Is potential energy real or fictious?

[Nano-Passion]

"Making sense" and "understanding" are rather vague subjective terms and quite irrelevant to the goal of physics: making quantitative predictions.

I'm not sure who defined the definition for the goal of physics. Physics, for many, is the quest to understand nature. To understand nature, it would help to realize what is a derivative and what might be an inherent part of nature--not be a calculation monkey.

The original question was whether potential energy is somehow "more made up to ensure CoE" than other forms of energy. It's not. All the formulas to calculate various forms of energy are designed to ensure of CoE. Without CoE the concept of energy would be useless.

Okay good point, see post below.

and many other quotes.

You are being very selective in your appreciation of Science. You base the above statement on a very narrow appreciation of the three example quantities. How can you be any more 'aware' of the presence of a mass or a charge other than by how they are reacting with you or something else? You drop a mass on your foot but its effect (how painful it gets) depends entirely upon its gravitational potential energy where you let it go. On Earth, it might break your toe but on the Moon it may just bounce off your shoe.

You are trying to impose a very personal view on all of this. Moreover, the further this thread goes, the more entrenched you seem to be getting. If you go away and think about this, rather than bouncing back with more and more arguments, trying to justify your view, then you may start to realize the advantage of thinking the way 'the rest of us' are thinking. When you do come to that conclusion, don't think of it as having been proved wrong. Just feel and enjoy the enlightenment. None of this is 'real'; it's just ways of thinking about things which allow us to make good predictions.

Okay I'll keep an open mind. But I don't understand why you choose to define the object's acceleration based on potential energy.

In this case, it can easily be described with kinetic energy and time. See I guess I don't have as much respect for potential energy because it seems to be a derivative, though I have no doubt that it is really useful.

Kinetic energy is very similar to potential energy in that they are both energies required to do work. But let us look closely at their definitions. Kinetic energy is the energy of an object in motion while potential energy is the energy stored, dependent on its position in a field.

Next thing, I'll define real as something that has a direct or indirect affect in a field.

So let us imagine a gravitational field and our choice of explaining gravitational acceleration is the graviton. Gravitons can give things kinetic energy, so long as there isn't an opposing force of equal magnitude. I realize that the definitions of energy are relatively arbitrary in a "real" sense, but you can describe the work being done on an object by kinetic energy alone. Gravitons can not however give something a potential energy, it is a more arbitrary definition. What the gravitons will do is increase an object's velocity, which we can arbitrary define as kinetic energy. However, gravitons will not increase potential energy, that only depends on an arbitrary reference point that are useful for calculation.

With this respect, kinetic energy is more real than potential energy.

 

[Reptillian]

I'm sure it has been said before in this thread, but I thought I'd chime in: Only differences in potential energy are physically meaningful.

 

[russ_watters]

My god you people keep on arguing on what is real or not, even making me confused when I wasn't before.

Look, energy is force * distance. When you are repelled by an object, it exerts a force on you. Your kinetic energy is converted to potential energy, which determines how close you get to the object before stopping.

For god's sake.

Absolutely. You can measure and perceive directly a force and a distance. The single step of multiplying them together, then labeling that quantity somehow causes some people great consternation.

 

[russ_watters]

Some things are more fundamental than others. This has been the case ever since we have looked for equations that describe the very small and ever since the search for unification.

Nonsense. Cite one prominent scientist who has ever referred to concepts that way.

I'm not sure why it is noted that kinetic and potential energy are on the same scale.

The kinetic energy "of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Potential energy "is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system"

Kinetic energy is more tangible in the sense that we can use it to describe a lot of everyday phenomena such as the energy imparted on a ball by a bat swing. Potential energy seems like an accountant's tool to make sure all the toys in the box and out count up to X.

I can use potential energy to describe a lot of everyday things as well, such as a car's behavior going up and down the hill -- not to mention you also need it when analyzing what happens between the bat and the ball. You have not provided an actual difference between the two: If one is an accounting trick, then the other is as well.

