# 英语煎蛋小学堂视频百科97：物死早系列之能量守恒定律的简单证明(MP3+中英双语)

cocotang 于2015-04-27发布 l 已有人浏览

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One of the fundamental principles in modern physics is that there's no absolute time.And I'm not not even talking about relativity making time go at different rates.if you're going near light sead,I just mean that any time is as good as any other to set your clock to zero,The predictions of physics work all the same,and it's not like there's some "absolute starting time". I mean,if there were,time zones wouldn't work,In addition to allowing time zones,the fact that there's no absolute time,also implies the law of conservation of energy.

“绝对时间不存在”是现代物理基本定理之一，我说的不是接近光速时 相对论使得，时间流逝速率不同，我是说 在任意时间将时钟归零都一样，物理所做的预测完全相同，“绝对开始时间”这种东西并不存在，如果有的话 那么时区就无效了，除时区之外“绝对时间不存在”也暗示着能量守恒定律.

Here's simple proof to show that if a force doesn't depend explicitly on time,then that force conserbes energy! First conserving energy just means that there's a certain number,called the energy,which doesn't change as time passes.If you compare the energy at two different times,you'll see no difference.And the total energy of a system isthe sum of its energy of motion,or kinetic energy,and its energy due to position-the potential energy,So all we need os to find the change in kinetic and potential energiesover time.and add them up!

Ok,we know the kinetic energy of an object is half of its mass times its velocity squared,So the change in kinetic energy over time is just,one half m times the differenceof the squares of the velocities,Some clever algebra can rearrange this expression to become,the average velocity times m times the CHANGE in velocity,But a change of velocity over time is just an acceleration,and mass times acceleration is equal to the force on the object,So the change in kinetic energy of an object over time is just velocity times force.

On the other hand,the change in the potential energy of an object ,is negative the amount of work it takes to get the object to its  current position form its previous position independent of the path taken,that is,potential energy is the negative of the foece applied times the change in position,This is where the "there's no absolute time"part comes into play,You can't have potential energy for a force that changes over time,And just to be clear, "no changing over time" doesn't mean that,an object can't experience a changing force along the course of journey,the foece might be different at different places,but at any particular place.the force must remain the same.

Anyway,this is all just to say that the change in potential energy is negative F times the change in position.The negative comes from the fact that if you let the force push you along,your potential energy decreases,while if you fight in opposition to the force your potential energy increases.So the change in potential energy  over time is the negative of the force times the change in position over time,but change in position over time is velocity!

Which means change in potential energy of an object over time is negative velocity times force.And thus the change in the total energy over time,which is the sum of the changes in the kinetic and potential energies over time,is v*F plus negative v*F,which equals zero!And zero change in energy over time is precisely conservation of energy!All for the same reason that time zones work.

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