Scalar or not scalar

Here is an excerpt from the link below:

" Cosmologists were very happy when the Higgs boson was discovered, partly because it’s a manifestation of a “Higgs field” – the first fundamental “scalar field” observed in nature. A scalar field is one that has a value at every point in space-time but no direction. An everyday example might be a pressure map on a weather forecast (values everywhere but no direction). A wind map, on the other hand, isn’t a scalar field as it has speed and overall direction.

"Apart from Higgs, all particles in nature are associated with “quantum fields” that are like the analogy of wind maps. It has been theorised that, like Higgs, dark energy could be another example of a scalar field."

https://theconversation.com/the-experiments-trying-to-crack-physics-biggest-question-what-is-dark-energy-52917

According to the link above high and low pressure areas in the atmosphere are directional and therefore not scalar. Is there another criteria to determine if a field is scalar or not besides that?

Originally posted by @metal-brain
Here is an excerpt from the link below:

" Cosmologists were very happy when the Higgs boson was discovered, partly because it’s a manifestation of a “Higgs field” – the first fundamental “scalar field” observed in nature. A scalar field is one that has a value at every point in space-time but no direction. An everyday example might be a pressure map ...[text shortened]... ore not scalar. Is there another criteria to determine if a field is scalar or not besides that?

You've provided one link that says that pressure is a scalar. You have not provided a link that says: "high and low pressure areas in the atmosphere are directional and therefore not scalar.".

The gradient of a scalar field is directional, but that does not make the scalar field itself directional.

The link seems to assume that dark energy definitely exists and incorrectly talks about it as if it is already a proven scientific fact. But it might not exist because, at least for now, it would be an unsafe assumption that it exists since cosmologists haven't even began to properly formulate, explore and test alternative explinations for the apparent increasing rate the universe is expanding. For all we know, the dark energy theory is destined to eventually become like the now disproved old Aether theories and become disproved with new and better understanding of physics explaining (and with evidence) how that theory is wrong.
Time will tell.

Originally posted by @deepthought
You've provided one link that says that pressure is a scalar. You have not provided a link that says: "high and low pressure areas in the atmosphere are directional and therefore not scalar.".

The gradient of a scalar field is directional, but that does not make the scalar field itself directional.

The link says this:

"An everyday example might be a pressure map on a weather forecast (values everywhere but no direction). A wind map, on the other hand, isn’t a scalar field as it has speed and overall direction."

A wind map is based on high and low pressure areas. Without high and low pressure areas there would be no wind, speed or direction. It is as if you accept the effect, but not the cause.

"The gradient of a scalar field is directional, but that does not make the scalar field itself directional."

I don't know what you mean by "gradient". I have looked up the words "gradient" and "magnitude", but the definitions are vague and lack specificity. Perhaps you can give me better definitions of those words in this specific context.

Originally posted by @humy
The link seems to assume that dark energy definitely exists and incorrectly talks about it as if it is already a proven scientific fact. But it might not exist because, at least for now, it would be an unsafe assumption that it exists since cosmologists haven't even began to properly formulate, explore and test alternative explinations for the apparent increas ...[text shortened]... derstanding of physics explaining (and with evidence) how that theory is wrong.
Time will tell.

"The link seems to assume that dark energy definitely exists and incorrectly talks about it as if it is already a proven scientific fact."

Nope. Read the last sentence in the article.

Originally posted by @metal-brain
"The link seems to assume that dark energy definitely exists and incorrectly talks about it as if it is already a proven scientific fact."

Nope. Read the last sentence in the article.

You mean;

"Of course all of these explanations may be wrong, dark energy could be something even stranger. "
?

It says dark energy "could be something even stranger", NOT that dark energy doesn't exist.
Do you know the difference between something not existing and something existing but being different from what it was thought to be?

Your link says;
"...the discovery in the 1990s of a completely unknown force dubbed dark energy that makes up 70% of the cosmos ..."

How can they refer to it as "the discovery", not merely a yet-to-prove theory, of something that "makes up 70% of the cosmos" if they didn't assume it exists? How can they be thinking a none existent thing might make up "70% of" anything physical? For something to make up "70% of" anything physical, it must as a minimum requirement exist else doesn't make sense. This is why I said;

"The link seems to assume that dark energy definitely exists and incorrectly talks about it as if it is already a proven scientific fact."

Originally posted by @humy
You mean;

"Of course all of these explanations may be wrong, dark energy could be something even stranger. "
?

It says dark energy "could be something even stranger", NOT that dark energy doesn't exist.
Do you know the difference between something not existing and something existing but being different from what it was thought to be?

Your link says; ...[text shortened]... definitely exists and incorrectly talks about it as if it is already a proven scientific fact."

I am proud of you. You have resisted the urge to assume. You are clearly evolving critical thinking skills.
I don't think the article is trying to say dark energy has to exist though. I think it is just easier to say "dark energy" instead of "the expansion of the universe is caused by" in every other sentence.

Originally posted by @metal-brain
The link says this:

"An everyday example might be a pressure map on a weather forecast (values everywhere but no direction). A wind map, on the other hand, isn’t a scalar field as it has speed and overall direction."

