# Absolute and relative motion/rest

Summary:
Why can't we say that a train is moving for sure when the train is run by an engine?
In matter of absolute rest and relative rest as per Newton's laws, one thing that confuses me. If a train or bus is moving for example, if one sets aside for a moment the rotation of the earth and its orbit around the sun, one could say that the earth was at rest and that a train on it was travelling north at ninety miles per hour or that the train was at rest and the earty was moving south at ninety miles per hour. My question is, yeah, if you say in respect of perspective then there is no way to tell if the train ir earth is moving. But, for a matter of fact, I am giving locomotive to the train, right? The force is exerted upon the train by the engine, so obviously the train will move. Why can't we say that the train is moving then? I hope I'm making sense. It would be nice if anyone could clear this confusion. TIA.

Delta2

PeroK
Homework Helper
Gold Member
2020 Award
Summary:: Why can't we say that a train is moving for sure when the train is run by an engine?

In matter of absolute rest and relative rest as per Newton's laws, one thing that confuses me. If a train or bus is moving for example, if one sets aside for a moment the rotation of the earth and its orbit around the sun, one could say that the earth was at rest and that a train on it was travelling north at ninety miles per hour or that the train was at rest and the earty was moving south at ninety miles per hour. My question is, yeah, if you say in respect of perspective then there is no way to tell if the train ir earth is moving. But, for a matter of fact, I am giving locomotive to the train, right? The force is exerted upon the train by the engine, so obviously the train will move. Why can't we say that the train is moving then? I hope I'm making sense. It would be nice if anyone could clear this confusion. TIA.
You can measure the (real/proper) acceleration of an object and come up with a quantity that is invariant across all inertial frames of reference: $$\vec F = m \vec a$$ applies in all inertial frames.

But, what you cannot do is give a quantity for its absolute velocity. The velocity itself is frame dependent. You can never say that the train is travelling absolutely at velocity ##\vec v##.

To argue whether the train is "really moving" or not is not what the physics is about. It's about whether the measured quantity for velocity is invariant across all frames. Moreover, you can always choose a reference frame where the instantaneous velocity is zero: i.e. where the object is instantaneously at rest. And, you can always choose a frame where the object is not at rest.

Last edited:
bhobba and Shafia Zahin
Janus
Staff Emeritus
Gold Member
Summary:: Why can't we say that a train is moving for sure when the train is run by an engine?

In matter of absolute rest and relative rest as per Newton's laws, one thing that confuses me. If a train or bus is moving for example, if one sets aside for a moment the rotation of the earth and its orbit around the sun, one could say that the earth was at rest and that a train on it was travelling north at ninety miles per hour or that the train was at rest and the earty was moving south at ninety miles per hour. My question is, yeah, if you say in respect of perspective then there is no way to tell if the train ir earth is moving. But, for a matter of fact, I am giving locomotive to the train, right? The force is exerted upon the train by the engine, so obviously the train will move. Why can't we say that the train is moving then? I hope I'm making sense. It would be nice if anyone could clear this confusion. TIA.
You have to apply a force in order to go from moving with respect to the Earth to at rest with respect to it also.
Now you might argue that you needed to use your engine to get moving relative to the Earth, and only had to apply brakes to come to rest, But you can also say that all the brakes are doing are coupling you to the Earth in order to transfer the Earth's motion to you.

bhobba and Shafia Zahin
Mister T
Gold Member
The force is exerted upon the train by the engine, so obviously the train will move.
No, the force is exerted on the train by the tracks. But an equal amount of force is exerted on the tracks by the train. As a result of this interaction both Earth and the train are set into motion relative to what they were doing before the engine was started. But Earth has a much much larger mass so it moves much much less.

jbriggs444
russ_watters
Mentor
A roller-coaster train is driven by rollers or belts/chains in the track...

bhobba
Dale
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2020 Award
Summary:: Why can't we say that a train is moving for sure when the train is run by an engine?

