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

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1. Feb 24, 2017

### larsa

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

2. Feb 24, 2017

### 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.

3. Feb 24, 2017

### larsa

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

4. Feb 24, 2017

### Staff: Mentor

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

5. Feb 24, 2017

### 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.

6. Feb 25, 2017

### BvU

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

7. Feb 25, 2017

### larsa

What do you mean?

8. Feb 25, 2017

### Staff: Mentor

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.

9. Feb 25, 2017

### 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?

10. Feb 25, 2017

### larsa

Yes, exactly this is what i am asking

11. Feb 25, 2017

### BvU

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

12. Feb 26, 2017

### EddiePhys

13. Feb 26, 2017

### larsa

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

14. Feb 26, 2017

### larsa

15. Feb 26, 2017

### vanhees71

Feynman is anything but never boring!

16. Feb 26, 2017

### Staff: Mentor

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

17. Mar 4, 2017

### davidge

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

18. Mar 4, 2017

### Staff: Mentor

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?

19. Mar 4, 2017

### davidge

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.

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

Last edited: Mar 4, 2017
20. Mar 4, 2017

### Staff: Mentor

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.