Again, all this is is your personal "feelings" about certain types of energy. There is no value here for physics.

 

[Nano-Passion]

All of physics is book keeping. What is a force except a number that is used to describe a change in momentum. It may seem more real because you can see something move. If you define that to be real, then you are correct.

I find that offensive, there are a large number of physicists who try to understand the laws of nature. Physics is more beautiful than book-keeping, which, in this respect, is a slightly offensive term that I used for potential energy. And I'm not talking about the romanticized view of physics either, calculations and problem-solving included of course.

Every physical system can be described in a formalism that uses only energy and not force. Very little modern physics considers forces at all. Instead, the formalism of Hamiltonian Mechanics is often used (I have to admit that a friend recently published a paper that heavily relied on forces for her analysis) which is based on kinetic and potential energy. Since the Newtonian and Hamiltonian Mechanics can both equally well describe the world without reference to the other, it seems to me that their basic components must be equally real.

Well that depends, just because something describes something else well does not mean its real. You only have to look at all the past false-leads in physics.

Also, look up Aharonov-Bohm effect. It is certainly not the same thing, but since the relationship of force to force field is similar to energy to potential field it might help convince you. In short, this effect shows that the electromagnetic potential field can have measurable effects on particles where there is no electric field. Weird, yes. Also very real.[/quote]

The Aharonov-Bohm effect puts a very good case on the table. One thing I noticed in physics is that many things can be redefined in different ways with a couple substitutions here and there (or even under a different paradigm). I wonder if that might be the case here, but given that I don't have the knowledge to dispute it, it is only fair to accept the phenomena.

What level of physics have you studied? I expect that when you get to an upper level Mechanics course and QM, you will be better convinced that potential energy and forces are on the same level. As to using the word "real", leave it to the philosophy majors. They need something to do.

Quite early in my study, I've studied some modern physics and a bit of classical mechanics (the work and energy section). But I'm still waiting to take modern physics next semester.

You may say so - I did not see all comments here, but that one looks fine to me - in that sense you could argue that potential energy (or at least, a difference or a ratio between potential energies) is "real".

For example a clock at higher gravitational potential (cet.par.) is found to be ticking faster, but a clock with equally more kinetic energy is found to be ticking at the same rate* - which also goes to illustrate, as mentioned earlier, that kinetic and potential energy could be said to be equally "real".

*for references you can look up information about satellite clocks or clocks on the geoid in relation to GR.

Yes, I'm aware of time dilation. Thing is though, I'm not completely fond of the potential energy concept to explain time dilation. Classical mechanics shouldn't take center-stage in this phenomena if you want to have a non-superficial understanding of the mechanics at work.

 

[russ_watters]

Okay I'll keep an open mind. But I don't understand why you choose to define the object's acceleration based on potential energy.

In this case, it can easily be described with kinetic energy and time. See I guess I don't have as much respect for potential energy because it seems to be a derivative, though I have no doubt that it is really useful.

You can describe it after it has happened with kinetic energy and time, but unless you use potential energy, you can't calculate ahead of time what is going to happen [to an object you drop] without potential energy.

Kinetic energy is very similar to potential energy in that they are both energies required to do work. But let us look closely at their definitions. Kinetic energy is the energy of an object in motion while potential energy is the energy stored, dependent on its position in a field.

You keep repeating the definitions over and over as if there is a meaningful philosophical difference there: we keep telling you there isn't. Not to scientists/engineers.

Next thing, I'll define real as something that has a direct or indirect affect in a field.

So let us imagine a gravitational field and our choice of explaining gravitational acceleration is the graviton. Gravitons can give things kinetic energy, so long as there isn't an opposing force of equal magnitude. I realize that the definitions of energy are relatively arbitrary in a "real" sense, but you can describe the work being done on an object by kinetic energy alone. Gravitons can not however give something a potential energy, it is a more arbitrary definition. What the gravitons will do is increase an object's velocity, which we can arbitrary define as kinetic energy. However, gravitons will not increase potential energy, that only depends on an arbitrary reference point that are useful for calculation.

