Special Relativity & Acceleration: Unequal Inertial Frames

[Martyn Arthur]

Given that one or both inertial frames must have been subject to acceleration at some point; resulting in an imbalance of application between the two inertial frames, why does the consequential effect of general relativity not feature in calculations.
Surely, as such, neither observer's situation can be regarded as eual to the other's.
Regards
Martyn

 

[Dale]

Given that one or both inertial frames must have been subject to acceleration at some point

Why?

why does the consequential effect of general relativity not feature in calculations

General relativity is needed to describe tidal gravity (curved spacetime). You do not need to use GR to handle acceleration in flat spacetime.

 

[Orodruin]

Given that one or both inertial frames must have been subject to acceleration at some point;

This is a false premise. Inertial frames do not accelerate by definition. They are abstractions and do not need to be connected to particular objects.

 

[Ibix]

Given that one or both inertial frames must have been subject to acceleration at some point

A frame is a choice of coordinates, not a physical object. Saying it must have accelerated is like insisting that the only way you can draw a map (a normal geographical one) is with north pointing up the page, and then rotating it if you don't want that. No. You just choose how you want north oriented. Similarly, you just pick a frame.

 

[Martyn Arthur]

Thanks, if one hypothesises that 2 inertial frames have been moving eternally with reference to one another then acceleration is not a requisite.
Given that the calculations are bases on a comparison of inertial frames moving relative to each other, If I understand correctly motion cannot occur spontaneously and requires the application of an acceleration to instigate it.
Then, taking the standard example of a train passing a "stationery" observer the train has been accelerated and cannot be judged on equal terms with the unaccelerated "stationery" observer?
Martyn

 

[PeroK]

Thanks, if one hypothesises that 2 inertial frames have been moving eternally with reference to one another then acceleration is not a requisite.
Given that the calculations are bases on a comparison of inertial frames moving relative to each other, If I understand correctly motion cannot occur spontaneously and requires the application of an acceleration to instigate it.
Then, taking the standard example of a train passing a "stationery" observer the train has been accelerated and cannot be judged on equal terms with the unaccelerated "stationery" observer?
Martyn

There are a lot of misapprehensions there. Your ability to understand SR now hinges significantly on your ability to accept that you have misunderstood the basic concepts.

Note that, for example, if a train is traveling West, then it is moving slower than the "stationary" passenger, as they are both moving East with the Earth's rotation.

The first concept to accept is that all motion is relative is there is no such thing as absolute rest or absolute velocity. This important idea dates back to Galileo.

 

[Ibix]

Then, taking the standard example of a train passing a "stationery" observer the train has been accelerated and cannot be judged on equal terms with the unaccelerated "stationery" observer?

Why not? As long as they are both moving inertially when we are doing the experiment, why would the earlier acceleration matter? How would the train remember it was the one that had been accelerated? How do you think the experiment would be different if, instead of a train and an embankment, you used two trains that were initially at rest with respect to the track and both accelerated in opposite directions?

 

[Martyn Arthur]

I am not a scientist yet (hopefully in the future) and am basing my question on textbook material.
I read that both inertial frames were initially at rest relative to the Earth, the train accelerated when it started moving relative to the Earth and the observer on the platform remined at rest relative to the Earth.
The textbook tells me that the circumstances of both are the same and produces calculations accordingly.
I get the general principle incidentally, but in what practical circumstances could there be two reference frames in motion relevant to one another without at least one having been subject to acceleration?
Thanks for your patience; just trying to learn!

 

[Ibix]

reference frames in motion relevant to one another without at least one having been subject to acceleration?

Because inertial reference frames are not physical things and do not accelerate. They are just you making a choice about what you want to call "at rest".

 

[Nugatory]

Then, taking the standard example of a train passing a "stationery" observer the train has been accelerated and cannot be judged on equal terms with the unaccelerated "stationery" observer?

If we consider a person who gets onto the train when it is stopped several stations away, and accelerates with the train until he reaches a constant speed relative to trackside person... Yes, the experience of that person is different from that of the guy standing next to tracks the while time. For example, the two people can carry accelerometers, and their accelerometers will show different readings and the associated physical effects.

However, once he's reached a constant speed relative to the train none of this past history matters. We can analyze the problem using the inertial frame in which the train is at rest and the trackside observer is moving at a constant speed, or we can use the inertial frame in which the track is at rest and the train is moving. (We could also choose to use a frame in which both of them are moving if we wish - if they were on two distant planets that we were tracking through a telescope in an observatory on Earth we probably would).

It's worth noting that our description of the previous history will be different according to which frame we choose. If we choose to use the frame in which the train is at rest and the trackside observer is moving, we would say that initially the train, trackside observer, train observer, and remote station where train was stopped were all moving at constant speed; then the train observer boards the train and the train decelerates until it is at rest while the trackside observer is moving. If we choose to use the frame in which the trackside observer is at rest, we would say that initially everything was at rest; then the train observer boarded the train and it accelerated until it reached its final speed.

 

[Janus]

Thanks, if one hypothesises that 2 inertial frames have been moving eternally with reference to one another then acceleration is not a requisite.
Given that the calculations are bases on a comparison of inertial frames moving relative to each other, If I understand correctly motion cannot occur spontaneously and requires the application of an acceleration to instigate it.
Then, taking the standard example of a train passing a "stationery" observer the train has been accelerated and cannot be judged on equal terms with the unaccelerated "stationery" observer?
Martyn

For that to be true, then by extension there would have to be a absolute rest frame against which all velocities could be measured against. But this is not the case.
The only accelerations that matter in any comparison between moving clocks are those that occur over the period during which we are comparing the clocks.

 

[PeroK]

I get the general principle incidentally, but in what practical circumstances could there be two reference frames in motion relevant to one another without at least one having been subject to acceleration?

There are no practical issues with setting up a reference frame.

For example, I have just imagined a reference frame where the Solar system is moving at a speed $c/2$ along the x-axis. That's it. That's a reference frame. Nothing practical needed to be done.

 

[Martyn Arthur]

Thank you mentor for a very clear explanation!

 

[Dale]

If I understand correctly motion cannot occur spontaneously and requires the application of an acceleration to instigate it.

You don’t apply accelerations, you apply forces. Forces are required to cause acceleration, but they are not required to cause velocity. Velocity is an initial condition

 

[Herman Trivilino]

If I understand correctly motion cannot occur spontaneously and requires the application of an acceleration to instigate it.

This is not a correct understanding. Motion can occur by an arbitrary choice of reference frames. It is not caused by acceleration, rather, acceleration is defined as a measure of how fast velocity is changing.