Can any physical quantity be vectorless?

[Addum]

Go easy on me please as I am just delving into the world of physics and the likes :D

I may have this completely misunderstood, so bear with me and correct me where I'm wrong please.

There are 2 types of currents, DC and AC. Correct?

AC stands for Alternating Current and DC stands for Direct Current.

In a Direct Current (DC) battery for instance, the electricity flows from a + (positive) to a - (negative) source, or in other words it flows in one direction from one place to another. With an Alternating Current (AC), the electricity flows back and forth reversing its direction periodically.

A vector is something that has magnitude and direction. Magnitude is another word for 'size' and direction is the motion of an object in relation to where it is traveling. So a DC current has a vector from + to -, but what about an AC current, if it is alternating back and forth? Does it have a vector? Not only that, but in relation to the Heisenberg Uncertainty Principle, it is impossible to know the exact location of anything at any given point in time, so does anything physical in the universe have a vector?

Basically what I'm trying to say is if something is alternating back and forth, does it have a vector or magnitude of direction? If so, is it only temporary until it reverses its course and changes direction? Say for example my vector (or direction of travel) is south at 2 MPH - then I travel north at 2 MPH, and repeat this infinitesimally, does my 'Alternating Current' (or better put Alternating Direction) have a vector? If so, does it only occur temporarily? If not, than I am vectorless, or I possesses no magnitude of direction in spacetime permanently, right? How can this be possible? Seems rather self-contradictory to me.

In order for something to exist, it has to have a location in space as-well as time. Right? Otherwise it has no vector or location and magnitude of direction. Hope what I'm saying makes sense and I spark some interesting conversations! :)

 

[anorlunda]

That's not such a bad question.

We usually depict AC as a rotating vector, like the hand of a clock.

Some things, like fields are spread out over lots of space and time. Yet they exist.

 

[Addum]

That's not such a bad question.

We usually depict AC as a rotating vector, like the hand of a clock.

Some things, like fields are spread out over lots of space and time. Yet they exist.

So was my conclusion or idea completely wrong since an AC current is a rotating vector? >.<

If so, would a non-rotating alternating current or direction be vectorless? Is it even possible for something to be vectorless?

 

[Khashishi]

Not all physical quantities are vectors. For example, the rest mass of an object is just a value with no direction. It's a scalar.

 

[phinds]

Is it even possible for something to be vectorless?

What direction is green? OK, maybe that's not fair since green is a characteristic, not an object. How about the charge on an electron, or better still, the charge on a sphere?

 

[anorlunda]

Temperature is a common example of a field with no direction.

 

[HelioGeo]

What direction is green? OK, maybe that's not fair since green is a characteristic, not an object. How about the charge on an electron, or better still, the charge on a sphere?

Is a sphere directionless? Anyway most of, if not all of the physical constants, dimensional or dimensionless, seems are presented vectorless.

 

[HelioGeo]

Temperature is a common example of a field with no direction.

Are you sure? What happens when you put a piece of ice on a hot pan?

 

[HelioGeo]

Not all physical quantities are vectors. For example, the rest mass of an object is just a value with no direction. It's a scalar.

To arrange this "rest" frame of reference, don't you refer to a direction?

 

[anorlunda]

Are you sure? What happens when you put a piece of ice on a hot pan?

Nice try. Heat flows from hot to cold, but that does not make a vector.

Consider the temperature of where you are right now. Does it have an up, down, north, south. East, west direction? The temperature is not the same every place but it has no direction.

Compare that with the wind field. Like temperature, wind has magnitude that varies from place to place. But wind also has direction.

 

[phinds]

To arrange this "rest" frame of reference, don't you refer to a direction?

No.

 

[HelioGeo]

Nice try. Heat flows from hot to cold, but that does not make a vector.

Consider the temperature of where you are right now. Does it have an up, down, north, south. East, west direction? The temperature is not the same every place but it has no direction.