With this respect, kinetic energy is more real than potential energy.

Gravity can, of course, act to change an object's potential energy. That's what happens when you drop something. You can also use the potential energy of one thing to change the potential energy of another: that's what a seesaw does. Moreover, since there is more than one type of potential energy, you can use one to change another: gravitational potential energy to increase spring potential energy, for example.

 

[russ_watters]

I find that offensive, there are a large number of physicists who try to understand the laws of nature. Physics is more beautiful than book-keeping, which, in this respect, is a slightly offensive term that I used for potential energy. And I'm not talking about the romanticized view of physics either, calculations and problem-solving included of course.

I submit that you don't know what you are talking about. What you display here is a deep misunderstanding of what physics is and so it is pretty silly for you to claim to know how physicists think.

 

[sophiecentaur]

I'm not sure who defined the definition for the goal of physics. Physics, for many, is the quest to understand nature. To understand nature, it would help to realize what is a derivative and what might be an inherent part of nature--not be a calculation monkey.

I'm not sure that the goal of Physics has ever been defined but I'm sure that it has never seriously been based an attempt to make people feel 'comfortable' with it. If it had then I'm sure QM would never have emerged. I should have thought that one of the main aims of Science is to challenge all those comforting old statements - like "heat rises" and to make them all stand up to scrutiny. You can bet your life that the cuddly concepts will be the first to fall under the cosh.
"Understanding"? As far as I'm concerned, that's just a feeling we get when we find that we can predict, to a reasonable accuracy, what will or should happen in some event or process. It's a word one should be careful with as it can easily lead to complacency. It's OK as long as it's treated as a journey and not a destination, in my view..

P.S. You are getting rather a lot of stick on this thread. Don't take it personally; it's all good fun and no more.

 

[Nano-Passion]

Nonsense. Cite one prominent scientist who has ever referred to concepts that way.

I wasn't talking about specific concepts with respect to the aforementioned statement. I was talking about the goal of some areas of physics in general.

Quantum mechanics is more fundamental than classical mechanics.
Relativistic mechanics is more fundamental than non-relativistic mechanics.
The search for a GUT is more fundamental than X.
And likewise for a TOE.

I don't have substantive evidence, but it might be the case that potential energy will become a derivative like classical mechanics.

I can use potential energy to describe a lot of everyday things as well, such as a car's behavior going up and down the hill -- not to mention you also need it when analyzing what happens between the bat and the ball. You have not provided an actual difference between the two: If one is an accounting trick, then the other is as well.

I've replied to that point of argument in here (read last comment on post).

You don't need potential energy to explain the car's behavior going up and down the hill as noted in the link above. But explain what happens between the bat and the ball in terms of energy, I want to see your point of view more clearly.

Again, all this is is your personal "feelings" about certain types of energy. There is no value here for physics.

If the argument is about what is of value for physics then I can assure you that there is a lot of value here. Not all physics is about calculation.

 

[Nano-Passion]

I submit that you don't know what you are talking about. What you display here is a deep misunderstanding of what physics is and so it is pretty silly for you to claim to know how physicists think.

So by your accusation, there isn't a good number of physicists who don't try to understand the laws of nature. Not even ponder about it from time to time? That strikes me as odd.

You can describe it after it has happened with kinetic energy and time, but unless you use potential energy, you can't calculate ahead of time what is going to happen [to an object you drop] without potential energy.

Okay great, it is helpful to calculate. But that has never been the point of argument.

You keep repeating the definitions over and over as if there is a meaningful philosophical difference there: we keep telling you there isn't. Not to scientists/engineers.

If there is to be an argument, we have to clearly define things.

You telling me "it isn't" doesn't change the fact that, at this present moment in time, I don't agree.

