What Is Energy: Physical Reality or Mathematical Construct?

[r16]

I've been throwing this term energy around for a while now, and thinking about it I have absolutely no idea what it is. Is it something that actually exists in the universe, or just a construct that we use to simplify problems?

Terms like kinetic energy, and even gravitational potential energy (from a Newtonian standpoint) are a little bit easier to understand because they are exist in everyday life, but when you get E&M (I've only studied classical E&M) you have this idea of a field, the field has energy and you need to calculate it? How does a field have energy?

Consider a conducting bar, moving on rails with a large resistor at one end bathed in a strong, uniform magnetic field. As the bar moves, the magnetic flux increases, inducing a current in the circuit and thus energy is lost in the resistor as heat, so the bar must be slowing down (it never actually stops even though it moves a finite distance, as I've calculated). I can ascertain what happens in this situation because I know about E&M, but it bothers me that I don't feel like I understand what is actually happening. If you showed me that and I didn't know physics, I would say the bar moves an infinite distance. How can some invisible field (with energy) stop a real, moving object? This is the whole idea of transfer of this energy which I don't know what it is?

Is there a good model of a physical interpretation of this phenomenon? Is it just a mathematical construct?

 

[Bob S]

Here is a real physical example of a conducting bar moving in a non-uniform magnetic field. I was working in a group using Enrico Fermi's cyclotron magnet for bending a very high energy beam of muons. The pole tip diameter was about 13 feet. We had opened up the gap so it was roughly 40 inches. The field in the center was about 1.5 Tesla, but we needed to measure it exactly. I was chosen to crouch/walk into the gap and place a NMR (nuclear magnetic resonance) probe in the center with the magnet ON. After placing the probe in the center, we needed to put the probe on a non-magnetic support. The only one we could find locally was a piece of 12 inch high. 6 inch wide, 24 inch long aluminum I beam. I started to pull the I beam into the magnet, and was met with resistance-lots of it. It was like pulling the I beam through molasses (honey). This was a problem only in the edge field, not in the center of the magnet (uniform field), as long as I rotated the I-beam only about a vertical axis (parallel to magnetic field). Rotating about any horizontal axis met with resistance. See eddy current explanation at:
http://en.wikipedia.org/wiki/Eddy_current

 

[Andy Resnick]

Energy is something I need more of.

 

[r16]

wow that story sounds pretty hardcore.

I was thinking about it, and you could define energy simply as the ability to do work, but then your stuck with the question again, what is work

 

[cragar]

Energy is anything that can be converted into mass , or that is already mass.
this may not be 100% accurate but i am trying to relate it to E=mc^2
like fore example a photon which is energy can decay into an electron positron pair.

 

[David0983]

If you could find out what energy is as a force, then i think you may find the answer to life itself.

Perhaps.

 

[Bob S]

Energy is anything that can be converted into mass , or that is already mass.
this may not be 100% accurate but i am trying to relate it to E=mc^2
like fore example a photon which is energy can decay into an electron positron pair.

Photons above roughly 5-10 MeV produce e-p pairs, which then produce heat (ionization). Photons under this energy produce heat via photoelectric effect or Compton scattering.
The end result of nearly all energy sources (including fissionable and fusionable materials)produce heat as an end product. If you want to watch the last throes of energy wasted as heat, put an ice cube in a glass of water.

 

[Chewy0087]

 

[Dale]

you could define energy simply as the ability to do work, but then your stuck with the question again, what is work

Work is force times distance (W=f.d)

 

[Cantab Morgan]

Is it something that actually exists in the universe, or just a construct that we use to simplify problems?

Is there a difference?

 

[cragar]

Work is force times distance (W=f.d)

How would you explain light using this.

 

[Dadface]

If it is moving or if it can make things move it has energy.We can calculate energy from the work formula or the variations of it such as the K.E. formulae. Energy is conserved(mass itself being a form of energy) and everything has energy.But what is energy and why is it as we observe it to be?At the most fundamental level we don't know.One of the books I read on energy had the following as the opening sentence;
Energy does not make sense.

 

[russ_watters]

How would you explain light using this.

You wouldn't.

Perhaps you could rephrase the question...?

 

[russ_watters]

But what is energy and why is it as we observe it to be?At the most fundamental level we don't know.

Yeah, we do - "the most fundamental level" is e=w=f*d. People who are looking for some deeper meaning to the word beyond the physics definition are attempting to attach a significance to it that simply doesn't exist and is completely unnecessary. IMO, this results from confusion about a possible link between the scientific and mystical definitions for the word "energy". In physics, "energy" is simply a name given to a useful mathematical relationship. That's it.

