What happens to the momentum of a moving mass converted to energy?

Factual Questions
21

[QUOTE=Exapno Mapcase]
Mass and energy are exactly the same things. They just manifest in different forms.
[/QUOTE]
Better yet, mass is energy that has the particular property of inertia, or resistance to change in velocity. Of course, an internally-reflective box of photons has mass, by this definition, so mass can be a property of a closed system as well as an inate property of components. Matter–that is, energy that has invariant or fixed mass–is (from a particle physics perspective) is composed of fermions, particles with a half-integer spin that are not able to occupy the same point in space simultaneously. It is possible for a fundamental particle and its antiparticle to combine destructively, turning the energy stored as invariant mass into photons, but Ring is correct in saying that this is only a local “mass defect”; if you do this inside of our hypothetical sealed box, and then shake the box to measure its inertia, it will remain the same as before the conversion.

Stranger

22

[QUOTE=Ring]
Well, as I’ve said many times before: Mass cannot be converted to energy.

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If you take one gram of matter and one gram of antimatter and put them together, you end up with what?

23

[QUOTE=Enola Straight]
If you take one gram of matter and one gram of antimatter and put them together, you end up with what?
[/QUOTE]

A different set of particles with the same total energy they started with.

24

[QUOTE=Exapno Mapcase]
A different set of particles with the same total energy they started with.
[/QUOTE]
And, enclosed within the same boundary, the same total inertia and momentum; in other words, the same amount of mass.

Mass and energy are properties of a system (including a system of one particle), not “things” in and of themselves.

Stranger

25

MikeS I’m afraid I must disagree with you on this one. In my opinion the phrase “mass can be converted to energy” represents the essence of crypticality(?)

Because of this terminology people get a mental picture of mass evaporating or something and out pops energy. This picture of the world is I think you must agree, total BS.

Imo it’s much clearer to say that the mass of a system (if you’re consistent in defining the system) is absolutely conserved. However one form of the system’s energy can be converted to another, and the individual particles that make up the system can change resulting in a local mass defect.

26

Again, you’re technically right but you’re arguing against decades of popular usage. That not only means that you will fail to change popular usage, but you will also confuse those who are trying to make sense of the popular usage.

It’s like arguing that begging the question can only mean an assumed premise. If nobody in popular speech ever uses the term that way then your reference to that usage without explanation will just cause everyone to go “huh?” rather than “of course, I concede your expertise in logic.”

The only way out is to explain both usages and clarify the differences explicitly.

BTW, I’m at least as much an expert in language as you are in physics, so by your logic you have to bow down to my rightness. :smiley:

27

I do bow down. I’m the world’s worst writer. I write awkward sentences and I haven’t a clue when it comes to punctuation. It’s truly terrible to be ashamed when I reread my own posts.I have great respect for people who can write well.

Nobody is ever going to make sense thinking of mass as a thing that turns into energy.

Popular usage also causes many to think that if you move fast enough you’ll turn into a black hole.

Mass is the magnitude of the Energy-Momentum four-vector and is absolutely conserved. Believe it or not this is not a tough concept to grasp. Any basic text on SR will explain it and people who know it will easily see the relation between mass, energy and momentum. E = mc^2 is not an identity.

28

Sir Denseness here. If the analogy of water being turned into vapor is valid, then why not matter turned into energy? Even if they are both two forms of the same thing, they have two names, indicating that they are different in some way. So, I’ll grant that the total amount of “stuff” doesn’t change when water evaporates, but I’d say - again, if that analogy is valid - that the water has turned into vapor. There is less water than before, although the total number of water molecules in both forms has not changed. And, I’m under the impression that when nuclear material fissions, the total mass of the sample you started with is less, explained by the fact that some of it is now in the form of energy. I need help.

29

[QUOTE=CC]
Sir Denseness here. If the analogy of water being turned into vapor is valid, then why not matter turned into energy? Even if they are both two forms of the same thing, they have two names, indicating that they are different in some way. So, I’ll grant that the total amount of “stuff” doesn’t change when water evaporates, but I’d say - again, if that analogy is valid - that the water has turned into vapor. There is less water than before, although the total number of water molecules in both forms has not changed. And, I’m under the impression that when nuclear material fissions, the total mass of the sample you started with is less, explained by the fact that some of it is now in the form of energy. I need help.
[/QUOTE]
This highlights why reasoning from analogy is just a poor means of deduction. An analogy is a comparison between two unlike things, suitable only for the purpose of illustration.

