Why is Newton's equation of motion invariant to time reversal

[larsa]

Is there any deep reason behind this? per example the principle of least action or something else?

 

[BvU]

Well, it has the second derivative wrt time in it. That's all. Replace t by -t and you get the same equation of motion.

 

[larsa]

Well, it has the second derivative wrt time in it. That's all. Replace t by -t and you get the same equation of motion.

What is so special about the second derivative? If it was the first derivative it wouldn't be time invariant?

 

[fresh_42]

What is so special about the second derivative? If it was the first derivative it wouldn't be time invariant?

What is the difference between $\dot{x}(t)$ and $\dot{x}(-t)$ according to the chain rule?

 

[rootone]

I don't know why time has a direction, but the usual answer for this is the concept of entropy.
Time just does have a direction; that is what is observed, even though math does not require it to be.
A broken glass does not reassemble, people don't reappear after death, and infants don't get unborn.

 

[BvU]

True enough, $\sqrt 1$, but the thread is about a different issue...

 

[larsa]

True enough, $\sqrt 1$, but the thread is about a different issue...

What do you mean?

 

[fresh_42]

What do you mean?

You've asked

Why is Newton's equation of motion time reversally invariant?

which is a question about a certain equation, and therefore about a certain frame and model, and not a question why time in general has only one direction as root-one $= \sqrt{1}$ has answered to.

 

[olivermsun]

I think the OP may be asking a more philosophical question about why an equation of motion consistent with observed physics ought to have the time-reversal property.

larsa, is that a fair reading?

 

[larsa]

I think the OP may be asking a more philosophical question about why an equation of motion consistent with observed physics ought to have the time-reversal property.

larsa, is that a fair reading?

Yes, exactly this is what i am asking

 

[BvU]

"Why ?" is generally not answered by physics unless there can be pinpointed a cause and effect situation.

 

[EddiePhys]

 

[larsa]

"Why ?" is generally not answered by physics unless there can be pinpointed a cause and effect situation.

There is a cause and effect situation in our case, which I am looking forward to learn. Physics is fruitful, agnosticism is boring.

 

[larsa]

[/QUO

Quotations are also boring.

 

[vanhees71]

Feynman is anything but never boring!

 

[fresh_42]

Feynman is anything but never boring!

If I had to choose among Michio, Neil, Carl or Richard, I would always chose Richard - and if it were for pure entertainment.

 

[davidge]

I would always chose Richard

Feynman supported the atomic bomb, while the others you mentioned did not. After all this, you still choose him.

 

[fresh_42]

Feynman supported the atomic bomb, while the others you mentioned did not. After all this, you still choose him.

The others were lucky not to have to. And they already knew what has been new to Feynman. It is always an easy task to judge history on values developed in the aftermath. Pythagoras was a questionable person addicted to numerology, something we would probably ban on PF. Does this stop you from using the law of cosines?

 

[davidge]

Pythagoras was a questionable person addicted to numerology, something we would probably ban on PF. Does this stop you from using the law of cosines?

Using a mathematical law that a man found is definitely not the same thing as becoming a fan of that man. Another person (mathematician) would have discovered the law of cosines, because it's a mathematical law, not a "Pythagoras invention" to humanity.

The others were lucky not to have to. And they already knew what has been new to Feynman.

Can't believe you think he did not know about the destruction and the effects that such a bomb would cause.

 

[fresh_42]

Can't believe you think he did not know about the destruction and the effects that such a bomb would cause.

On the contrary. I'm sure he knew. But in my opinion it is not fair, to judge historical events by the knowledge and values of different epochs. Participants in the Manhattan project believed it would end the war immediately, which it did, and save many thousands of potential losses. A similar argument can be applied to the use of chemical weapons in WWI. They knew what they did, but cruelty wasn't an issue at the time - and often isn't nowadays. The fact we have forbidden them must not be applied to the decision made in WWI to use them. Both have simply to be measured by different rulers.

I will end this debate here, as it doesn't belong into this thread. If you want to discuss Feynman's role in the Manhattan project, please open a separate thread.