Why don't people look for similar "most fundamental level"/deeper meanings for the word "speed"? If there should be more to energy, there should be more to speed too.

 

[cragar]

E=hf

 

[cragar]

Why don't people look for similar "most fundamental level"/deeper meanings for the word "speed"? If there should be more to energy, there should be more to speed too.

people do look for deeper meanings in speed , relativity , time dialtion .
the faster you go time slows down and your mass becomes bigger , as I'm sure you are aware.

 

[Dadface]

.But what is energy and why is it as we observe it to be?At the most fundamental level we don't know.

Yeah, we do - "the most fundamental level" is e=w=f*d. People who are looking for some deeper meaning to the word beyond the physics definition are attempting to attach a significance to it that simply doesn't exist and is completely unnecessary. IMO, this results from confusion about a possible link between the scientific and mystical definitions for the word "energy". In physics, "energy" is simply a name given to a useful mathematical relationship. That's it.

Why don't people look for similar "most fundamental level"/deeper meanings for the word "speed"? If there should be more to energy, there should be more to speed too.

Just one of the things we observe energy to be is a conserved quantity.At the most fundamental level we don't know why this is the case,it is just that our definitions and observation show that it is so.Are you saying that we do know why energy is conserved?

 

[Dale]

How would you explain light using this.

Light can exert a force on an object. When that object moves the light does work according to W=f.d. Therefore light has the ability to do work (energy).

 

[cragar]

are you talking about radiation pressure , so would W=(F)(d) come up with the same
answer as E=hf

Does light have kinetic energy?

 

[Dale]

are you talking about radiation pressure

Yes.

so would W=(F)(d) come up with the same answer as E=hf

Yes.

Does light have kinetic energy?

I would say that a photon's energy is purely kinetic energy.

 

[cragar]

ok thanks for clarifying
Can we define energy as anything that affects time . for example time dilation and gravitational time dilation
like if our speed increased time would slow down and our kinetic energy would increase
and if we were in a strong gravitational field we would be around a lot of mass
which we could relate to E=mc^2 and we would experience gravitational time dilation
And light creates a gravitational field which would also have gravitational time dilation

 

[Cantab Morgan]

Just one of the things we observe energy to be is a conserved quantity.At the most fundamental level we don't know why this is the case,it is just that our definitions and observation show that it is so.Are you saying that we do know why energy is conserved?

Energy is conserved in those systems where the equations of motion are independent of time. This is a consequence of Noether's theorem. So, yes, we do know why energy is conserved: forces in the universe, say from Coulomb's law for example, do not depend on time.

 

[Dale]

Can we define energy as anything that affects time

Why would we want to do that?

Stick with the standard definition (capacity to do work). If you redefine existing terms you just get confusion, miscommunication, and pointless semantic arguments.

Now, if you want to use a new word then I have nothing against the rest of what you said.

 

[russ_watters]

E=hf

That too. Perhaps the key discoveries of the Rennaisance scientists are deriving the relationships between different kinds of energy.

people do look for deeper meanings in speed , relativity , time dialtion .
the faster you go time slows down and your mass becomes bigger , as I'm sure you are aware.

That's not equivalent - those are implications of speed, not "meanings" (definitions) of speed. People don't accept the definition of energy because they think there should be more to the definition than there really is. No one has ever asked on this forum why speed isn't s=d^2/t, but people ask all the time why you have c^2 in e=mc^2

Just one of the things we observe energy to be is a conserved quantity.At the most fundamental level we don't know why this is the case,it is just that our definitions and observation show that it is so.Are you saying that we do know why energy is conserved?

Yeah, we do. It's simple logic/math. If the universe is to be internally consistent, there must be conservation law. 1+1=2 is conservation law.

Can we define energy as anything that affects time .

No! You're again looking for things that are beyond the definition: the definition really is as simple as it says. No, we cannot define energy as anything that affects time (because it doesn't).

 

[Phrak]

Energy was once conserved. But in 1905 a violent upheaval of the ether ensued laying waste to the universe as it was.

 

[Dale]

Energy is still conserved. For the reason that Cantab Morgan stated.

 

[cragar]

No! You're again looking for things that are beyond the definition: the definition really is as simple as it says. No, we cannot define energy as anything that affects time (because it doesn't).

So you are saying that energy does not affect space-time , and are you implying
that we know every thing there is to know about energy.

 

[russ_watters]

...and are you implying
that we know every thing there is to know about energy.

No, we don't know everything there is to know about energy. But we do know that the definition that we have works extrordinarily well and we know that the things you are suggesting are gibberish.

 

[Dadface]

Just one of the things we observe energy to be is a conserved quantity.At the most fundamental level we don't know why this is the case,it is just that our definitions and observation show that it is so.Are you saying that we do know why energy is conserved?

