality are not allowed to exist), is not very fair.
On the contrary, it is completely fair. The postulates are accepted as facts characteristic of our universe. If one hasn't accepted them as facts, then they are not justified in discussing anything about SR because then you are just saying that the theory is wrong. Anyone that claims such a theory is incorrect, their argument is not very strong without theoretical and experimental proof.

@Kyle.Nemeth (post 6) :

You could never obtain the constant speed without at some point in the past having accellarated to some degree.
It is like saying let us imagine an experiment were a guy is hanging in the air, and exclude the rest of reality.
Being that he must have been jumping first, or perhaps have fallen out of a plane etc.
It is cutting a shorter clip from the entire scene.
Suppose we do want to imagine an experiment where some guy is suspended in air on earth. Because we omit the fact of where he came from or how he got there does NOT imply that we are omitting reality itself. The fact of the matter is that he is there and a certain set of rules (physical laws) will apply to him. How he got there actually may not matter at all, depending on what we are trying to determine.

For example, If we want to know how long this guy has been suspended in free fall then we might want to know how exactly he got there in the first place. If, say, we wanted to know his acceleration (if indeed he is in AIR on earth), we could immediately say that it is 9.8 m/s2. We can assume this because we have accepted this value of the earth's gravitational acceleration near the surface of the earth as FACT. Thus, we need not know ANY details about how he got there.

If we accept the postulates of SR as facts, we can make assumptions that my seem confusing but are valid.

@Kyle.Nemeth (post 6) :

>What validity does the original SR thought experiment have if you deliberately handicap the observer (trainguy is not allowed to use his memory) and omit essential information ? How could any predictions about the laws of physics in general be correct, when derived from this limited and unreal situation ?
Handicapping an observer is not a main feature of the SR thought experiments. However, many demonstrations of said thought experiments do have this feature to make for simpler understanding of the underlying CONCEPT.

If you remember that it was you who accelerated away from the train station to a constant speed because you operated the train yourself, SR is not implying that you must forget that ever happened in order to understand the perspective of the other inertial frame.

Once you finally reach your constant speed, you are then in an inertial frame because you can NOT feel any changes in your motion or acceleration. When we claim you are now in an inertial frame, we are not implying that everything that happened before you reached the inertial frame didn't happen. Obviously, all of that stuff DID happen and you remember, so you KNOW that it was you who sped up the train to some constant speed. SR isn't contradicting these facts.

SR claims that the notion of the train station moving away from YOU at a constant speed, rather than you moving away from it, is completely vaild regardless of whether it is ACTUALLY you who is moving. The reason it is completely fine to assume this validity is because we have accepted the postulates as facts (justifiably so).

I'd like to recommend this website:

WorldscienceU.com

This website offers a course in SR, taught by Brian Greene, professor of physics at Columbia University. He does an outstanding job and not to mention it is a fun course.

#### Noa Drake

@Nearlynothing

You said :
"His acceleration can be measured locally, with accelerometers, so this can be defined in absolute terms, with no reference to coordinates. Now in this frame he sees the station failing to remain stationary, he interprets his own acceleration as a means to remain stationary in that frame."

An interesting angle, i'll have to let that sink in for a while.

#### Kyle.Nemeth

SR is perfectly applicable for accelerated motion.
SR is NOT applicable at all for accelerated motion. In fact, the reason for being in an inertial frame is that you are NOT accelerating and thus can not PHYSICALLY distinguish whether it is you and the vehicle who is moving, or the world around you that is moving.

#### nearlynothing

SR is NOT applicable at all for accelerated motion. In fact, the reason for being in an inertial frame is that you are NOT accelerating and thus can not PHYSICALLY distinguish whether it is you and the vehicle who is moving, or the world around you that is moving.
But SR is not limited to inertial frames at all.

#### Kyle.Nemeth

But SR is not limited to inertial frames at all.
Actually, it is. SR is based on inertial frames.

Gamma is the "fudge factor," so to speak, that explains the difference in coordinates between perspective frames of reference.

Time dilation is the notion of time that observers experience with respect to other observers/objects frames of reference.

Length contraction is a phenomenon observed with respect to observers/objects frames of reference.

Lorentz transformations are equations recognized by Einstein (not originally formulated by him) that allow for one to transform coordinates from one reference frame to another.

A perspective in which one is accelerating is not an inertial frame, this is even stated by Newton's First Law of Motion, or the Law of Inertia.

#### nearlynothing

Actually, that is what SR is all about.
Not quite, SR does stress the equivalence of all inertial frames, but it's not at all a theory confined to them. You can define frames that are not inertial in minkowski space, nothing about space-time is changed by the use of these coordinates

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