But, for a matter of fact, I am giving locomotive to the train, right? The force is exerted upon the train by the engine, so obviously the train will move. Why can't we say that the train is moving then?
The same justification for why the train is moving also can be used to show that the earth is moving. And the sun is also moving by the same argument. And the galaxy is also moving. And the cluster of nearby galaxies …

So if we do assert that the train must be moving then true same logic shows everything else is moving too. It is of no benefit to try to assert some particular state as the “real” rest state.

cianfa72, bhobba and hutchphd
bob012345
Gold Member
The closest thing to defining a universal rest frame is the Cosmic Microwave Background i.e. the frame where the CMB is the lowest temperature but that would still only be an arbitrary definition and would be very inconvenient for everyday life.

Mister T
Gold Member
for example, if one sets aside for a moment the rotation of the earth and its orbit around the sun, one could say that the earth was at rest
Yes, you have the freedom to do that because all inertial frames are equivalent.

256bits
Gold Member
Summary:: Why can't we say that a train is moving for sure when the train is run by an engine?

Why can't we say that the train is moving then
You can say that. But moving at a particular velocity wrt the earth surface.

But consider, a hamster running on its wheel.
Think of the hamster as the train ( with its locomotive ), and the wheel as the earth - the wheel not being very massive.
From your perspective looking at the situation, the hamster is staying in one place even if it is supplying the energy for locomotion ( just like the train ), but the wheel is moving.

Let the hamster out to run on the floor, and now you would say the hamster is moving.

Can you tell the difference in the reference frames for this running hamster?

Delta2
jbriggs444
Homework Helper
Yes, you have the freedom to do that because all inertial frames are equivalent.
Wait, what? If we are considering classical Newtonian mechanics then neither the Earth nor the Sun has an inertial rest frame. Both are accelerating around their combined barycenter.

If we move on to General Relativity then neither the Earth nor the Sun has an inertial rest frame because there is no such thing in the curved space-time of the universe we inhabit.

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PeroK
Mister T
Gold Member
Wait, what? If we are considering classical Newtonian mechanics then neither the Earth nor the Sun has an inertial rest frame. Both are accelerating around their combined barycenter.
In this situation I was assuming those accelerations were small enough to be ignored.

italicus
Gold Member
@Shafia Zahin

you can’t say that an object is moving or is at rest, if you don’t specify “the reference frame” with respect to which you are considering the object. If you are seated in that train, are you in motion or at rest? Well, I can say both, it depends on the reference frame.

bob012345
Gold Member
In this situation I was assuming those accelerations were small enough to be ignored.
I think it's more than that. If the accelerations were uniform over a scale bigger than our measurements we would not detect any difference from Newton's laws in a true inertial frame. For example, if I measure the weight of an object on a scale at the surface of the earth, it's not like the object is subjected to centripetal acceleration of the earth's rotation yet the scale isn't.

Mister T
Gold Member
For example, if I measure the weight of an object on a scale at the surface of the earth, it's not like the object is subjected to centripetal acceleration of the earth's rotation yet the scale isn't.
Doesn't matter about the scale. The centripetal acceleration of the object is accounted for in the value of ##g## which in turn affects the value of the weight. At sea level most of the variation in ##g## across Earth's surface is due to Earth's spin.

bob012345
Gold Member
Doesn't matter about the scale. The centripetal acceleration of the object is accounted for in the value of ##g## which in turn affects the value of the weight. At sea level most of the variation in ##g## across Earth's surface is due to Earth's spin.
Ok, that was a bad example. However for a non-rotating frame accelerating in some gravitational field, I think it holds. You could not tell the difference from a true inertial frame.

jbriggs444
Homework Helper
Ok, that was a bad example. However for a non-rotating frame accelerating in some gravitational field, I think it holds. You could not tell the difference from a true inertial frame.
That's the equivalence principle, yes. It applies to local measurements.

It is not immediately clear (to me) whether this is relevant for measurements of the CMBR since those are inherently non-local.

sophiecentaur