Great, you are nearly saying flow doesn't make a vector? I'm in 39 C tropical area, I 'm cooling the airs around me, am I not making cold wind?

 

[HelioGeo]

No.

How?

 

[phinds]

Great, you are nearly saying flow doesn't make a vector? I'm in 39 C tropical area, I 'm cooling the airs around me, am I not making cold wind?

What does that have to do with vectors ?

 

[phinds]

How?

You misunderstand how PF works. If you make an unsubstantiable claim, it is not up to me to refute it, it is up to you to support it.

 

[HelioGeo]

What does that have to do with vectors ?

Temperatures are measures of energy state, energy flow has directions but not the state of the energy, if I interpreted correctly.

 

[HelioGeo]

You misunderstand how PF works. If you make an unsubstantiable claim, it is not up to me to refute it, it is up to you to support it.

To confess, I have difficulties in understanding mass, especially rest mass and mass in general. Why should mass, an energy equivalent, has no direction?

 

[phinds]

To confess, I have difficulties in understanding mass, especially rest mass and mass in general. Why should mass, an energy equivalent, has no direction?

HUH ? You are conflating two different posts that have nothing to do with each other. Look back. My "no" was in answer to your question about frames of reference, nothing to do with mass even though you mentioned mass in your earlier post. Mass ALSO has no vector but that's a separate issue.

Look, a frame of reference is just a set of arbitrarily defined coordinates. You may choose, for example to assign your chair as a frame of reference. If you wanted to fully explicate it, you would say perhaps that your personal forward direction was the X axis and your up direction was the Z axis and off to your left was the Y axis. Now, in the rest frame of the chair, which is also your rest frame, assuming that you are not fidgeting too much, you are at rest and your mass in that frame of reference is your rest mass. What does that have to do with vectors?

If you think that the XYZ coordinate system is a set of vectors as regards the point of this thread then you are completely missing the point of the thread. Your rest mass has no vector.

 

[phinds]

Temperatures are measures of energy state, energy flow has directions but not the state of the energy, if I interpreted correctly.

You are getting too far afield. Think simply of a sold body with a steady temperature, the same as that of its surroundings. Where's the vector? There IS a value for the temperature but there is no vector associated with it.

 

[phinds]

@HelioGeo you may think we are being rough on you, but this is a serious science forum and poor arguments are jumped on. It's nothing personal. Attacks are only against statements/arguments, not people.

 

[HelioGeo]

@HelioGeo you may think we are being rough on you, but this is a serious science forum and poor arguments are jumped on. It's nothing personal. Attacks are only against statements/arguments, not people.

I would not associate physics to personal. Personal opinion does not change Physics!

 

[Khashishi]

Are you sure? What happens when you put a piece of ice on a hot pan?

You are thinking about the gradient of the temperature. The gradient of the temperature is a vector field. The temperature itself is not.

 

[Nugatory]

Are you sure? What happens when you put a piece of ice on a hot pan?

You are confusing the temperature with the gradient of the temperature. The first is a scalar, the second is a vector.

One way of telling the scalars and the vectors apart is to ask yourself "How many numbers does it take to specify the value at a single given point?"; the answer will be "one" for a scalar and "three" for a vector. For example: The temperature at a single point is given by a single number, whatever a thermometer placed at that point reads; this is a scalar. The velocity of an airplane requires three numbers: rate at which the latitude is changing, rate at which the longitude is changing, rate at which the altitude is changing; this is a vector.

 

[FrankL]

Kinetic energy is an example of a physical quantity with no direction. A 1kg ball traveling right at 10 metres per second will have the same KE if it was traveling left at 10 metres per second (or any other direction for that matter). As others have said, charge is not a vector; the same can be applied to other fundamental properties, like mass, quark colour, and perhaps strangeness.

Angular displacement is not a vector because it does not obey the commutative law of vector addition. That is, you cannot add angular displacements the same way you add vectors (or natural numbers for that matter); the order makes all the difference!

