Energy & Momentum

This conversation started in an OT thread on spirituality, but has now gone far astray. It seems better suited to the Science forum at this point.

Our discussion of energy and momentum has raised several points for me that I can’t seem to understand. I may be asking them poorly or just being thick. Let me try again by raising a whole bunch of questions that for me “point to” the issues at hand. There might be a single answer that can wrap them all up at once. Or perhaps you can see better than I can where I am missing things. There may be redundancies.

Part of this is an attempt to separate what is only math from what “physically exists” and see the boundaries between the two.

How do energy and momentum relate to matter/particles in a physical sense like quarks relate to proton, protons relate to atoms etc.?

Are energy and momentum only concepts that show up when we look at particles as equations?

If particles are only probabilities until we observe them, then what are they while unobserved? Are they "real" in that state? Do they even exist while unobserved?

If matter at the particle at level can only be described through mathematics, what is it that is being described?

Where does the physical universe begin? Are quarks and their kin the edge of it? What does “physically exist” mean?

Do energy and momentum have any other characteristics besides those shown through mathematics? If the answer is no, then, again, what does “exist” mean?

What are the assumptions in all this and what is derived from those assumptions? There must be some starting place.

If energy and momentum exist as something real and not just as mathematical concepts (which may express their characteristics) then what are they?

Bird, the way to learn this is to first learn Newtonian physics. Unless you have a solid grasp of it, you will be lost when it comes to the other stuff.

Why is that? Why can't smart guys like you explain how the concepts relate under the assumption that the math is all true what ever it is?

Birdjaguar said:

Why is that?

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Because Newtonian physics outlines the vocabulary of physics, the most basic concepts needed for understanding, if you do not have this basic vocabulary we cannot hold a fruitful discussion.

Birdjaguar said:

Why can't smart guys like you explain how the concepts relate under the assumption that the math is all true what ever it is?

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Because the language we use to talk about these concepts is the language of physics, we cannot simply translate it into laymen.



If you want to learn how physicists think, you need to learn some physics!

Perfection said:

Because Newtonian physics outlines the vocabulary of physics, the most basic concepts needed for understanding, if you do not have this basic vocabulary we cannot hold a fruitful discussion.

Because the language we use to talk about these concepts is the language of physics, we cannot simply translate it into laymen.

If you want to learn how physicists think, you need to learn some physics!

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Using your logic I could not understand contracts without going to law school.

It is not a question of how physicists think, it is what conclusions they draw. The details of most professions are rooted in jargon and strange ways of talking and thinking about things, but the experts in those fields can usually generalize and draw conclusions to explain them in meaningful ways that the non specialist can understand. It is a very powerful skill.

My questions involve energy, momentum, and particles and how they are related to physical existence (however you define it) and mathematics.

Suppose this were an essay question, how would you answer it?

Can you answer this one question?

What are the assumptions in all this and what is derived from those assumptions? There must be some starting place.

Birdjaguar said:

Using your logic I could not understand contracts without going to law school.

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That's a ridiculously terrible analogy. I never said you need to do physics professionally to talk about it meaningfully, but you need to understand the most basic things about physics. That's Newtonian physics.

Birdjaguar said:

It is not a question of how physicists think, it is what conclusions they draw. The details of most professions are rooted in jargon and strange ways of talking and thinking about things, but the experts in those fields can usually generalize and draw conclusions to explain them in meaningful ways that the non specialist can understand. It is a very powerful skill.

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Sure, we can say "this will go up" or "this will crash into that", but you're not asking those questions. You're asking questions about how physics operates, and what the nature of physics is. To talk about this reasonably you need to be versed in the most basic of physics.

Birdjaguar said:

My questions involve energy, momentum, and particles and how they are related to physical existence (however you define it) and mathematics.

Suppose this were an essay question, how would you answer it?Can you answer this one question?

What are the assumptions in all this and what is derived from those assumptions? There must be some starting place.

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How energy, momentum and matter relate to each other IS what Newtonian physics is all about, and no I can't teach you Newtonian physics in a single post.

Bird, there isn't an easy way out here. If you want to understand energy and momentum and the like, you need to know Newtonian physics. Learning and doing Newtonian physics is how we become familiar enough with these concepts to be able to apply them.

Birdjaguar said:

Using your logic I could not understand contracts without going to law school.

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No, that's still not analogous. (though in some ways, it is true that laws/contracts can't be understood without extensive knowledge, so that ad absurdum isn't even really wrong.)

It might be like talking to some gender-theorist if you refused to use or understand any of their definitions of "gender" and "privilege" and so on, that is always fun. Or various things in economics if one decided never to learn any textbook or other definitions of "supply" and "demand" and "debt" and so on. The point is Perfection is still right that you have to understand basic vocabulary of the field.