Energy is conserved in those systems where the equations of motion are independent of time. This is a consequence of Noether's theorem. So, yes, we do know why energy is conserved: forces in the universe, say from Coulomb's law for example, do not depend on time.

It is theories that are informed by observations and not the other way round observations being informed by theories.Any good theory, including Noethers, must conform to the observations it predicts and although Noethers,which is based on other theories, predicts conservation it does not explain why there should be conservation.

Yeah, we do. It's simple logic/math. If the universe is to be internally consistent, there must be conservation law. 1+1=2 is conservation law. .

True in that according to all the obervations made so far energy is conserved and the sums add up.But who told the universe that it is to be internally consistent?Remember that the observations that we have are limited and that our measurements are subject to experimental errors some of which may not be negligible.

 

[cragar]

No, we cannot define energy as anything that affects time (because it doesn't).

Energy does affect space-time

 

[Phrak]

Energy is still conserved. For the reason that Cantab Morgan stated.

I would write that as, energy is conserved for the reason Cantab Morgan stated.

I shouldn't be so trit. Going to wikipedia, one can find a couple other conditions not stated. Also, on a curved manifold, are all the conditions met? I don't know.

I realize it's not easy to come up with all the conditions to ensure that some particular symmetry statement is true. As well, it may not even be fair to talk about curved spacetime in a general physics forum. A PF faq would be nice.

The thought experiment I rather like involves a laser beam, first split, and then crossed at some obtuse angle. It seems as though the energy should be conserved thoughout. The energy flux into the region where they cross is equal to the energy flux out. However, the energy flux density within the intersection can be made arbitrarily small as the angle approches 180 degrees. The conserved quantity in this case is mass_0 density, $\rho_0$, where rho is the density of the so called invariant mass.

 

[Cantab Morgan]

It is theories that are informed by observations and not the other way round observations being informed by theories.Any good theory, including Noethers, must conform to the observations it predicts and although Noethers,which is based on other theories, predicts conservation it does not explain why there should be conservation.

Your comment is intelligent, and it also reveals that I did not express myself clearly enough.

Noether's theorem is not a Physical theory. It is Mathematics. It is true.

Now, I suppose that what is up for grabs is whether the universe can really be modeled accurately by a Lagrangian formulation, because that is Physics. But there has been quite a lot of success doing this, so I hadn't questioned it in my original post. Strictly speaking, we say that such a Physical theory is useful rather than true. But if the universe can be modeled in this way, then Noether's theorem applies.

Noether's theorem tells us that if the equations of motion (basically F=ma) have no explicit dependence on time, then energy must be conserved. When we think of all the "F"s in the world, like Coulomb's Law for example, we don't see any time dependence. It is in this sense that we say that Noether's theorem tells us why energy must be conserved.

 

[Phrak]

Your comment is intelligent, and it also reveals that I did not express myself clearly enough.

Noether's theorem is not a Physical theory. It is Mathematics. It is true.

Now, I suppose that what is up for grabs is whether the universe can really be modeled accurately by a Lagrangian formulation, because that is Physics. But there has been quite a lot of success doing this, so I hadn't questioned it in my original post. Strictly speaking, we say that such a Physical theory is useful rather than true. But if the universe can be modeled in this way, then Noether's theorem applies.

Noether's theorem tells us that if the equations of motion (basically F=ma) have no explicit dependence on time, then energy must be conserved. When we think of all the "F"s in the world, like Coulomb's Law for example, we don't see any time dependence. It is in this sense that we say that Noether's theorem tells us why energy must be conserved.

I don't get energy conservation from a pulsed laser beam. The beam is split, then crossed. As the beams cross the energy is reduced during the time of crossing.

 

[zoobyshoe]

Yeah, we do - "the most fundamental level" is e=w=f*d. People who are looking for some deeper meaning to the word beyond the physics definition are attempting to attach a significance to it that simply doesn't exist and is completely unnecessary. IMO, this results from confusion about a possible link between the scientific and mystical definitions for the word "energy".

I think this is true, but the confusion also results from concepts of energy thrown around in science fiction movies, TV shows, and comic books. You end up with a notion that energy is a sort of self-contained, power-packed fluid transferable from one thing to another.

 

[Dale]

I don't get energy conservation from a pulsed laser beam. The beam is split, then crossed. As the beams cross the energy is reduced during the time of crossing.

That is incorrect. Maxwell's equations http://farside.ph.utexas.edu/teaching/em/lectures/node89.html" in general, the specific details of how you pulse your laser beam don't matter.

Please post a rigorous derivation if you believe otherwise.