Nature of Energy

[little_monkey]

Before we get into any discussion we need to establish some parameters only to avoid what happened in a previous thread where insults were thrown, and hopefully since then, we've reconciled. However, to remind you, I was a professor for years, today I'm retired, but the professor is still in me. I'm used to walk into a class, where I'm the authority, and my students listen. I've also been to many seminars in which I sat quietly and listened because the person in front of me had greater authority than me in the matters presented. So I know when it's time for me to be  the professor and when I should be the student. Right now, I've read your posts in this thread, and I can only come to the conclusion that you are a confused student. You might know a lot, and perhaps more than me, but in the understand department, there is definitely a lot of room to improve. I hope you don't take this last remark as an insult. If that's okay with you so far, we can proceed.

This is neither a classroom nor a seminar, it is a discussion.  I can only come to the conclusion that you are a confused retired professor.

Whatever rocks your boat...

[brewer]

Clarification: I wasn't saying that energy is wrong in my post to Alex, but my comment pertained in how important it is. It is important but not as important as he would like to think. As to the rest of your post, I'm not qualified to shed any light.

This is your arrogant opinion only. I find your arrogance quite off putting.

[Panatheist]

If it makes sense to say time is infinitely divisible doesn't that imply that it isn't linear?  

How would one (nonlinear) follow from the other (infinitely divisible)? I don't see that.

What I mean is, if a segment of time is infinitely divisible does that pose any problems for our common notions of how time flows? Could it mean time is static if we could view the universe as a whole? I am not trained in these things so it's hard for me to explain or think it through, thus my bad attempts at this.

[Alex K]

@little_monkey

You misunderstood. I didn't mean that energy is the most important concept in physics in general. Read again what I wrote, the sentence is: "Other conserved quantities,...but.....", so I was saying that among the conserved quantities encountered in systems, energy tends to be the most powerful one because it is encountered in most systems, and because it is often closely related to the hamiltonian which describes  the dynamics of the system.

Me, misunderstanding?? No way, 

Your Hamiltonian is important because we need it to do perturbation theory. It doesn't play much of a role in non-perturbative theories ( for instance, String Theory). The Lagrangian is far more important - it's with the Lagrangian you get your symmetries checked out, and most importantly, your Lorentz invariance is absolutely crucial  to go from QM to QFT, and you get your theory Lorentz invariant through the Lagrangian. Moreover, the people in the 50's and 60' couldn't figure out the nuclear forces, both the weak and the strong. You don't know the force you're pretty much handicapped in developing any dynamical theory. So the whole plan was: try guessing the Lagrangian - you know if you have it right, you also know you have the right equation of motion. It was a nice way to circumvent not knowing the nuclear forces, and with Yukawa's idea, we could ignore "force" and replace it with "interaction".

Working with the Lagrangian in QFT is so much more fun for the reasons you mention, no argument about that. Especially if you're willing to employ path integrals from the get-go. Still, defining the S-Matrix and showing its unitarity is a bit of a shlep based purely on Lagrangian path integrals, compared to using the Hamiltonian time evolution.

However, your comment is not relevant for my point that Energy is important conceptually because - among other things - it is often directly related to the Hamiltonian which specifies the dynamics of the system. Whether going to the Lagrangian is more advantageous for some calculations is beside the point.

[little_monkey]

Me, misunderstanding?? No way, 

Your Hamiltonian is important because we need it to do perturbation theory. It doesn't play much of a role in non-perturbative theories ( for instance, String Theory). The Lagrangian is far more important - it's with the Lagrangian you get your symmetries checked out, and most importantly, your Lorentz invariance is absolutely crucial  to go from QM to QFT, and you get your theory Lorentz invariant through the Lagrangian. Moreover, the people in the 50's and 60' couldn't figure out the nuclear forces, both the weak and the strong. You don't know the force you're pretty much handicapped in developing any dynamical theory. So the whole plan was: try guessing the Lagrangian - you know if you have it right, you also know you have the right equation of motion. It was a nice way to circumvent not knowing the nuclear forces, and with Yukawa's idea, we could ignore "force" and replace it with "interaction".

Working with the Lagrangian in QFT is so much more fun for the reasons you mention, no argument about that. Especially if you're willing to employ path integrals from the get-go. Still, defining the S-Matrix and showing its unitarity is a bit of a shlep based purely on Lagrangian path integrals, compared to using  the Hamiltonian time evolution.

Yeah, well, the problem is tit for tat: with the Lagrangian, it's manifestly Lorentz invariance, but then you need to check if it's unitarity. The Halmitonian gives you the reverse headache, it's manifestly unitarity but you need to check if it's Lorentz invariance. The advantage for the Lagrangian is what you need to calculate your time ordered product of fields in the LSZ formula, from there you get rid of your infinities if you have any by adding your counter terms. So you work more with the Lagrangian than the Hamiltonian. 

However, your comment is not relevant for my point that Energy is important conceptually because - among other things - it is often directly related to the Hamiltonian which specifies the dynamics of the system. Whether going to the Lagrangian is more advantageous for some calculations is beside the point.

You've got that backward. It's your Lagrangian that will guarantee if you have the right equation of motion.  Your Hamiltonian is just needed to get the free theory in there, of which you know the eigenstates and the eigenvalue. But once that's fixed, you work with the Lagrangian all the way to propagators to deal with various different interactions. By that point, you can forget that you have ever used the Hamiltonian.

[Alex K]

Before we get into any discussion we need to establish some parameters only to avoid what happened in a previous thread where insults were thrown, and hopefully since then, we've reconciled. However, to remind you, I was a professor for years, today I'm retired, but the professor is still in me. I'm used to walk into a class, where I'm the authority, and my students listen. I've also been to many seminars in which I sat quietly and listened because the person in front of me had greater authority than me in the matters presented. So I know when it's time for me to be  the professor and when I should be the student. Right now, I've read your posts in this thread, and I can only come to the conclusion that you are a confused student. You might know a lot, and perhaps more than me, but in the understand department, there is definitely a lot of room to improve. I hope you don't take this last remark as an insult. If that's okay with you so far, we can proceed.

This is neither a classroom nor a seminar, it is a discussion.  I can only come to the conclusion that you are a confused retired professor.

I even already had to take an exam in theoretical physics at little_monkey University, in case you missed it

http://atheistforums.org/thread-41595-po...pid1220816

[IATIA]

Can we have fields without energy?

[IATIA]

Do we actually know what energy or matter fundamentally is?

No.  We have theories and equations and papers and arguments, but nobody really knows.  The matter/energy that we know of is only 5% of the universe with dark matter/energy comprising the rest and we know pretty much next nothing of that.  We live in a three dimensional reality and energy folds into different dimensions of which we can only describe mathematically, but are unable to see, touch, feel, smell or taste.

Is it even possible to know?

Good question.  Certainly not in our lifetime, but far into the future?  I do not know and I do not think anyone can answer that beyond opinion.

[Alex K]

Ok, @little_monkey, you've come here, had the gall to call me a "confused student" and claimed that I write nonsense, yet the only "criticism" you produced is something you misunderstood because you didn't read properly what I wrote, and some absolutely irrelevant (for this discussion) factoids about lagrangians and hamiltonians. I think an apology is in order lest people here are falsely led to believe that what I originally wrote is incorrect.

[I_am_not_mafia]

I think someone isn't taking to retirement too well