Your questions are actually answerable, though I know Perfection/others could do better, if you really must get answers I might as well.

Birdjaguar said:

How do energy and momentum relate to matter/particles in a physical sense like quarks relate to proton, protons relate to atoms etc.?

Are energy and momentum only concepts that show up when we look at particles as equations?

If particles are only probabilities until we observe them, then what are they while unobserved? Are they "real" in that state? Do they even exist while unobserved?

If matter at the particle at level can only be described through mathematics, what is it that is being described?

Where does the physical universe begin? Are quarks and their kin the edge of it? What does “physically exist” mean?

Do energy and momentum have any other characteristics besides those shown through mathematics? If the answer is no, then, again, what does “exist” mean?

What are the assumptions in all this and what is derived from those assumptions? There must be some starting place.

If energy and momentum exist as something real and not just as mathematical concepts (which may express their characteristics) then what are they?

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The very first and very last statements are hardest to answer, but a start to an answer is: energy and momentum describe physical quantities which are perfectly understandable/observable/intuitive on a macroscopic scale. Energy is the ability to do work - apply a force over a distance etc... and we're familiar with kinetic energy, heat energy and so on. Momentum is a quantity representing mass and velocity - and again we're familiar with it, moving vehicles, kicking/tossing balls and sports and so on. These concepts are applied and adjusted as we proceed to non-Newtonian particle or relativistic physics, but they can often be thought of in similar ways.

The other questions are trivial. Unless you after philosophical mumbo-jumbo of some sort that you have not made obvious, either the questions have straight answers or there is an easy misconception to clear up, and again the answer is straightforward.

No. See above. The quantities when we discuss particles are not exactly the same as for macroscopic, Newtonian physics but are understood to represent real physical properties, not just some element of math, though mathematical manipulation is helpful.

They are not "only probabilities." A particle is described by a wavefunction, and

Yes, they do "exist." And no, existence is not dependent on being observed by a human. In fact, nothing in any common interpretation of physics requires "we" as "humans" to observe things. (Yes, there are some various weird theories/ruminations out there, but no, this is NOT a proper interpretation of physics as is understood and is generally just a popular misconception applied in all sorts of fiction or whatever) Various events refer to interactions/entanglement with other particles, but the "observer" part is best thought of as a metaphor.

Premise invalid.

Not asking a question related to physics. It might best be said that the fundamental constituency of matter and energy after all isn't physical "blocks" of stuff like might be intuitive to a human on a macroscopic scale, but there's no other distinctions to be made here. Matter and energy (like light) both "physically exist" and macroscopic objects are just made up of such.

Yes; if branch unnecessary.

The "assumptions" dealt with in physics are a various number of physical laws based upon observations of reality, combined with appropriate mathematical and other manipulations convenient to working with and understanding.

edit: Well, Perfection might xpost grill me here but anyway, what he said is also good, again.

I agree with perfection, a textbook or course on Newtonian physics can explain momentum and energy better than I can in a few posts.

Birdjaguar said:

Are energy and momentum only concepts that show up when we look at particles as equations?

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Depends on what you mean. Explain more.

If particles are only probabilities until we observe them, then what are they while unobserved? Are they "real" in that state? Do they even exist while unobserved?

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Yes, particles can be described by a wave function when unobserved. The wave function doesn't have properties like a real position or momentum or any normal qualities that we measure and associate with particles. But it does have a quantity that dictates what the value of the measured quality would be if it were measured.

If matter at the particle at level can only be described through mathematics, what is it that is being described?

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Something that is something like a wave and something like a ball. And whether it behaves like a ball or a wave depends on how you measure it. So really something very unlike anything we encounter in life.

What you're really getting to here is the [wiki]Interpretations of quantum mechanics[/wiki], which is an unresolved metaphysical issue.

What does “physically exist” mean?

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If it has an effect on the world, then it exists. I don't think that's a perfect definition, but it's a start, and saying more would confuse the issue.

Do energy and momentum have any other characteristics besides those shown through mathematics? If the answer is no, then, again, what does “exist” mean?

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It's not clear what "shown through mathematics" means.

What are the assumptions in all this and what is derived from those assumptions? There must be some starting place.

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Well it all goes back to the fact that science assumes that the universe is governed by unchanging laws. Conservation of momentum and energy are two such laws.

Earthling said:

Not asking a question related to physics. It might best be said that the fundamental constituency of matter and energy after all isn't physical "blocks" of stuff like might be intuitive to a human on a macroscopic scale, but there's no other distinctions to be made here. Matter and energy (like light) both "physically exist" and macroscopic objects are just made up of such.

