4 four momentum energy component direction

[whatif]

Energy and momentum are different quantities, of course. The reason why 4 vectors are introduced in relativity, is not just to have a common units. What is far more important is that time and space individually do not transform properly under Lorentz transformation. You have to transform them together. Hence it becomes natural to talk about spacetime, and to define position 4-vector, where the 0th component represent the timelike coordinate of an event. But you still keep in mind that space and time are not the same, as you know intuitively. The same applies to energy and momentum. They cannot be properly transformed individually, but if you define a 4-vector, which you construct using the classical 3D momentum of a particle plus using its energy as the 0th component, the whole new beast will transform properly under Lorentz transformation. I don't see any reason why we should regard energy as having any direction...

… for consistency.

Langauge m2 = E2 – p2 is a relationship between the components of 4 momentum. The timelike component is called energy, not timelike momentum component. For the purposes of the equation we are distinguishing between energy and momentum. The 4 vector does not make this distinction, in the sense that we may not call the timelike part of the vector, energy (mathematically it works). That is OK, so long as we keep track of what is being done.

Does the 4 momentum vector have units of kilograms? I ask because I would think so but you might say no. If so, then these units are a measure of energy in the spacelike direction and momentum in the spatial directions.

How is the timelike part of the 4 momentum vector to be interpreted (what does it mean to have kilograms moving in the time direction)? The answer to this question is left hanging. You might be able to tell me. You might say you do not know, which would be OK. However, it should have meaning. If you cannot tell me then, although it would still difficult to make sense of, I suggest energy moving forward in time is the “obvious” interpretation. It would seem that making the timelike part of the 4 momentum vector, energy, would put 4 momentum energy on a par with how timespace is treated in terms of language and interpretation.

 

[whatif]

It is sloppy, but pretty reasonable and not too problematic.

I agree with you. However, I did it unwittingly and it seems to be extremely problematic to others.

I don’t think there is a wrong or right in this.

Others strongly disagree and insist that energy does not have direction. There has to be a definitive answer for the purpose of agreement. I think the answer is in explaining what it is that is moving forward in time (i.e. why it is different from kilograms of energy). It seems to me that, in effect, an decision has been to define energy as non directional.

 

[whatif]

The reason is because you can't, as you claim above, add components to get vectors.

I made no such claim in terms of what you understand "component" to mean. What I did in the first instance was to unwittingly use the word 'component' in a way that I did not realize had a specific restricted meaning. The way I meant it, using general usage, does not disagree with the principles that you are conveying to me. The way you mathematically try to explain it does not directly convey the distinction.
I willingly concede that there is good reason to use common language.

 

[PeterDonis]

Langauge m2 = E2 – p2 is a relationship between the components of 4 momentum.

Yes, but all of the quantities in that equation are scalars. None of them are vectors. So if you are going to call those quantities "components", then you are implicitly defining "components" to be scalars, not vectors.

Does the 4 momentum vector have units of kilograms?

If you choose that system of units, yes. Note that in that case, you will either need to use the same units for energy and momentum, or put in factors of $c$ where needed to make the units come out right.

It seems to be more common in the literature, or at any rate the classical relativity literature, to use either momentum or energy units for 4-momentum; in that case, again, you either need to pick the same units for all the components, or put in factors of $c$ as required.

In quantum field theory, the natural units of energy and mass are inverse length (because Planck's constant is taken to have no units).

How is the timelike part of the 4 momentum vector to be interpreted (what does it mean to have kilograms moving in the time direction)?

It's the energy in mass units. More precisely, it's the energy that the object would be observed to have by an observer at rest in the inertial coordinates being used.

You should not get hung up on the units; they're irrelevant to what we're discussing.

If you cannot tell me then, although it would still difficult to make sense of, I suggest energy moving forward in time is the “obvious” interpretation.

No, the "obvious" interpretation is that energy is 4-momentum in the time direction. And momentum is 4-momentum in the spatial directions. Momentum doesn't move. It's a property of the motion of something. Energy is just momentum in the time direction, so it doesn't move any more than ordinary momentum does. It just describes the "motion in time" of an object, the way ordinary momentum describes its motion in space.

