Earlier this year, I embarked on a daunting journey to study Einstein’s special theory of relativity. I was only about a page or two into Robert Resnick’s Introduction to Special Relativity and the word “Inertial Frames of Reference” popped up. The book simply wrote it off “as a framework that is not under acceleration”.
That seemed fair enough to me, and I didn’t think much of it. But five pages into the book, the word was getting repetitive, so much that I began to wonder whether I understood what that meant at all.
The concept of inertial frames of references is very fundamental to physics, yet deceivingly intuitive. Like when was the last time you woke up in the morning and wondered, “Am I really stationary or am I moving?” It’s so ridiculous of a question that unless you are high (on drugs), no one really asks himself or herself, but maybe they should.
To really get the grip of inertial frames of references, contemplate the following hypothetical scenario.
“Pull up your curtains!”
Think of one of those lazy Sunday mornings where you don’t really feel like doing anything. You are awake for 15 minutes, but too lazy to get off your bed. You are just lying there scratching your stomach, staring at the ceiling.
A scene reminiscent of the Bruno Mars hit, “Today I don’t feel like doing anything, I just wanna lay in my bed …”
You don’t remember how you got back home after partying all night the previous night with friends.
With an effort, you get off your bed, stretch-up, squat, and even skipped, in an attempt to shake-off your wooziness.
You’re on your way to the bathroom to wash up when your phone rings: It’s your friend, Amy.
In part, Amy is responsible for the hangover you are feeling this morning. She was the one encouraging you drink the night before – always prompt to refill your glass.
You answer the phone.
She says she’s standing right outside your house, urging you to look out the window as she has a surprise for you.
Clutching the phone to your ear, and hoping she is not holding yet another bottle of champagne, you briskly walk over to the window. You pull up the curtains and … you are in a moving train!
<What!>
Apparently, somehow, you are in a compartment that’s made to look exactly like your bedroom.
While you were 100% sure a minute ago that your bedroom is stationary, fixed on Earth, all that was ripped apart.
Think of this as an over-the-top prank by your crazy friends who just went a whole lot of extra miles with it. Apparently, after getting you to party all Saturday night, they parked your knocked out body in a prearranged replica of your room in a train cabin and waited for you to freak out – and it worked!
Now this whole story seems highly unlikely, especially about the part where you failed to notice that you were in a moving train the whole time. Surprisingly, that’s perhaps the only element of truth in this story. With everything in place, even a stone-cold sober person couldn’t have known that he or she was in a moving train. Your friends knew the principle of inertial frames of references and they were counting on that.
It’s puzzling – but true.
Idealising this story
For clarity, let’s push this weird story even further. If we seek to understand the paradoxical nature of inertial frames of references, we ought to add three more equally unlikely assumptions to the already fictitious scenario. We are essentially going full-mode thought experiment here on!
- First, we assume the train had been traveling at a constant velocity in a straight line the entire time. The path was straight; there were no corners or elevations of any kind the entire time.
- Second, we assume the rails were ever so smooth. There was no such thing as rattling or the tiniest of vibrations.
- Third, we assume that you were deprived of all external clues. Windows were shut tight, the curtains pulled down – there was no light, air, or sound from outside the entire time.
Now why didn’t you notice you were in a moving train?
In this article.
The answer to this question and the concept of inertial reference frames in general comprises the objective of this article. This is for the common reader. Those that want to make sense of inertial frames of references in a casual article-based format of a text. As such some concepts may come off as over-simplified to the experienced, but it is only for clarity. This is just me putting things together in a way that (I hope) will make sense.
Although the introduction of this article hinted at special relativity, and the conclusion will hint at special relativity, this article in general is not about special relativity. Special relativity is used in here only to show how different concepts in physics integrate with one another.
The law of Inertia
With inertial frames of reference is another closely related concept called inertia. This property, inherent to all matter, enforces a body to maintain its state of either being at rest or moving at a constant velocity in a straight line.
Simply put, a body at rest remains at rest, and a body in motion keeps moving with an unchanging speed in a straight line unless acted upon by an unbalanced external force.
This statement is Newton’s first law of motion also called the law of inertia; it is also the formal definition of inertia.
It may come off as a no brainer and perhaps the most intuitive law in all of physics, but don’t be so sure. For now, remember that statement, we’ll come back to it later.
What we mean by frames of references
Without being too formal, you can think of a reference frame as a portion of space in which a physical event that can be observed happens. We, therefore, have all forms of frames of reference, such as a laboratory frame of reference or a classroom frame of reference, or a bedroom frame of reference, and if we wish to be more generic, we can have the Manhattan frame of reference or even the Earth frame of reference.
Literally, when you wake up in the morning, you are in your bedroom frame of reference, you get into the shower, and you are in your bathroom frame of reference. You jump into your car, you are in your car frame of reference, you get to your office, and you are in your office frame of reference, and so forth.
In our train scenario earlier, we could say you are in the train frame of reference, and your friend Amy who is standing on Earth is in the Earth frame of reference (Makes sense?).
While there are obviously countless cases of frames of references, they can all be grouped into only two categories: Inertial and Non – Inertial frames of reference.
Frames of reference and the law of inertia.
Physicists use the law of inertia to identify “Inertial Frame of References” from a whole bunch of frames of references.
Think of the “waking up in a train” situation at the introduction of this article.
Assume you don’t know yet that you are in a moving train, and you are just lying in your bed trying to remember what happened the previous night.