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This line is confusing. It valid in some contexts to say that light "is" energy, but at the level that Birdjaguar is trying to understand, light is a thing that carries energy. So something may emit light, thereby loose energy. The light itself will then have an energy equal to the energy lost. It may then hit something else and be absorbed. When this happens, the energy of the light, which is equal to the energy of the original energy lost by the emitter, is added to the energy of the thing it's hitting. In this way light is a carrier of energy. By the same token light can be a source of energy if the thing doing the emitting is not under anyone's control. So you can say that solar panels are powered by sunlight. You could also say that they are powered by the sun. You could even say that they are powered by nuclear fusion in the sun, but this isn't generally a useful thing to emphasize.

Earthling said:

Your questions are actually answerable, though I know Perfection/others could do better, if you really must get answers I might as well.

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Thanks. There is no "must" but I think the answers to such questions are important enough that they should be available to those with a modest understanding of the vocabulary.

The very first and very last statements are hardest to answer, but a start to an answer is: energy and momentum describe physical quantities which are perfectly understandable/observable/intuitive on a macroscopic scale.

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When you say "describe physical quantities" do you mean just mathematical values or does the "physical" refer to something that is not energy or momentum? Are you saying: The energy = 6 or are you saying the energy of A = 6? It you mean the latter, then A would be something different than energy. What?

I fully agree that we can see the results of what happens when 6 energy is released at some macro level.

I need to go to bed, but will come back to this tomorrow. Thanks for your effort.

Thanks Souron. I'll reply tomorrow to you too.

Birdjaguar said:

Thanks. There is no "must" but I think the answers to such questions are important enough that they should be available to those with a modest understanding of the vocabulary.

When you say "describe physical quantities" do you mean just mathematical values or does the "physical" refer to something that is not energy or momentum? Are you saying: The energy = 6 or are you saying the energy of A = 6? It you mean the latter, then A would be something different than energy. What?

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Replace energy with size.

The size = 6 for the chair or size of chair = 6. What's the difference?

Energy is a quality of something. It is not a thing. Just like size is not a thing.

I also suggest learning Newtonian mechanics.

Momentum is just the name given to the property of matter that it takes more energy to accelerate/decelerate a large or fast moving object.

Birdjaguar said:

What are the assumptions in all this and what is derived from those assumptions? There must be some starting place.

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You're right, there must be some starting place, and there is: There are two fundamental assumptions concerning energy and momentum:

- The laws of physics are time invariant. That means the result of an experiment does not depend on whether I do it today, tomorrow or next year (If it is done under the exact same conditions)

- The laws of physics are invariant to spacial translations. The result of an experiment does not depend on where it is done. (Again if i can create the exact same conditions in all the places).

From these two assumptions one can derive mathematically, that there are two quantities that are conserved, i.e. if one sums up these quantities over all objects this will aways give the same result. The quantities come with rules how to calculate them and have been called energy and momentum. (There are other symmetries which lead to other conservation quantities, but we're not talking about them)

We can use these calculation rules to assign properties called "energy" and "momentum" to any object we make up. I say make up, because all the objects we think in are just concepts we use to describe nature. We tend to think of particles as well "particles", but if we try hard enough we can make every particle to do things that do not fit into the particle concept. But we can also describe things that are clearly not particles as particles, because there are collective excitations that act as if they were particles.

Thus to ask, whether energy and momentum "physically exist" ore "are real", you first have to define what "physically exist" means. Energy and momentum are fundamental concepts to our description of the universe, the same as particles or fields. So you need those to describe nature. Whether that means, that particles, fields, momentum and energy "physically exist" is a philosophical debate, that probably strongly depends on definitions.


That's also the case with this question:

If particles are only probabilities until we observe them, then what are they while unobserved? Are they "real" in that state? Do they even exist while unobserved?

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We can always assign the term "particle" to a wave packet, even if it is unobserved. So in that sense they always exist. However, "particle" is just a description of the weird physics going on, so in another sense they don't exist and are just a description of something more fundamental.

If particles are only probabilities until we observe them, then what are they while unobserved? Are they "real" in that state? Do they even exist while unobserved?

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I read a book recently (can't recall which one, at the moment) that tried to explain the whole observer thing a little more. The book was about information theory, and postulated that interactions between particles and fields amounted to observations. This eliminated the popular misconception of the need for human observers for the collapse of the wave function; thusly particles, states, and fields are indeed real entities that exist independently of observation.

It made sense to me when I read it, which makes me wonder if it is in fact true, since events on the quantum level are often at odds with common sense

I have to agree with Perf in that I wouldn't try explaining this stuff without Physics 101 under the belt.

You need: 1. vectors to appreciate particles, 2. waves to appreciate the other stuff. Even if you drop the calculations, you still need to appreciate the variables, which are the language, as Perf stated.