 

[whatif]

So if you are going to call those quantities "components", then you are implicitly defining "components" to be scalars, not vectors.

I understand that and I was trying to make it clear that I understand that. Are you trying to say that I have defined energy to not be a vector? It is others that have implicitly defined energy to not be a vector and I am just showing that I understand. Where I am going is that energy could be treated as the timelike part of the 4 momentum vector and there is reason to do so.

Energy is just momentum in the time direction, so it doesn't move any more than ordinary momentum does.

Yes, OK, it does not move. However, I expect that you meant energy is just the magnitude of momentum in the time direction because otherwise you seem to be saying that energy does have direction.

No, the "obvious" interpretation is that energy is 4-momentum in the time direction.

That does not really explain anything meaningful because while it is correct it ignores that a distinction is made between momentum and energy, and is why I should get hung about units.

You should not get hung up on the units; they're irrelevant to what we're discussing.

Why are units irrelevant? Just because the same units are used does not mean the timelike part has the same character (if I may use that word) as the spacelike parts. A meter of time is different from a meter of space despite being measured in the same units. The speed of light, c, provides the relationship that facilitates the analysis of spacetime. Similarly, whatever units are used, a unit of that energy is different from that unit of momentum.

 

[lomidrevo]

(what does it mean to have kilograms moving in the time direction)?

What do you think it means for an object to move in the time direction?

I agree with you. However, I did it unwittingly and it seems to be extremely problematic to others.

Quite contrary, you look like the only one in this thread who is having troubles with the interpretation of the energy. Instead you would accept the more natural interpretation provided in the previous posts, you insist that it might have a direction. OK, it is free country, you can do it obviously, but: What would be the interpretation of the "direction"? Would be such definition anyhow helpful for solving problems? As far as the concept is not compatible with observations/experiments, how it can be useful? It is meaningless...

 

[whatif]

What do you think it means for an object to move in the time direction?

As PeterDonis pointed out having direction does not mean it moves. The unit kilogram is a measure of energy so it makes sense to say energy is pointing in the direction of time. It makes more sense, to me, to regard the timelike component 4 momentum as energy than simply stating that the "obvious" interpretation is that energy is 4-momentum in the time direction (because a kilogram of energy is not the same as a kilogram of momentum, or whatever units you use).

Your second quote comes from a post in reply to someone who treats energy as having direction. Also, you are taking the second quote out of context.

What would be the interpretation of the "direction"? Would be such definition anyhow helpful for solving problems? As far as the concept is not compatible with observations/experiments, how it can be useful? It is meaningless...

The direction is already defined by the timelike part of 4 momentum. It is completely compatible with observations/experiments as far as I can see. It is a matter of interpretation and it would be useful by way of consistency with the relationship of time with space and incorporating that a unit of energy is not the same as that unit of momentum.

Your intuition is probably working backwards from the formal mathematical definition, assigning physical significance to the "vanishing" of the time component. This is exactly backwards from the mathematical approach, which treats vectors as abstract entities with abstract properties, and the "frame of reference" of an observer is a physical interpretation of the mathematical representation of a set of mutually orthogonal basis vectors associated with the observer.

Maybe, I do not know but I am not convinced that is the source of a problem. However, it implies the physical interpretation must mean that energy must be treated as it is. I think that the physical interpretation, as is, incorporates an implied definition that energy is a component and nothing more (probably to simply correspond with the classical idea of energy being a scalar). I can live with that and I have already written so. Since then it has not been that I am insisting that energy has direction but putting a physical interpretation that seems to be reasonable (and more consistence, in my view).

 

[whatif]

It makes more sense, to me, to regard the timelike component 4 momentum as energy than simply stating that the "obvious" interpretation is that energy is 4-momentum in the time direction (because a kilogram of energy is not the same as a kilogram of momentum, or whatever units you use).

I made two mistakes here:

1. Old habits die hard. I used component where I should not have.
2. PeterDonis wrote:

   No, the "obvious" interpretation is that energy is 4-momentum in the time direction.