Matter is already energy, just bound into a form that has the property of a fixed inertia; indeed, one can make an comparison between electric charge in relation to electromagnetic forces, and and mass in relation to inertial and gravitational forces. Converting matter–fermions–into some other form of energy doesn’t change the total energy or inertial mass of the system enclosed and isolated within a boundary (i.e. it cannot radiate or otherwise transmit energy away from the system).

Stranger

30

Saying mass is converted to energy is like saying monkeys evolved into humans. It’s not technically correct, but it gets the general idea across. What we used to call mass was obvious: mass was, well, stuff. When Einstein showed us that mass and energy were just a c^2 away from each other, it is then that we realized that they are just different forms of the same thing.

But if you go up to Area Man and start talking about conservation of mass-energy momentum vectors, they’re not going to understand or care. Area Man has only a basic idea of what “mass” and “energy” are, and no one really cares about the finer points except for physicists.

“Energy” is already a pretty vague word to begin with, meaning different things in a colloquial sense than in a physical sense. If we’re talking about nuclear power, then it’s true that mass is converted to energy in a colloquial sense, even if physically there’s no change in energy.

31

In what sense were the things which evolved into humans not monkeys?

Exapno, I understand what you’re saying about popular usage, but unfortunately, popular usage simply isn’t relevant here. It often happens in science that a particular concept is described using a pre-existing word, and the popular meaning of that word won’t exactly correspond to the technical meaning. If we’re going to be making scientific statements about “mass” and “energy” at all, we need to use the technical meanings of those words. And under the technical meanings of those words, mass is a form of energy, and the amount of energy in a closed system which is in the form of mass cannot change.

32

[QUOTE=Chronos]
In what sense were the things which evolved into humans not monkeys?

Exapno, I understand what you’re saying about popular usage, but unfortunately, popular usage simply isn’t relevant here. It often happens in science that a particular concept is described using a pre-existing word, and the popular meaning of that word won’t exactly correspond to the technical meaning. If we’re going to be making scientific statements about “mass” and “energy” at all, we need to use the technical meanings of those words. And under the technical meanings of those words, mass is a form of energy, and the amount of energy in a closed system which is in the form of mass cannot change.
[/QUOTE]

Sigh. I have never said that the people making the correct arguments shouldn’t *correct * popular usage. I keep saying that they must *acknowledge * popular usage and then *explain * why it doesn’t apply in this technical sense.

If you don’t acknowledge this you wind up with statements like **Ring’s ** “Mass is the magnitude of the Energy-Momentum four-vector and is absolutely conserved.” The four-vector? Are you kidding me? Most of people who are trying - sincerely, painfully trying - to understand have never gone past high school math. Heck, they didn’t pay much attention in the first place and don’t remember what they did learn. They never encountered the concept of vectors so it’s a gibberish word to them.

Analogy certainly has its dangers. CC, the part of the analogy I thought you would get is that when water vapor turns into ice, nothing intrinsic actually changes, just outward appearances. So they have two names. So do you. But whether you call yourself CC or your real name is mere appearance, not a real change.

Not everybody gets analogies. But some people do and they are useful pedagogical tools. Talking four-vectors to non-math people is not useful and can’t ever be.

33

C’mon Exapno I didn’t use any terms that the average lay person wouldn’t understand until the very last paragraph in my very last post.

Besides, it was your post I was responding to, and you certainly know what a four-vector is.

34

[QUOTE=Chronos]
In what sense were the things which evolved into humans not monkeys?
[/quote]

Monkeys are just as far removed from our earlier primate ancestors as humans are. They might share some superficial structural similarities with what we can figure out about those extinct animals from fossil remains, but that’s about it. The split between the branches goes back at least 30 million years, and is probably even farther back. Some species have changed hugely during that time, others have remained largely the same. Monkeys and humans are contemporary species. That’s why saying that humans evolved from monkeys is a useful but very inaccurate way to describe the real situation.

35

[QUOTE=Ring]
It means that for a system at rest the energy of the system is equal to its mass times the speed of light squared. In other words this is a system that has energy of E and a mass of m.