The alternative would be to go to some kind of animated applet.

peter grimes said:

I read a book recently (can't recall which one, at the moment) that tried to explain the whole observer thing a little more. The book was about information theory, and postulated that interactions between particles and fields amounted to observations. This eliminated the popular misconception of the need for human observers for the collapse of the wave function; thusly particles, states, and fields are indeed real entities that exist independently of observation.

It made sense to me when I read it, which makes me wonder if it is in fact true, since events on the quantum level are often at odds with common sense

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This is only partly true. I think it is a misconception, that somehow humans are needed as observers. After all, humans rarely observe quantum physics themselves, but have some measurement device to do that for them. And if this device is automated it shouldn't make a difference, whether I am in the lab or not (Well, except for me moving around my seat and thus altering the magnetic field...).

However, the notion that every interaction with particles or fields amounts to an observation is also wrong. Particles and fields can interact with each other without causing an observation, which would destroy the quantum state. The whole field of quantum information processing would make no sense if each interaction destroyed the state. But the condition for that is that the interaction is reversible. As long as the processes are reversible you can think of doing everything backwards to get to the original state again (there are actually techniques exploiting this, e.g. spin-echo). However as soon as the process is irreversible, entropy is created and information is lost, you cannot get back to the original state no matter what you do and the state is destroyed and thus an observation has happened. For example if you detect a single photon on a photodiode, there is no way to reverse this: the photon cannot come out anymore and the quantum state the photon was in is destroyed, leaving only partial classical information in the photodiode signal.

I had an unexpectedly long day at work today and am just digesting all these great posts. thanks very much. Souron, your link was especially good.

Lord Olleus said:

As to what assumptions physicists make the answer is none. Physics is not deduced but observed in experiments. That is why it is different to mathematics. The mathematical deduction is there simply to indicate what the next experiment should be and to make predictions which can then be tested.

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This is wrong. Physicists make assumptions all the time. Physics would not be even possible without the fundamental assumption that there are actually laws of nature to discover instead of nature just being random behavior of a higher being or something similar.

And all theories have some underlying assumptions needed for the theories to work. And because positive proof of such assumptions is not possible in science one can only assume things and look for violations of these. If such a violation is found one has to give up that assumption, but as long as there is no counterexample certain things have to be assumed.

And experiments do not work without assumptions either. For example you have to assume, that the results you get, which will always be a subset of all things that happened are a fair sample and that the things you did not observe are behaving according to the same rules.

And I already provided the two underlying assumptions of energy and momentum.

But if you really want them here:

Momentum = mass * velocity
Work done = Force {integrated over} distance
Potential energy = - {Sum of} All work done on particle from an arbitrary point
Kinetic energy = 1/2 * mass * velocity^2

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If you are going to provide formulas, at least provide the relativistic four-momentum and not the depreciated Newtonian formulas:

( E , p ) = (m / sqrt(1 - v^2) , m*v / sqrt(1- v^2) )

Where E is the energy, p is the momentum vector, m is the resting mass and v is the velocity vector in units of the speed of light.

And the corresponding Lorentz invariant:
E^2 - p^2*c^2 = m^2*c^4

Part of this is an attempt to separate what is only math from what “physically exists” and see the boundaries between the two.

Birdjaguar said:

How do energy and momentum relate to matter/particles in a physical sense like quarks relate to proton, protons relate to atoms etc.?

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Well, particles have a kinetic energy. It's directly proportional to the square of the velocity of said article. You can also talk about the relativistic energy of the particle, which is proportional to the mass of the particle. There are also potential energies depending on charges, environment that the particle is in, etc. Momentum is simply the mass of the particle times the velocity.

Birdjaguar said:

Are energy and momentum only concepts that show up when we look at particles as equations?

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This is rather a meaningless question. Energy and momentum are real things, which are expressed as equations. It's like asking "is the direction to the neighborhood grocery store only a concept that shows up when we look at a map?"

Birdjaguar said:

If particles are only probabilities until we observe them, then what are they while unobserved? Are they "real" in that state? Do they even exist while unobserved?

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This is a profound misunderstanding of the HUP. The position of a particle is a probability which is inversely proportional to the accuracy in its momentum, and vice versa. The particle is always very real. It has nothing to do with observation.

Birdjaguar said:

If matter at the particle at level can only be described through mathematics, what is it that is being described?

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The particle.

Birdjaguar said:

Do energy and momentum have any other characteristics besides those shown through mathematics? If the answer is no, then, again, what does “exist” mean?

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I do not know of any properties of energy and momentum that cannot be expressed mathematically. Johnny has 4 apples. Susie takes away two apples. Johnny now has two apples. I have just expressed apples mathematically. That does not mean apples do not exist.

Birdjaguar said:

If energy and momentum exist as something real and not just as mathematical concepts (which may express their characteristics) then what are they?

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Energy is the ability to do work. Momentum is the product of mass and velocity.