   I think he meant to write: 'No, the "obvious" interpretation is that energy is the magnitude of 4-momentum in the time direction.' Otherwise, he appears to be agreeing with me.

I meant to write that it makes more sense, to me, to regard the timelike part of the 4 vector, 4 momentum as energy than simply stating that the "obvious" interpretation is that energy is the magnitude of the 4 vector, 4-momentum in the time direction (because a kilogram of energy is not the same as a kilogram of momentum, or whatever units you use).

 

[PeterDonis]

Are you trying to say that I have defined energy to not be a vector?

In the particular statement you made that I responded to, yes.

Where I am going is that energy could be treated as the timelike part of the 4 momentum vector and there is reason to do so.

Both viewpoints are reasonable, and neither one is "right" or "wrong". You can adopt whichever one seems to be most helpful for a particular problem. There is no reason why one viewpoint must always be taken.

Just because the same units are used does not mean the timelike part has the same character

That's correct, and that's exactly why you shouldn't get hung up on units: because the difference between "timelike" and "spacelike" is not that we usually use different units to measure them. We can use the same units to measure them and they're still different. So the difference must be something else other than the units; hence, you shouldn't get hung up on the units because they're irrelevant to figuring out what the difference is.

 

[PeterDonis]

I think he meant to write: 'No, the "obvious" interpretation is that energy is the magnitude of 4-momentum in the time direction.'

No, I made the statement ambiguous on purpose, to illustrate that both interpretations are useful, and neither one is "right" or "wrong".

 

[PeterDonis]

the difference between "timelike" and "spacelike" is not that we usually use different units to measure them

both interpretations are useful, and neither one is "right" or "wrong".

In fact, to emphasize that both interpretations are useful, consider the following: the difference between "timelike" and "spacelike" is not units, and it's also not that we normally consider energy a scalar and momentum a vector. We can consider energy to be a vector pointing into the future, i.e., "momentum in the time direction", and the difference between timelike and spacelike is still there. So the difference can't be related to the difference between scalar and vector either.

 

[whatif]

Energy doesn't have a direction, and "the direction of time" (i.e., "into the future") is not the energy, or the direction of the energy.

No, I made the statement ambiguous on purpose, to illustrate that both interpretations are useful, and neither one is "right" or "wrong".

I know there have been problems with my language but I do not see the ambiguity because it specifically gives energy direction.
Anyway, thank you, that explains why you have appeared to me to agree and disagree in different messages.

the difference between "timelike" and "spacelike" is not units, and it's also not that we normally consider energy a scalar and momentum a vector. We can consider energy to be a vector pointing into the future, i.e., "momentum in the time direction", and the difference between timelike and spacelike is still there. So the difference can't be related to the difference between scalar and vector either.

That is an abstract mathematical explanation that effectively allows two valid but different physical interpretations (in one energy cannot be a vector by implicit or explicit definition and in the other energy is a vector).

Also, some have been saying that the component (scalar) is just a number. If it is just a number then units have to come into it in another way. If the units are considered to be part of the component (scalar), then it is not just a number. Either way, the timelike momentum has a direction and the direction is in the direction of time (and kilograms associated with a vector is not the same as kilograms only associated with a scalar).

No, the "obvious" interpretation is that energy is 4-momentum in the time direction.

If the timelike momentum is not energy then what is it (rhetorical question)? Just calling it momentum in the timelike direction is nebulous. Both the timelike and spacelike parts are called momentum even though the same units of timelike momentum have a different meaning when applied to spacelike momentum.Anyway, attaching a scalar to a vector gives meaning to the vector, including units. I still have to get my head around kilograms in the timelike direction. However, I get it and in the end my initial understanding of was valid but language was a hangup.Thank you.

 

[whatif]

I don't think that they would claim in text that whole 4 momentum ("including direction") represents energy of the particle.

I am not sure what is meant by whole 4 momentum. The discussion has been about timelike momentum (the energy part).

