# Relativity for [one of the] Dummies

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Looking for help to understand some very basic ideas. I'd like to start with this:

"In the "flat" space-time of special relativity, where gravity is absent, the laws of mechanics take on an especially simple form: As long as no external force is acting on an object, it will move on a straight line through space-time: at a constant velocity along a straight path."

Why? Why will an object move at all if no external force is acting on it?

How does this relate to "an object at rest will remain at rest..."

If you can point me in the direction of understanding this, thanks in advance.

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objects at rest tend to stay at rest unless acted upon by an external force

objects in motion tend to stay in motion unless acted upon by an external force

why would the object stop? it's already begun to move in some direction at some speed, and it's assumed there are no external forces acting on it.

an external force would result in an acceleration.

Edited by andrewcellini
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The main direction for understanding this in my opinion is: Forget about relativity in this context. It is a statement that stems from non-relativistic mechanics (and happens to still be true in relativity). You can actually define force as a change of momentum, which for most objects relates to change of velocity. The statement "an object remains at rest" is just a special case of "an object keeps its current velocity" (for the special case of this velocity being zero). So both statements are not contradictory.

Edited by timo
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There is no such thing as 'absolute' rest; it's always relative to some object i.e. moving in the same direction with the same speed. Also, from the position of the observer, moving inertially (constantly), he is always at rest.

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There is no such thing as 'absolute' rest; it's always relative to some object i.e. moving in the same direction with the same speed. Also, from the position of the observer, moving inertially (constantly), he is always at rest.

This may be true if you only think in terms of space-time. But if you think in terms of energy conservation, then there has to be a hierarchy of references, including zero, or else the law of energy conservation is rendered void.

For example, if I was traveling on a train, I will see the train station moving at V, while someone at the station will see the train moving at V. Fo many things, motion appears relative. If we do an energy balance, the train (t), moving at V, has kinetic energy 1/2 M(t)V2, while the station (s) has kinetic energy, 1/2M(s) V2. If these are not the same, we have added or subtracted energy from the universe by simply assuming all references are relative, which is in violation of a law. You can't have it both ways, with a law of science (energy conservation) trumping a theory guideline.

In the twin paradox, where one twin travels near the speed of light and the other remains on earth, the twin in the space ship returns being younger than the stationary twin. Both see relative velocity or both see each other moving at V, but only one ages slower. This is connected to energy conservation. Only the twin with real energy has real relativistic affects. If we don't include an energy balance, both references might assume they have the real affects. This works as long they don't meet to compare. If they do meet, then energy conservation will separate the real affects from the relative affects.

Edited by puppypower
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Thanks for the replies. All of that makes perfect sense. I think my misunderstanding stemmed from an incorrect interpretation of the excerpt I used. I accidentally jumped to the conclusion that "an object" referred to "all objects", or another way I could describe it is I mistook

"As long as no external force is acting on an object"

as saying

"As long as no external force has acted on an object"

I was confused because I thought, "if no external force has acted, why and how would the object be moving in a straight line?"

Edited by turpinrt
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Very clear statement , andrew. +1.

turpint,

This was the great breakthrough by Newton when they realised that bodies will continue indefinitely in their state of motion if you leave them alone.

It is common for beginners to think otherwise and it was believed for centuries before Newton.

One spin off from that.

It takes no energy for the body to keep on in its state of motion (or rest).

The body has energy by virtue of its motion, but it doesn't loose any, just because it is moving.

If it does loose energy and slow down this means that a force must be acting on it (eg friction, air resistance etc)

Edited by studiot
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..... but as a beginner can I get away with just believing this is pretty much true?

It's true.... it is a basic tenet. PP is speculating.

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It's true.... it is a basic tenet. PP is speculating.

Okay. Thanks for clarifying.

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For example, if I was traveling on a train, I will see the train station moving at V, while someone at the station will see the train moving at V. Fo many things, motion appears relative. If we do an energy balance, the train (t), moving at V, has kinetic energy 1/2 M(t)V2, while the station (s) has kinetic energy, 1/2M(s) V2. If these are not the same, we have added or subtracted energy from the universe by simply assuming all references are relative, which is in violation of a law. You can't have it both ways, with a law of science (energy conservation) trumping a theory guideline.

This is just wrong. Energy is observer dependent. You can't equate energy seen by one observer with the energy seen by another.

In the twin paradox, where one twin travels near the speed of light and the other remains on earth, the twin in the space ship returns being younger than the stationary twin. Both see relative velocity or both see each other moving at V, but only one ages slower. This is connected to energy conservation.

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This may be true if you only think in terms of space-time. But if you think in terms of energy conservation, then there has to be a hierarchy of references, including zero, or else the law of energy conservation is rendered void.

For example, if I was traveling on a train, I will see the train station moving at V, while someone at the station will see the train moving at V. Fo many things, motion appears relative. If we do an energy balance, the train (t), moving at V, has kinetic energy 1/2 M(t)V2, while the station (s) has kinetic energy, 1/2M(s) V2. If these are not the same, we have added or subtracted energy from the universe by simply assuming all references are relative, which is in violation of a law. You can't have it both ways, with a law of science (energy conservation) trumping a theory guideline.

No, that's energy invariance, not energy conservation. Conservation only applies within a frame of reference.

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• 4 weeks later...

Not really keen on the language indicating movement at some velocity. No such thing from inside a spaceship with no mass such as a planet or distant sun around to provide any kind of reference. Either your accelerating or not accelerating. To a passerby, then your moving at a fixed velocity but to you, it's the other guy who's moving.

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