Gravity can, of course, act to change an object's potential energy. That's what happens when you drop something. You can also use the potential energy of one thing to change the potential energy of another: that's what a seesaw does. Moreover, since there is more than one type of potential energy, you can use one to change another: gravitational potential energy to increase spring potential energy, for example.

Yes, gravity can affect a myriad of things. Potential energy, kinetic energy, velocity, position, and even acceleration given enough distance. That is not the point. There are some things that are relatively fundamental in physics. That is,

Velocity, position, and acceleration.

Following on that premise, kinetic energy can ride along that boat. Potential energy, however, seems more and more to be useful for calculation with every point of argument you provide.

 

[Nano-Passion]

I'm not sure that the goal of Physics has ever been defined but I'm sure that it has never seriously been based an attempt to make people feel 'comfortable' with it. If it had then I'm sure QM would never have emerged. I should have thought that one of the main aims of Science is to challenge all those comforting old statements - like "heat rises" and to make them all stand up to scrutiny. You can bet your life that the cuddly concepts will be the first to fall under the cosh.

"Understanding"? As far as I'm concerned, that's just a feeling we get when we find that we can predict, to a reasonable accuracy, what will or should happen in some event or process. It's a word one should be careful with as it can easily lead to complacency. It's OK as long as it's treated as a journey and not a destination, in my view..

It strikes me odd that I'm more comfortable with the concepts of Quantum Mechanics than potential energy.

See the thing is, nature doesn't have to adhere to your intuition. In fact, it doesn't care at all. The quarrel here is what is a part of nature and what is useful because it helps us calculate. And I don't mean it in the literal philosophical sense. See post above where I argue that kinetic energy has more merit than potential energy. But hey, I'm not claiming I'm absolutely right, its part of the discussion. If someone comes with a good argument then I will accept it. One good argument was the Aharonov-Bohm effect.

P.S. You are getting rather a lot of stick on this thread. Don't take it personally; it's all good fun and no more.

It's all part of the love. :!)

 

[sophiecentaur]

It strikes me odd that I'm more comfortable with the concepts of Quantum Mechanics than potential energy.

Actually, it's not that strange. It could be a matter of 'distance lends enchantment' and 'familiarity breeds contempt'.

 

[Dale]

It strikes me odd that I'm more comfortable with the concepts of Quantum Mechanics than potential energy.

Are you aware that potential energy is a fundamental part of the Hamiltontan and Lagrangian, which are central to Quantum Mechanics?

Btw, I think that the problem with all questions of the form "is X real" is the concept of "real" rather than than the nature of X.

 

[Nano-Passion]

Actually, it's not that strange. It could be a matter of 'distance lends enchantment' and 'familiarity breeds contempt'.

But I'm more familiar with PE than QM. Who knows though, maybe I'll change my mind as I progress in my study. I'll be sure to update this topic.

Are you aware that potential energy is a fundamental part of the Hamiltontan and Lagrangian,

Yes.

which are central to Quantum Mechanics?

To that, I plead ignorance.

I can only talk about potential energy under things in classical mechanics. If you do suggest that we need to talk about quantum mechanics to argue about potential energy, then we should wait about a year or so.

It is probably better that way.

 

[sophiecentaur]

So you are saying that you have fewer problems with QM (about which you know very little) and classical PE, which you have studied formally?
When you know QM to the same level as your classical knowledge then you can make a valid comparison, I think, and not until.

 

[Dale]

I can only talk about potential energy under things in classical mechanics. If you do suggest that we need to talk about quantum mechanics to argue about potential energy, then we should wait about a year or so.

I don't think that QM is essential for talking about PE, but PE is essential for talking about QM. So if you think that you are more comfortable with QM than with PE then I think you are kidding yourself.

 

[Nano-Passion]

I was speaking of the concepts in the QM, not the mathematical frameworks.