Actually, Taylor and Wheeler call 4 momentum, 'momenergy' and describe energy as the "Time Part" of momenergy. They do so in headings and the text. From Taylor and Wheeler text:

Energy is only the time part of the momenergy 4-vector.

So, in the text, they actually do treat energy as a vector part, the timelike part, and that includes direction.

That would be your own definition of energy. Whenever any other physicist talks about "energy", you would say "magnitude of energy" etc. It would simply be different terminology.

That comment came in response to a reference to Taylor and Wheeler. Taylor and Wheeler refer to energy as timelike.
Anyway, I get it.

 

[lomidrevo]

I fully agree with the statement: "Energy is only the time part of the momenergy 4-vector." That is what I claimed in my previous posts.

So, in the text, they actually do treat energy as a vector part, the timelike part, and that includes direction.

But I don't agree with this conclusion. Even though you can construct a vector as a linear combination of basis vectors, the component itself is not a vector. It is just a number representing the weight (or magnitude if you wish) of the corresponding basis vector.

In my opinion, another reason to look at energy as it is just a number (you may notice I am not saying scalar, because it is not invariant under Lorentz transformation): In a low speed limit, the special relativity must reduce to Newtonian mechanics. Where the "direction of energy" disappeared? Why you now got just a real number instead of a vector? It is inconsistent...

Energy is very closely related to time coordinate: conservation of energy is related to the symmetry of physics under translation in time. Similar relationship is between conservation of momentum and the space-translation symmetry. So that may give you a hint why in the 4-momentum you can find the energy as the time-like component and components of the classical 3D momemntum as the space-like components. But again, this doesn't make the energy being a vector quantity.

In summary, I don't see any benefits of considering the energy as a vector quantity. And probably that is the reason why you never see symbols like $\vec E$ to represent energy in textbooks.

That comment came in response to a reference to Taylor and Wheeler. Taylor and Wheeler refer to energy as timelike.

That's OK, we all agree on that.

 

[whatif]

"Energy is only the time part of the momenergy 4-vector." That is what I claimed in my previous posts.

That agrees with Taylor and Wheeler but says that energy if a part of a 4 vector (it misses the word 'component').

Energy is the timelike component of the momentum 4vector.

That is was you wrote in a previous post and is not the same thing as my quote from Taylor and Wheeler. The Taylor and Wheeler quote does not have the word 'component'.

Even though you can construct a vector as a linear combination of basis vectors, the component itself is not a vector.

Knowing the meaning of the word 'component' as used in this context that is a correct statement. At the same time, that is not the point; the point being whether you treat energy as a vector, being the timelike momentum. I understand and see the point of those who have said that neither interpretation is right or wrong (but at the moment I would regard the timelike momentum to be energy whether it is called that or not).

In my opinion, another reason to look at energy as it is just a number

Energy has units. It is not just a number.

In a low speed limit, the special relativity must reduce to Newtonian mechanics.

At low speeds, Newtonian mechanics approximates relativistic mechanics. Also, timelike parts (timelike vectors) are irrelevant in Newtonian mechanics and need to be given a physical interpretation.

In summary, I don't see any benefits of considering the energy as a vector quantity.

The benefit in my view is that it is a better physical interpretation. Others have said that each interpretation is useful.

 

[lomidrevo]

That is was you wrote in a previous post and is not the same thing as my quote from Taylor and Wheeler. The Taylor and Wheeler quote does not have the word 'component'.

Both statements tells the same thing:
"Energy is only the time part of the momenergy 4-vector." = "Energy is the timelike component of the momentum 4vector."

Energy has units. It is not just a number.

I haven't said it is a dimensionless number. It was said to you several times before, that units are irrelevant in the context of this discussion. If you think it is relevant, then you didn't get the point yet.

Also, timelike parts (timelike vectors) are irrelevant in Newtonian mechanics and need to be given a physical interpretation.

I think you mean timelike component of a vector. So you are claiming that energy is irrelevant in Newtonian mechanics?

The benefit in my view is that it is a better physical interpretation.

You can do it. You can actually define any physical quantity as you want, but if it is not useful in solving problems, nor it is conceptually natural, then there is no point to define such quantity. Just don't be disappointed if you don't find "vector energy" in any paper or textbook.