Suddenly, you look beside you and see your phone sliding off the bedside table and dropping to the floor.
(Assume the train driver had slowed down a little – but you don’t know this)
You don’t know what (or who) caused the phone to slide off and fall down.
From your perspective, this movement of your phone would be in direct contradiction to the law of inertia, which requires that bodies at rest remain at rest, unless acted upon by a force. But you can’t think of any force that acted on the phone.
Perhaps one of the following happened:
- You are still hung over, disoriented and imagining things.
- You are dreaming.
- Its magic
- The law of inertia could be wrong
Let us roll with the fourth option, as it’s the one that’s mostly pertinent to our discussion. If the law of inertia is wrong then objects initially at rest can begin to move on their own without any forces compelling them. This would explain the conundrum.
Limitation of the law of inertia.
Well, it turns out the law of inertia isn’t as general as we first assumed. It is not universal; the law is only valid in special situations – inertial frames of references!
In fact, by definition, an inertial frame of reference is the one in which the law of inertia holds. If the law of inertia is violated in any way, then whatever that frame is, it is not an inertial frame of reference.
A good example of an inertial frame is the Earth. If you leave an object rest, it will remain at rest forever, and one in motion will keep moving with a uniform motion provided no net external force acts on the object. In the Earth frame of reference, the law of inertia holds for most practical purposes.
An example of a non-inertial frame is an automobile moving on a rocky road, or one that is turning a corner. If you were to put a book on the dashboard, it would slide off or move somehow, even though the no force is applied on the book. This is because the frame of reference, in this case the car frame of reference is accelerating, so the law of inertia is not valid here.
In this frame, we have what physicists call fictitious forces or pseudo forces to account for the law of inertia. Simply put, physics becomes much harder in these frames of references because we have to account for these imaginary forces.
For example, when the train slows down in our story, books might fall off the shelf, a may phone slides off the bedside table and you feel pushed to the edge of your bed. You cannot account for these forces from your perspective; the law of inertia is disobeyed. To account for the law of inertia in such a scene, you ought to introduce imaginary forces.
Train frame of reference Vs Earth frame of reference.
Since inertia is realised for bodies at rest and bodies that moving with uniform motion, it follows that the law of inertia is also valid in a frame of reference that is at rest or a frame of reference moving with a uniform motion relative to another frame of reference.
Given our scenario on the train, your room on the train and your room back on “stationary” Earth both comprise inertial reference frames. One being stationary and the other moving with uniform motion relative to the other.
Bodies (such as your bed, phone and everything in your room including yourself) contained in these two different scenes develop the same inertia – the same resistance to change in motion. As far as the bodies are concerned, the two scenarios are exactly similar by virtue of the inertia developed by the bodies in the two environments.
You had the advantage over everything else in your room of perceiving your environment using your five senses. Which is why, we had to go to great lengths to deprive you of all clues indicating you are in a moving train, your body, like everything else in the room behaved in a way that was indistinguishable to what it would have in a stationary setting.
Inertial Frames and the Laws of Physics.
One interesting property of inertial frames is that laws of mechanics hold in all inertial frames of references in exactly the same way.
This is crucial to the reason why you didn’t notice that the train was moving. The laws of mechanics that work on ground will also work on any frame of reference moving with a uniform velocity respect to the ground, such as your train.
Thus, you couldn’t notice anything peculiar as you were stretching or rope-skipping because the same laws that govern elasticity and free-fall of objects on the ground works exactly the same way in your train frame of reference.
If your friend Amy had called you and said right away that you were on a moving train, you wouldn’t believe her. As long as the train kept on moving in a straight line on a smooth rail at constant velocity, there was no way for you to know that you were moving.
In fact, the only way for you to realize that you were on a moving train was to pull up the curtains and see the scenery moving past you.
There is no experiment that you could have done on the train that would let you know that you are moving relative to the ground.
This introduces an important fact: observers in different inertial frames will generally not agree on who is moving and who is stationary.
Each experiment they do will bring about identical results. There is no experiment that could establish who is moving and who is stationary.
In fact, the laws of physics are the same in all inertial frames of reference.
This is the principle of special relativity, proposed by Albert Einstein in 1905.
Who is moving then?
Since laws of physics are the same in all inertial frames of references, then observers in different inertial frames will not agree on who is moving and who is stationary. All they can say is that, “Observer X” is moving a certain velocity with relative to me.
The phrase, “I am standing still” only makes sense when you specify from what reference you are standing still. It could be the Earth, a bus or a train.
According to physics therefore, the question, “Am I really standing still?” doesn’t really mean much unless we specify a reference frame. You could well be standing still in one reference frame and be moving in another. More on this check out what is motion (article).
Conclusion
One cannot overstate the importance of frames of references. Physics would be very confusing if we hadn’t make the useful distinction between inertial and non-inertial reference frames. For example, the laws of physics are in their simplest form when formulated in an inertial frame of reference. In a non-inertial frame of reference, we have to account for other fictitious forces that act on an object because the law of inertia is not valid in those frames.
This is of course an informal introduction to inertial frames of references. If you are looking for a more formal analysis of these concepts including principle of relativity and fictitious forces follow these Wikipedia links. As for a beginner’s book, check out David Morin’s Special Relativity for the Enthusiastic Beginner. For an eBook, you might want to read the first chapter of Brian Greene’s The Elegant Universe. Or you can pretty much cram all these (including this article) by watching this wonderfully made YouTube video (it’s about 30 mins, but totally worth it!)