And no I am not kidding myself, nothing in nature says that it has to adhere to our intuition.

So you are saying that you have fewer problems with QM (about which you know very little) and classical PE, which you have studied formally?
When you know QM to the same level as your classical knowledge then you can make a valid comparison, I think, and not until.

Can't argue with that.

 

[harrylin]

[..] Yes, I'm aware of time dilation. Thing is though, I'm not completely fond of the potential energy concept to explain time dilation. Classical mechanics shouldn't take center-stage in this phenomena if you want to have a non-superficial understanding of the mechanics at work.

Science has little to do with fondness - it has more to do with what we learn from nature, if we like it or not. So, you may not like such ideas as energy, the relativity principle and the equivalence principle which indeed emerged from classical mechanics, but such things turned out to be very useful. Note that such concepts as energy only "explain" in a limited sense: they started out as book keeping concepts but turned out to be at least related to invisible but nevertheless physical entities. And I'm afraid that currently that's about as far as we can look "inside" - so that we have little choice but to stick to such superficial descriptions.

 

[Dale]

I was speaking of the concepts in the QM, not the mathematical frameworks.

And no I am not kidding myself, nothing in nature says that it has to adhere to our intuition.

PE is a basic concept in QM. If you are uncomfortable with PE then you simply cannot be comfortable with QM. It has nothing to do with intuition, just logic. It is an illogical position to say that you are comfortable with QM but not with PE when PE is part of QM.

 

[A.T.]

What the gravitons will do is increase an object's velocity, which we can arbitrary define as kinetic energy. However, gravitons will not increase potential energy, that only depends on an arbitrary reference point that are useful for calculation.

Velocity also depends on an arbitrary reference frame that is useful for calculation.

With this respect, kinetic energy is more real than potential energy.

Define "more real".

 

[cosmik debris]

Define "more real".

More real is a bit less than really real.

 

[Berney123]

Why does potential energy give mass to an object potential energy is only the "potential" for an object to have energy. How does being at a higher location cause an object to gain mass.

 

[sophiecentaur]

This is not a valid "Why" question. There are very few of those in Physics, aamof. Any answer will only take you a bit further down the road. It is possible to describe what happens but not why it happens. i.e. it's a completely different system that we're working with, here, and it is just not intuitive.
Do not get too hung up on the word "potential" and its meanings in other contexts. There are many Science words that are used differently by non -Scientists.
Mass and energy can be regarded as being interchangeable 'versions' of the same thing. Rather than saying that the object gains Potential Energy, it might be better to say that the Object-Earth system gains PE whilst the system loses a small amount of measurable mass. The only time this mass change is actually measurable is during nuclear reactions, in which the energy change is enough to produce a significant proportion of mass change (the Mass defect).

 

[Mentalist]

Kinetic energy seems more real than potential energy. Potential energy just says particle A has so and so potential.

Kinetic energy tells me that I can deal this much damage with a bullet with mass m and velocity v.

Kinetic Energy: 1/2(m(v)^2)
Potential Energy: mgh

I don't see why you'd think one is different from the other, shouldn't they both be just as fictitious? But you must account for the reference frame as well.

I don't understand what you are talking about, explain.

 

[Khashishi]

Science has no answer to this question, so it's more a question of philosophy.

 

[sophiecentaur]

Science has no answer to this question, so it's more a question of philosophy.

The real "why" questions are, as you say, not Science and can only be 'answered' by those pesky Philosophers. I find it very annoying that Science education assumes that there are answerable 'why' questions when what they really mean is "how does this work?" or, even more basic, "what happens when ...?"
I am often amazed that so few people in this world (with the exception of some PF members haha) seem to accept this basic fact of life.
I can feel this thread getting moved away from its place in General Physics.

 

[Berney123]

When we try to explain why, almost everything will resort to philosophy and as more and more questions are answered the more and more difficult it will be for these answers to be explained. I am also amazed that some people can just accept things without asking why. Thanks so much for the thoughtful answers to this very difficult questions.