 

[HelioGeo]

Kinetic energy is an example of a physical quantity with no direction. A 1kg ball traveling right at 10 metres per second will have the same KE if it was traveling left at 10 metres per second (or any other direction for that matter). As others have said, charge is not a vector; the same can be applied to other fundamental properties, like mass, quark colour, and perhaps strangeness.

Angular displacement is not a vector because it does not obey the commutative law of vector addition. That is, you cannot add angular displacements the same way you add vectors (or natural numbers for that matter); the order makes all the difference!

What about the "temperature gradient " the others mentioned?

 

[jbriggs444]

What about the "temperature gradient " the others mentioned?

Let's define gradient first.

A "scalar field" is a function that takes vectors (such as three dimensional positions) as input and produces scalar values (such as temperature) as output. If you take temperature readings over a volume of space, this amounts to a scalar field. The temperature values are scalars. The points at which you take measurements are vectors.

A "vector field" is a function that does a similar thing. But it takes vectors as input and produces vector values as output. If you take wind readings over a volume of space, this amounts to a vector field. The wind speed/direction values are vectors. The points at which you take measurements are also vectors.

If you look at a point on in a small region in a scalar field, you can [often] find a direction in which the scalar value increases most rapidly. You can also determine how rapidly it increases in that direction. That "direction and rate of change" has both magnitude and direction -- it is a vector. It is also called the "gradient" of the scalar field at the selected point.

If you start with a scalar field and take its gradient at all points, what you wind up with is a vector field.

You can, for another example, consider gravitational potential. This is the potential energy which a unit mass would possesses at a given point in space due to gravity. Gravitational potential is a scalar field. Take the gradient of this field and you get gravitational force. That is, the force which gravity would exert on a unit mass at the given point in space. Gravitational force is a vector field.

None of this means that temperature or energy are vectors.

 

[Ron G]

Did @Addum give up and let @HelioGeo take over? We do seem to have strayed a little.

@phinds has tried hard not to open the firehose and still give sensical answers even though the question is based on imprecise use of terms. Physics is a compendium of theories each of which have boundaries of applicability, or domain. It is easy for us to get terms mixed up when our discussion unknowingly crosses these boundaries. Mass is a perfect example. In Newtonian Physics, which is valid for almost all your daily concerns, mass is simply the weight of the object at sea level here on earth. Once we introduce Relativity, we learn that mass will change with the relative velocity of the object with respect to the frame of reference. Therefore, we redefine mass as the inertia or resistive force of the object when at rest within our frame of reference. We have switched from the domain of Newtonian Physics to that of Relativity; so, terms can and do take on different meanings.

To address your confusion about mass being a vector-less quantity (or scalar), as we progress beyond the simple F = ma of Newton we must specify mass as a resting quantity, it has no direction by definition. Do not confuse resting mass, which is a quantitative measurement, with the object that it applies to. If the object under study is moving, then the resting mass scalar combines with forces and instantaneous velocities of the object to create energy.

The energy created by the mass comes in two forms, kinetic and potential. As you might suspect, potential energy accumulates as forces are applied accelerating the object overtime, and kinetic energy is a function of mass and velocity. The sum of these energies are conserved. So, if one increases the other energy must decrease, and that is the case, because potential energy is a negative or resistive reaction to the application of the forces acting on the object. Bottomline, resting mass is a scalar value that is applied to the vectors of the forces accelerating the object and to the opposing instantaneous velocity vector opposing the forces. That is how mass affects energy in the relativistic domain.

You also made a statement that you thought mass was energy. Unless an object is radioactive, its energy is conserved. If your objective is to release the potential energy bound up in the atom's structure, we are leaving Relativity for events covered in the domain of Quantum Mechanics. Because QM deals with features of nature that we cannot witness in our everyday lives, the terms adopted to describe sub-atomic events are down right misleading in context of the common vernacular. So, be patient. Your journey gets tougher; but, the revelations are truly astonishing. -Ron G