 

[PeterDonis]

That is an abstract mathematical explanation that effectively allows two valid but different physical interpretations (in one energy cannot be a vector by implicit or explicit definition and in the other energy is a vector).

These aren't two different physical interpretations of what's actually happening; they're just two different ways of assigning a meaning to the term "energy". "Energy" is just a word. You can't change the physics by changing the meaning you assign to a word.

some have been saying that the component (scalar) is just a number. If it is just a number then units have to come into it in another way. If the units are considered to be part of the component (scalar), then it is not just a number.

Again, you're getting hung up on words instead of looking at the physics. "Just a number" simply means "a scalar", i.e., "has no direction". Units are irrelevant, as we've already seen.

You are making things much more difficult than they need to be by getting fixated on particular words instead of looking at the physics.

If the timelike momentum is not energy then what is it (rhetorical question)?

You can use "energy" to mean "the timelike momentum", meaning the vector that you get by multiplying the timelike component of 4-momentum, a scalar, by the timelike basis vector of whatever coordinate system you are using. That won't change what it is at all; it's just your choice of words. You can't change the physics by changing the words you use.

Physically, the question is why you would want to focus attention on this particular vector--i.e., not the 4-momentum vector itself, but the vector you get by multiplying the timelike component of 4-momentum, a scalar, by the timelike basis vector of whatever coordinate system you are using. As far as I know, this particular vector does not play any role in any physical calculation. So I'm having trouble understanding why you are so fixated on it.

I am not sure what is meant by whole 4 momentum.

Perhaps this is part of your problem. The whole 4-momentum, a 4-vector, has two important properties:

(1) It points in the direction in spacetime that lies along the object's worldline, i.e., its direction, in spacetime, is the same as the direction in spacetime in which the object's worldline points (more precisely, the future direction of the worldline).

(2) Its magnitude is the rest mass (also called the invariant mass, which is more relevant in this discussion) of the object.

 

[pervect]

If we're trying to make things more precise, Energy-as-a-number is the time component of an energy- momentum 4-vector in some particular basis. It's under-specific to say that it applies to just any basis without some addditional restriction, as I believe it's quite possible to have multiple timelike vectors in a basis. It's not very common to chose such a basis, but it's possible. (Afterthought: I should probably add, that this may be an advanced topic, it's not at all uncommon in an introductory textbook to assume that the basis vectors are ortohgonal and of unit length. With these additioanl assumptions, it's not possible to have more than one timelike basis vector). Thus to define the notion of Energy-as-a-number, we need to pick out _one particular timelike basis vector_, then the dot product of the energy-momentum 4-vector and this particular choice of timelike basis vector determines Energy-as-a-number.

The idea of Energy-as-a-vector says that we multiply the chosen basis vector, that we used to define the energy-as-a-number, by the number. But we still can't find "energy-as-a-vector" without picking a particular basis vector. A different choice of basis vector yields both a different Energy-as-a-number and a different Energy-as-a-vector. So we can't skip the step of picking a particular timelike basis vector to define either notion of energy.

There also seems to be some argument about what we mean when we use the word "energy". I would tend to agree that with the observation that most authors mean "energy-as-a-number" when they say energy. It's a bit of a reach to assume that a reader would interpret the word "energy" as "energy-as-a-vector", you may or may not be able to convince a particular reader to go along with that word choice.

 

[pervect]

While I'm thinking about it, let me add a less mathematical example of why we need to choose a particular timelike basis vector, and the physical significance of doing so. Suppose we have a 1kg weight, that is "at rest". Then we would generally say that the energy associated with this 1kg weight is given by the famous formula E=mc^2.

Now, suppose this weight is moving at 3/5 the speed of light. Then the energy of that moving weight is larger than it's rest energy - if you go through the numbers, it turns out to be $\gamma \, m \, c^2$, and when v=3/5 c, $\gamma = 5/4$.