BTW the complete equation is

E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]2[sup]2[/sup]
[/QUOTE]

I’m missing something here. Why isn’t the last element of that equation … + 4p[sup]2[/sup]

36

[QUOTE=aldiboronti]
I’m missing something here. Why isn’t the last element of that equation … + 4p[sup]2[/sup]
[/QUOTE]

The 2 is merely a typo – it should be a c, making the whole equation E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup]

37

No, because “monkey” isn’t a species, it’s a whole big group of species. And by any definition of that group, the last common ancestor of humans and modern monkeys would itself be called a “monkey”.

Now, it’s fair to say that we’re not descended from rhesus monkeys, or capuchin monkeys, or Barbary monkeys. But we are descended from monkeys, just monkeys which are no longer extant.

38

[QUOTE=Chronos]
No, because “monkey” isn’t a species, it’s a whole big group of species. And by any definition of that group, the last common ancestor of humans and modern monkeys would itself be called a “monkey”.
[/QUOTE]

If you want to be nitpicky, then I can be too. “Species” in my sentence is plural. Notice I didn’t say “a species.” And our common ancestors could be called primates, but they sure as heck weren’t monkeys any more than modern lemurs are monkeys or great apes are monkeys.

39

[QUOTE=Sleel]
If you want to be nitpicky, then I can be too. “Species” in my sentence is plural. Notice I didn’t say “a species.” And our common ancestors could be called primates, but they sure as heck weren’t monkeys any more than modern lemurs are monkeys or great apes are monkeys.
[/QUOTE]
Humans and other Great Apes are joined to Old World monkeys in camcorders Catarrhini, which are joined with New World Monkeys in infraorder Simiiformes (colloquially, simians) which are one branch of order Primates, along with tarsiers, lemurs, and other miscellaneous prosimians. Although humans and other apes are not monkeys, it is unquestionable that, at least from a strictly cladistic assessment, the common ancestor of all would be regarded as a monkey, as are all more primitive and extinct species in this clade. They would be quite distinct from antecedent lemurs or other prosimians primates. It is entirely accurate to state that Homo sapiens, and indeed all Great Apes, as well as modern Old World and New World monkey species, are descended from the group of antecedent monkeys.

Stranger

40

Good grief, I didn’t mean for this to be a discussion of mass, momentum, and monkeys. Let’s get back on track here…

[QUOTE=UncleFred]
I don’t disagree at all but that helps me ralize how confused I am about this.

First, I am a bit confused as to the relationship of Kinetic Energy (.5Mvv) and Momentum (Mv) ; the fact that they both depend on Mass and velocity makes me wonder if Momentum is just some re-statement of Kinetic energy.

Actual calculations are further compounded by rotation; A spinning top, (or a flywheel) has rotational momentum and kinetic energy although the whole object’s center of gravity/mass has zero velocity.

Also; does heat represent a form of enery? Given two items with equal mass, velocity, and altitude ( same Ke and Pe and Pt, presumably) if one is 'hot" and the other is “cold”, does one have more total energy than the other?

It would have been just like my Physics professor to ask for a calculation of the total energy of a red-hot yo-yo taken to the top of a mountain, spun, and then thrown sideways.

I’m not sure what question I’m even asking here but I am seeing there is a lot to the subject of measuing the energy of a system.
[/QUOTE]

One fundamental way that energy is different from momentum is that momentum is a vector (it has a direction) while energy is a scalar (just a number).

Heat is indeed a form of energy, as given by the 1st law of thermodynamics:

Total energy = Q + W

where Q is the change in heat, and W is the work done on or by the system (this equation is really just stating the law of conversation of energy).

As for a hot vat vs cold vat, it doesn’t really make sense to say one has more energy than the other, as you’d have to specify what kind of energy. Just plain old energy isn’t a quantity you can ascribe to something except a whole system, and then all you can say is that it has the same amount it started with.

Energy can take on many different forms, like heat, work, electromagnetic, gravitational, rotational, pressure waves, and radiation. A moving object is said to have a high kinetic energy, but that doesn’t mean much until we introduce another object into the system for it to collide with, in which case the kinetic energy will probably be converted into heat, sound, and pressure waves rocking through the objects. In the end, the energy will be in different forms but put it all together and you’ll have the same amount you started with.