How does conservation laws work in physics

[DarkFalz]

Hello,

this thought I'm having might be difficult to explain, but i will do my best. Ever since i learned about conservation of energy, conservation of mass (or mass plus energy due to E=mc^2) and conservation of linear/angular momentum, i always found it weird that things in nature can change to a diferente state, but still conserve all these quantities.

Lets consider that I'm on the floor at position x=0

I start moving at 1 m/s for 5 seconds, meanwhile Earth begins moving backward in order to conserve linear momentum.

When i stop at x=5, both me and Earth stop so that momentum remains conserved. My first question, is why can i stop after i start moving, what is involved here? Is it that once i stop moving my feet adhere to the ground and force me and Earth to reach a stable state of zero velocity for both? This something i don't quite know how to explain, am i far from the true answer?

Also, in order for me to start moving, i have to spend energy. Where has this energy gone once i stop moving? Should it return to me since i stopped moving and linear momentum got conserved? If the energy does not return, will nature somehow cause me to return to my initial position using that energy? This last point might seem strange, but I've been wondering about it, does nature also eventually lead things to the original state? Say the situation where i was at x=0 by somehow using the energy i spent to move in order to return me to my original position?

 

[mfb]

(or mass plus energy due to E=mc^2)

Still just energy. Mass is a type of energy.

My first question, is why can i stop after i start moving, what is involved here? Is it that once i stop moving my feet adhere to the ground and force me and Earth to reach a stable state of zero velocity for both?

If you would be a car, this would just be friction. With legs, it is more complicated, but the idea is the same: you get some force between you and earth, accelerating you backwards (and therefore slowing you down).

Also, in order for me to start moving, i have to spend energy. Where has this energy gone once i stop moving?

Converted to heat in your muscles and remaining body. Some cars can re-use this energy, humans cannot.

This last point might seem strange, but I've been wondering about it, does nature also eventually lead things to the original state?

No. You can move backwards, but you'll need even more energy that gets converted to heat. Most real-life processes are not reversible as entropy always increases.

 

[SteamKing]

It's unclear what you are describing, but it's not the conservation of momentum, linear or otherwise.

If you start moving relative to the earth, the Earth doesn't move, you're the one who is moving. The Earth is going to move only if a force acts on it. To start your movement, did you jump off the ground? Are you walking down the street? It's not clear from your post.

 

[mfb]

If you start moving relative to the earth, the Earth doesn't move, you're the one who is moving.

Both are moving, but the motion of the Earth is extremely tiny (but its mass is huge).

 

[DrStupid]

In the first place place conservation laws are very simple: The conserved property remains constant in an isolated system. The problem start when the system is not isolated.

Lets consider that I'm on the floor at position x=0

I start moving at 1 m/s for 5 seconds, meanwhile Earth begins moving backward in order to conserve linear momentum.

When i stop at x=5, both me and Earth stop so that momentum remains conserved. My first question, is why can i stop after i start moving, what is involved here?

In this example the total system consisting of you and Earth can be assumed as isolated. That means that the sum of your momentum and the momentum of Earth remains constant during this process. That's the simple part of the conservation.

You may change your momentum because you are not isolated. You exchange momentum with your environment (in this case with Earth). This exchange of momentum is quantified with the force acting between you and Earth. The total force acting on you is per definition equal to the derivation of your momentum with respect to time.

 

[DarkFalz]

Still just energy. Mass is a type of energy.

If you would be a car, this would just be friction. With legs, it is more complicated, but the idea is the same: you get some force between you and earth, accelerating you backwards (and therefore slowing you down).
Converted to heat in your muscles and remaining body. Some cars can re-use this energy, humans cannot.
No. You can move backwards, but you'll need even more energy that gets converted to heat. Most real-life processes are not reversible as entropy always increases.

Your answer was very insightful mfb. I was not familiar with the concept of entropy. I have been Reading about it, but from what i read, it seems that the universe tends to a state where useful energy will no longer exist =X why is it that there is always some amount of energy that is irrecoverable?

 

[dauto]

Your answer was very insightful mfb. I was not familiar with the concept of entropy. I have been Reading about it, but from what i read, it seems that the universe tends to a state where useful energy will no longer exist =X why is it that there is always some amount of energy that is irrecoverable?

There are physical processes that are irreversible. For instance, if you leave a cup of water with ice in it and come back a few hours later you might find that the ice melted. Nothing strange. If you leave a cup of water and come back later to find a cup of water with ice in it you will know somebody added ice to it. The possibility that ice spontaneously formed from the water will never even cross your mind. You know it is not possible. Why isn't possible? After all, the opposite process of ice melting didn't make you raise an eyebrow. You know that some processes are irreversible. Entropy allows us ti figure which processes are possible and which ones are not. Processes like the melting ice in the example above lead to increase in entropy while the reverse processes lead to decreased entropy and are impossible. The second law of thermodynamics tells us that entropy never decreases.

 

[mfb]

why is it that there is always some amount of energy that is irrecoverable?

This comes from probability. To take the example with the cup of water: if you look at all ways atoms in the room can be arranged (properly counted - this can be done in quantum mechanics), very few of them correspond to a cup with cold ice. Basically all of them correspond to a cup with water at room temperature.
If you wait long enough to have a random state, you won't see ice. In theory it would be possible, but the probability is something like 0.00000000000000000000000001%. Therefore, we can easily see ice melt, but we'll never observe the opposite (in a warm room).

 

[DarkFalz]

The ice cup exemples seems like good exemples. Let me ask just one last question regarding entropy, and possibly, the probabilistic approach presented by mfb. Given a state S of a system, is it possible for the state to occur more than once in the universe's lifetime? I mean, can a given state of, for instance, earth, repeat in time? Like every particle on earth, every photon on earth, the speed of each particle, etc etc, be the same more than once in Earth's lifetime? Or does the 2nd law of thermodynamics and the entropy concept prevent this?

 

[mfb]

Given a state S of a system, is it possible for the state to occur more than once in the universe's lifetime?

Yes. For very small systems, this can be very likely. For large systems (and the Earth is a HUGE system, and not even isolated properly), it is too unlikely to be of practical relevance.
Poincaré recurrence theorem

 

[DarkFalz]

Wow, so does it mean someday Earth's story may repeat itself? Like Newton and Einstein being reborn? Or the Roman Empire re-rising once more? Maybe we're already a remake of a previous version of Earth? I still wonder if such possibilities could exist for the universe as whole? If the galaxies keep getting farther apart from each other, how could the universe have a minimal chance of getting closer once again in order to reach a same state as before?

 

[mfb]

Wow, so does it mean someday Earth's story may repeat itself?

Earth (or even the whole universe as it currently looks like) won't live that long. Not even for a single grain of sand, which is a much smaller system.