Now, what's the difference between a weight that's "at rest", and one that is "moving at 3/5 c"? The difference is just in our choice of reference frame - in one reference frame, the weight is stationary, in another, it's moving. So, we can't tell what the energy of the weight is until we make a choice of reference frame.

This talks about concepts that may seem more intuitive, observers, rather than reference frames. The link between the two is when we realize that we can specify an observer by specifying a set of 4 basis vectors (usually an orthonormal set of basis vectors) that are associated with that observer.

 

[Dale]

I believe it's quite possible to have multiple timelike vectors in a basis. It's not very common to chose such a basis, but it's possible

Good point. It is also possible to have a basis comprised entirely of null vectors. Usually we are thinking in terms of tetrads which, by definition, consist of one timelike and three spacelike orthonormal vectors. But the set of all basis vectors is larger than the set of all tetrads.

 

[PeterDonis]

I believe it's quite possible to have multiple timelike vectors in a basis.

In general, yes, it is, but any such basis cannot be orthonormal, or even orthogonal. Any set of four orthogonal vectors in spacetime must consist of one timelike and three spacelike vectors.

 

[SiennaTheGr8]

I'm surprised that the term component vector hasn't come up in this thread. See "Pitfall Prevention 3.2" here: https://books.google.com/books?id=XgweHqlvtiUC&pg=PA59

 

[Dale]

In general, yes, it is, but any such basis cannot be orthonormal, or even orthogonal. Any set of four orthogonal vectors in spacetime must consist of one timelike and three spacelike vectors.

All null vectors are sort of orthogonal in a kind of “technicality” sense

 

[robphy]

1. All null vectors are sort of orthogonal in a kind of “technicality” sense

   
   Each null vector is Minkowski-orthogonal to itself... but generally not to other null vectors.

 

[Dale]

Each null vector is Minkowski-orthogonal to itself... but generally not to other null vectors.

D’oh! You are right. I can’t believe I never noticed that.

 

[whatif]

"Energy is only the time part of the momenergy 4-vector." = "Energy is the timelike component of the momentum 4vector."

So you are insisting that ‘time part’ equates to ‘timelike component’ and there is no such thing as a timelike vector. Is that defined anywhere, in particular, anywhere that I should think that is what Taylor and Wheeler meant?

I haven't said it is a dimensionless number. It was said to you several times before, that units are irrelevant in the context of this discussion.

Just a number is just a number. Numbers do not mean anything without application. Units are irrelevant to the abstract mathematics, so long as the units have been made alike beforehand (e.g. kilograms for both energy and momentum). So long as the concepts are understood, the mathematics is made simpler. After the abstract mathematics is done, units have to be reapplied for physical meaning, and it has to be understood that a kilogram of energy is not the same as a kilogram of momentum (and a kilogram of the space part of the 4 momentum, 4 vector, is not the same as a kilogram of the time part of part of the 4 momentum, 4 vector).

I think you mean timelike component of a vector. So you are claiming that energy is irrelevant in Newtonian mechanics?

By your interpretation of timelike, the word ‘component’ is redundant here (see first quote). Just saying (you might just be reinforcing the point).

I do not mean timelike component of a vector and I am not claiming energy is irrelevant to Newtonian mechanics. I mean that ‘timelike’ is a notion that applies to relativistic mechanics and not Newtonian mechanics. Ideas of Newtonian mechanics are revised in relativistic mechanics.

 

[whatif]

"Energy" is just a word. You can't change the physics by changing the meaning you assign to a word.

You are right, they can be called apples and oranges and all kinds of fruit and it makes no difference to the mathematical relationships. Likewise, there are not really 2 interpretations, each of which has its own use. We just choose words that help keep a sense of what we are talking about.

Perhaps this is part of your problem. The whole 4-momentum, a 4-vector, has two important properties:

(1) It points in the direction in spacetime that lies along the object's worldline, i.e., its direction, in spacetime, is the same as the direction in spacetime in which the object's worldline points (more precisely, the future direction of the worldline).

(2) Its magnitude is the rest mass (also called the invariant mass, which is more relevant in this discussion) of the object.