 

[sophiecentaur]

When we try to explain why, almost everything will resort to philosophy and as more and more questions are answered the more and more difficult it will be for these answers to be explained. I am also amazed that some people can just accept things without asking why. Thanks so much for the thoughtful answers to this very difficult questions.

You are not making the distinction between "explaining why" and 'describing roughly how it works'.
The 'how it works' approach actually has an answer because it uses a model that you already understand to describe a new phenomenon. The 'why' question can be answered at so many levels that it is almost meaningless.

See the famous 'Why" question that Richard Feynman dealt with in his quirky fashion.

Everyone asks 'why' about things but they all have different frames of reference. If the answer they get is enough to satisfy them (or you) then they and you will get a nice feeling about it. The reason that many people stop asking 'why' is that the answers they keep getting have got too hard for them to cope with or they are actually just too plain busy to find the time to pursue it further.

 

[JayJohn85]

Consider someone on the top floor of a 400 floor building, and someone on the ground floor.

If they both have the same human body and are going to push 100kg desks, then they both have the same potential energy to do work on these desks, regardless of their gravitational potential energy with respect to each other. The way you asked your original question about their capacity to do work while being at different heights, and your implication that you wonder if potential energy is not real lead me to think that your contention is that the increase in gravitational potential energy gives the person a higher absolute potential energy with respect to the objects that they might do work on, as in your example objects on the same floor as the person. If that were true, which it isn't, then it would make sense for you to question if potential energy is not real since this is not what we experience.

Just because one person has a higher gravitational potential energy does not mean that that potential energy is relevant when you compare two people's ability to do work. When you talk about their capacity to do work, such as pushing a desk, you are using 2 different potential energy references for the two cases, and so it does not make sense to say a person on a higher floor has more potential energy when any work they do on that floor will be at the same gravitational potential energy, and thus cancel out when compared to someone on a different floor in the building.

This is an awesome post. Basically your saying the energy is different potential chemical energy and potential gravitational energy. That the gravitational energy of the guy on the high floor gets canceled out by the floor? Same as the guy on the bottom. The top guy would only have more potential if he was to come crashing down of the top floor onto like a spring or something.

But if they had the same mass and potential for work they would have the same chemical potential energy. Did I understand this correctly?

 

[physwizard]

All forms of energy are introduced just to make conservation of energy possible. The is no other purpose to the whole concept of energy, than to have a conserved quantity.

this sounds interesting. but wouldn't the very fact that it is possible to maintain such a conserved quantity be of physical significance?
the lagrangian and hamiltonian formalisms give a good physical significance to energy. in fact i would say that these formalisms give a very concrete definition of, and significance to the concept of energy. if the lagrangian is time translationally invariant, then energy is conserved. before these formalisms were known, it had been the fashion to define new forms of energy whenever it was observed that a particular form of energy was disappearing.
if energy in the universe is conserved, then it has a very strong physical significance. it means that the laws of physics do not change with time!
as per relativity, energy contributes to the mass, though i don't know how much this has been tested in the laboratory for the different forms of energy.
not sure of how energy conservation would shape up in the light of quantum mechanical uncertainty though.

 

[WannabeNewton]

the lagrangian and hamiltonian formalisms give a good physical significance to energy. in fact i would say that these formalisms give a very concrete definition of, and significance to the concept of energy. if the lagrangian is time translationally invariant, then energy is conserved.

This is not entirely correct. If we have that $\partial_{t}L = 0$ then we know $H = \text{const.}$ where $H$ is the Hamiltonian but in the lab frame the Hamiltonian is not necessarily the total energy of the system. The standard example is that of a bead sliding on a hoop that rotates with constant angular velocity about the z-axis. In this case the Lagrangian is time translation invariant and thus implies the Hamiltonian is constant but it is not equal to the total energy in the lab frame (the total energy isn't even conserved for this system!). If you transform to the frame co-rotating with the hoop and associate a "potential energy" with the centrifugal force then this gives a physical interpretation of the Hamiltonian for this system. It should be stressed however that in the lab frame the total energy is not necessarily the Hamiltonian.

if energy in the universe is conserved, then it has a very strong physical significance. it means that the laws of physics do not change with time!

