What is Energy? Is Energy conserved?

why save energy if physics says energy is conserved anyway did einstein really say that energy is not conserved and what does energy have to do with time this is what we will talk about today i looked up energy in the encyclopedia britannica and they told me that energy is the capacity for doing work which brings up the question what is work the encyclopedia says work is a measure of energy transfer that seems a little circular and as if that wasn't enough the encyclopedia goes on to say well actually not all types of energy do work and also energy is always associated with motion which actually it is not because e equals m c squared i hope you are sufficiently confused now to hear how to make sense of this a good illustration for energy conservation is a roller coaster at the starting point it has only potential energy that comes from gravity as it rolls down the gravitational potential energy is converted into kinetic energy meaning that the roller coaster speeds up at the lowest point it moves the fastest and as it climbs up again it slows down because the kinetic energy is converted back into potential energy if you neglect friction energy conservation means the roller coaster should have just exactly the right total energy to climb back up to the top where it started in reality of course friction cannot be neglected this means the roller coaster loses some energy into heating the rails or creating wind but this energy is not destroyed it is just no longer useful to move the roller coaster this simple example tells us two things right away first there are different types of energy and they can be converted into each other what is conserved is only the total of these energies second some types of energy are more others less useful to move things around but what really is this energy we are talking about there was indeed a lot of confusion about this among physicists in the 19th century but it was cleared up beautifully by emmy neuter in 1915. neuter proved that if you have a system whose equations do not change in time then this system has a conserved quantity physicists would say such a system has time translation invariance energy is then by definition the quantity that is conserved in a system with time translation invariants what does this mean time translation and variance does not mean the system itself does not change in time even if the equations do not change in time the solutions to these equations which are what describe the system usually will depend on time time translation and variance just means that the change of the system depends only on the amount of time that passed since you started an experiment but you could have started it at any moment and gotten the same result whether you fall off a roof at noon or at midnight it will take the same time for you to hit the ground that's what time translation and variance means so energy is conserved by definition and neuter's theorem gives you a concrete mathematical procedure to derive what energy is okay i admit it's a little more complicated because if you have some quantity that is conserved then any function of that quantity is also conserved the missing ingredient is that energy times time has to have the dimension of planck's constant basically it has to have the right units i know this sounds rather abstract and mathematical but the relevant point is just that physicists have a way to define what energy is and it's by definition conserve which means it does not change in time if you look at a simple example for example that roller coaster then the conserved energy is as usual the kinetic energy plus the potential energy and if you add air molecules and the rails to the system then their temperature would also add to the total and so on but if you look at the system with many small constituents like air then you will find that not all configurations of such a system are equally good at causing a macroscopic change even if they have the same energy a typical example would be setting fire to coal the chemical bonds of the coal molecules store a lot of energy if you set fire to it this causes a chain reaction between the coal and the oxygen in the air in this reaction energy from the chemical bonds is converted into kinetic energy of air molecules this just means the air is warm and since it's warm it will rise you can use this rising air to drive a turbine which you can then use to say move a vehicle or feed it into the grid to create electricity but suppose you don't do anything with this energy you just sit there and burn coal this does not change anything about the total energy in the system because that is conserved the chemical energy of the coal is converted into kinetic energy of air molecules which distributes into the atmosphere same total energy but now the energy is useless you can no longer drive any turbine with it what's the difference the difference between the two cases is entropy in the first case you have the energy packed into the coal and entropy is small in the latter case you have the energy distributed in the motion of air molecules and in this case the entropy is large a system that has energy in a state of low entropy is one whose energy you can use to create macroscopic changes for example driving that turbine physicists call this useful energy free energy and say it does work if the energy in the system is instead at high entropy the energy is useless physicists then call it heat and heat cannot do work the important point is that while energy is conserved free energy is not conserved so if someone says you should save energy by switching off the light they really mean you should save free energy because if you let the light on when you do not need it you convert useful free energy from whatever is your source of electricity into useless heat that just warms the air in your room okay so now we have seen that the total energy is by definition conserved but that free energy is not conserved now what about the claim that einstein actually told us energy is not conserved that is correct i know this sounds like a contradiction but it's not here's why remember that energy is defined by nuthur's theorem which says that energy is that quantity which is conserved if the system has a time translation in variance meaning it does not really matter just at which moment you start an experiment but now remember that einstein's theory of general relativity tells us that the universe expands and if the universe expands it does matter when you start an experiment an expanding universe is not time translation invariant so nutra's theorem does not apply now strictly speaking this does not mean that energy is not conserved in the expanding universe it means that energy cannot be defined however you can take the thing you called energy when you thought the universe did not expand and ask what happens to it now that you know the universe does expand and the answer is well it's just not conserved a good example for this is cosmological redshift if you have light of a particular wavelength early in the universe then the wavelength of this light will increase when the universe expands because it stretches but the wavelength of light is inversely proportional to the energy of the light so if the wavelength of light increases with the expansion of the universe then the energy decreases where does the energy go it goes nowhere it is just not conserved no it really isn't however this non-conservation of energy in einstein's theory of general relativity is a really tiny effect that for all practical purposes plays absolutely no role here on earth it is really something that becomes noticeable only if you look at the universe as a whole so it is technically correct that energy is not conserved in einstein's theory of general relativity but this does not affect our earthly affairs in summary the total energy of a system is conserved as long as you can neglect the expansion of the universe however the amount of useful energy which is what physicists call free energy is in general not conserved because of entropy increase this video was sponsored by not vpn and i hope you will stay around to hear some words about them because without my sponsors these videos would not exist nordvpn is a software that you install on your laptop or phone and it keeps you safe as you browse the internet you use the nordvpn app to connect to one of their servers and browse the web from there this keeps your data safe even on a public wireless using this app has the added benefit that you can choose your virtual location from any one of their more than 5000 servers all over the world so if you ever encounter a video or website that is blocked where you are just choose a different server problem solved you can now get 68 of their two-year plan and one additional month free if you go to notvpn.org sabine and use the kupo code zabina that's s-a-b-i-n-e not vpn works on pretty much 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Channel: Sabine Hossenfelder

Views: 277,524

Keywords: physics, science, education, what is energy, what is free energy, what is energy in physics, why save energy, general relativity, is energy conserved, why is energy conserved, is energy conserved in general relativity, energy conservation violated, hossenfelder, einstein, noether, emmy noether, noether theorem

Id: ZYM6HMLgIKA

Length: 10min 18sec (618 seconds)

Published: Sat Oct 31 2020