That is what I thought. Given that understating, “whole 4 momentum” did not seem helpful in the context in which it was raised.

 

[whatif]

I'm surprised that the term component vector hasn't come up in this thread. See "Pitfall Prevention 3.2" here: https://books.google.com/books?id=XgweHqlvtiUC&pg=PA59

I started with that term and it was the source of a big problem. I found the term in your reference. Where I found it in the text of your referrence, it was written in italics to distinguish it from its other use of the word ‘component’. The term makes good sense, however, the word ‘component’ here is restricted to correspond with the other meaning of the word ‘component’ used in your reference. In other words, the term 'component vector' and its meaning is effectively not acceptable here.

 

[PeterDonis]

In other words, the term 'component vector' and its meaning is effectively not acceptable here.

It's not that the term is "not acceptable" here, it's that we didn't understand what you meant by it earlier in the thread. It helps a lot if you give a reference that uses the term the way you are using it, as @SiennaTheGr8 did. As you note, that reference explains exactly the distinction between "component vectors" and "components" that was discussed earlier in this thread.

 

[Dale]

I'm surprised that the term component vector hasn't come up in this thread.

I am glad you posted that. I didn’t know the term.

 

[whatif]

It helps a lot if you give a reference that uses the term the way you are using it, as @SiennaTheGr8 did.

It is the very first term used. I then used the word 'component' in that context, which created an issue. Why would I give a reference when I do not know that there is a necessity (especially when I thought it was commonly used term).

(Actually, the meaning is acceptable here but I would try and avoid the term if I knew beforehand the problem that would cause with the word 'component'.)

 

[PeterDonis]

It is the very first term used.

In that particular textbook, yes. I have not seen it in other textbooks I have read. (Apparently @Dale hasn't either given his post a little bit ago.)

Why would I give a reference when I do not know that there is a necessity

The fact that you were running into problems getting others to understand what you were saying might have helped to indicate that a reference would be helpful.

(especially when I thought it was commonly used term).

The fact that you were running into problems getting others to understand what you were saying, particularly since three of them were Mentors, might have helped to indicate that the term was not as commonly used as you thought it was.

 

[whatif]

I'm surprised that the term component vector hasn't come up in this thread.

It is the very first term used. I then used the word 'component' in that context, which created an issue.

In that particular textbook, yes.

Not in the textbook but the very first term I used at the start of this thread (/conversation/in the first message). I have never known about that textbook before now. It is also a term that in common English conveys the correct concept for the topic.

I fully appreciate the importance of using common terminology, that my language has been a problem and that I have made mistakes. I tried to not use the word when I understood the problem. On the other hand, I would expect the experts to pick up where I was using a word that made sense in common English and used appropriately in that sense, but had a special meaning to them rather than just saying I was wrong and/or confused. (Its a bit like computer program writers writing the help for a computer application that is not much help to anybody but other computer programmers).

Anyway, it has been instructive to me, if that is any consolation.

Thank you.

 

[SiennaTheGr8]

In that particular textbook, yes. I have not seen it in other textbooks I have read. (Apparently @Dale hasn't either given his post a little bit ago.)

Just had a quick look at some other popular university physics texts. Young/Freedman (13th) use the term component vector. Halliday/Resnick (9th) use vector component (as opposed to scalar component, which is what they always mean by plain component).

While we're on the subject of terminology...

The "parallel" / "antiparallel" vector nomenclature bugs me. Better would be "codirectional" / "contradirectional," so that "parallel" can be used unambiguously as a catchall for both. Here's a snippet from p. 76 of that Young/Freedman edition, regarding the resolution of the acceleration vector into components parallel and perpendicular to the velocity vector:

If the speed is decreasing, the parallel component has the direction opposite to $\vec v$ ...

This is doubly sloppy. First, they use component where they mean component vector. Second, they're using parallel as a catchall, but their earlier definition of parallel vectors was restricted to vectors that point in the same direction. According to their own nomenclature, the component vector in question is antiparallel to $\vec v$, not parallel.

 

[PeterDonis]

Not in the textbook but the very first term I used at the start of this thread

Ah, got it.