Energy conservation is very complicated in General Relativity. Non-stationary space-times do not have in general a globally conserved energy current. The RW metric (for the RW cosmological model) is an example of a non-stationary metric (no time-like killing vector field).

 

[physwizard]

The standard example is that of a bead sliding on a hoop that rotates with constant angular velocity about the z-axis. In this case the Lagrangian is time translation invariant and thus implies the Hamiltonian is constant but it is not equal to the total energy in the lab frame (the total energy isn't even conserved for this system!). If you transform to the frame co-rotating with the hoop and associate a "potential energy" with the centrifugal force then this gives a physical interpretation of the Hamiltonian for this system. It should be stressed however that in the lab frame the total energy is not necessarily the Hamiltonian.

quite true. but here there are unknown forces of constraint involved. it would be really interesting if you could provide a real world classical mechanics example where all the forces involved are accounted for in the potential energy function (Edit: and the relation between generalized and cartesian coordinates is not does not have an explicit dependence on time.) and still the conservation of the energy function (which works out to be numerically equal to the hamiltonian in the hamiltonian formalism(just to avoid using the term 'hamiltonian' when dealing with the lagrangian formalism)) works out to be a different idea from the conservation of energy (T + V) .

Energy conservation is very complicated in General Relativity. Non-stationary space-times do not have in general a globally conserved energy current. The RW metric (for the RW cosmological model) is an example of a non-stationary metric (no time-like killing vector field).

interesting. does this mean that the global energy conservation principle should be abandoned in GR? is there any experimental/observational evidence of this? (for eg. a star just disappearing suddenly without its energy showing up in any other form.)how would an observer perceive this loss/gain of energy?

 

[WannabeNewton]

quite true. but here there are unknown forces of constraint involved. it would be really interesting if you could provide a real world classical mechanics example where all the forces involved are accounted for in the potential energy function and still the conservation of the energy function (which works out to be numerically equal to the hamiltonian in the hamiltonian formalism(just to avoid using the term 'hamiltonian' when dealing with the lagrangian formalism)) works out to be a different idea from the conservation of energy (T + V) .

Hi phys! Thanks for responding. Let me think about this for a bit because I can't immediately grasp what you are asking for with regards to "real world" examples, thanks!

interesting. does this mean that the global energy conservation principle should be abandoned in GR? is there any experimental/observational evidence of this? (for eg. a star just disappearing suddenly without its energy showing up in any other form.)how would an observer perceive this loss/gain of energy?

It has its uses when it can be applied (e.g. in the case of stationary space-times) so no it isn't abandoned but you should note that local energy conservation always applies i.e. $\nabla^{a}T_{ab} = 0$ always holds, so that prevents such things. The failure of the existence of global energy conservation for general space-times is rooted in the issue of isometries (or lack thereof) of general curved space-times and is quite an interesting textbook matter. I don't think a forum post could do it much justice unfortunately.

 

[physwizard]

Hi phys! Thanks for responding. Let me think about this for a bit because I can't immediately grasp what you are asking for with regards to "real world" examples, thanks!

okay, let me just add that i would like an example where the relation between the generalized coordinates and cartesian coordinates does not have an explicit time dependence. i will edit my earlier forum post to include this.
"real world" would mean something which can be built and tested quite easily in the laboratory, in other words, not some kind of theoretical thought experiment.

 

[Johnahh]

"real world" would mean something which can be built and tested quite easily in the laboratory, in other words, not some kind of theoretical thought experiment.

Isn't GR based on the thought experiment of a light clock? I'm pretty sure the effects of GR are "real".