A wind map is based on high and low pressure areas. Without high and low pressure areas there would be no wind, speed or direction. ...[text shortened]... specificity. Perhaps you can give me better definitions of those words in this specific context.

https://en.wikipedia.org/wiki/Gradient

Originally posted by @metal-brain
The link says this:

"An everyday example might be a pressure map on a weather forecast (values everywhere but no direction). A wind map, on the other hand, isn’t a scalar field as it has speed and overall direction."

A wind map is based on high and low pressure areas. Without high and low pressure areas there would be no wind, speed or direction. ...[text shortened]... specificity. Perhaps you can give me better definitions of those words in this specific context.

If you could measure the actual pressure at each point on a helium filled balloon, it rises because the pressure on top of the balloon is different from the air pressure on the bottom and so if you charted that pressure in micro increments, you would find say 14.0000001 PSI on the bottom but 14.0000000 PSI on the top and that pressure gradient is what generates lift, So gradient is just the measure of the change of pressure from top to bottom of the balloon. There is a pressure gradient from the bottom to the top or in reverse from the top to the bottom of the helium filled balloon.

Originally posted by @kazetnagorra
https://en.wikipedia.org/wiki/Gradient

Since Deepthought is slow to respond perhaps you can explain why he said time dilation is scalar when the Higgs field” is the only “scalar field” observed in nature according to wikipedia and the link I posted.

Originally posted by @metal-brain
Since Deepthought is slow to respond perhaps you can explain why he said time dilation is scalar when the Higgs field” is the only “scalar field” observed in nature according to wikipedia and the link I posted.

Because time dilation is a difference between coordinate systems and depends on the state of motion of observers. A field is a physical thing which doesn't depend on the presence of observers at all.

Regarding gradients. I'll restrict this to two dimensions, but the extension to three or more is essentially trivial. Suppose there is a scalar function f = f(x, y). We are interested in how the function changes along some curve on the plane. The curve is given by x = x(t) and y = y(t), where t is a parameter. You can think of x and y being the coordinates of a walker and t being the time they have been walking for, f might be the height above sea level as they walk through hilly country. Along the curve the function f takes the form f = f(x(t), y(t)). We can find the rate they are climbing at (walking up a slope) by differentiating this: df/dt. Now using the chain rule for differentiation we get:

df/dt = (∂f/∂x dx/dt + ∂f/∂y dy/dt)

dx/dt is just the horizontal velocity along x, call that v_x, similarly v_y. So we have:

df/dt = (∂f/∂x v_x + ∂f/∂y v_y)

As a vector the velocity is v = i v_x + j v_y, where i and j are understood as basis vectors.

We now have:

df/dt = (i ∂f/∂x + j ∂f/∂y) ∙ v

Which is the usual vector dot product. Introduce a differential operator called the gradient ∇ = (i ∂/∂x + j ∂/∂y), this then gives:

df/dt = ∇f ∙ v

The gradient of the scalar f is ∇f and it gives the rate of change of the field f as a vector quantity. The rate that the function is changing in a particular direction is then obtained using a dot product as above.

Originally posted by @deepthought
Because time dilation is a difference between coordinate systems and depends on the state of motion of observers. A field is a physical thing which doesn't depend on the presence of observers at all.

Regarding gradients. I'll restrict this to two dimensions, but the extension to three or more is essentially trivial. Suppose there is a scalar funct ...[text shortened]... he function is changing in a particular direction is then obtained using a dot product as above.

Higgs field” is the only “scalar field” observed in nature according to wikipedia and the link I posted.

You claimed time dilation is scalar. That contradicts the above statement. Both cannot be correct. Either you are wrong or the above statement is wrong. Which is it?

Originally posted by @metal-brain
Higgs field” is the only “scalar field” observed in nature according to wikipedia and the link I posted.

You claimed time dilation is scalar. That contradicts the above statement. ...

No, it DOESN'T. There is NO contradiction there.

Time dilation isn't a field so it wouldn't matter if Higgs field is the only observed scalar field because that would still mean time dilation still can be scalar. This is because a "scalar field" IS a "field" (that is why it is so called) and time dilation isn't.

Originally posted by @metal-brain
Higgs field” is the only “scalar field” observed in nature according to wikipedia and the link I posted.

NO. So even your premise is false (AS WELL as your inference). The wiki link certainly doesn't say something even vaguely sounding like this. Your OP link doesn't exactly says this although admittedly I can see how you could think otherwise with the potentially misleading assertion (to the layperson; NOT to the average physicist) in your OP link of;

"..a “Higgs field” – the first fundamental “scalar field” observed in nature..."

I think they should have stated that more clearly But still the operative word above is the slightly vague word "fundamental"; Less 'fundamental' scalar fields HAVE been observed before that and including temperature distributions in space etc.

https://en.wikipedia.org/wiki/Scalar_field
"... Examples [of scalar field] used in physics include the temperature distribution throughout space,..."

You couldn't be much more wrong.

Originally posted by @metal-brain
Here is an excerpt from the link below:

" Cosmologists were very happy when the Higgs boson was discovered, partly because it’s a manifestation of a “Higgs field” – the first fundamental “scalar field” observed in nature. A scalar field is one that has a value at every point in space-time but no direction. An everyday example might be a pressure map ...[text shortened]... ore not scalar. Is there another criteria to determine if a field is scalar or not besides that?

You are mistaken. Pressure is not directional. That link does not claim it is.

According to the link above high and low pressure areas in the atmosphere are directional

That is false. You misunderstand the link.