The attributes "old" and "established" do not describe the accuracy of a thing.
Humans believed that the earth was flat for thousands of years in various cultures - old, established, and wrong.
The geocentric model of the cosmos prevailed for about fourteen centuries until the emergence of heliocentric theories - old, established, and again, wrong.
To be clear, I'm not arguing one way or the other about the accuracy of the hypothesis you mentioned, but simply that the age and popularity of any hypothesis has little to do with whether or not it will eventually be disproven.
A scalar field is a field with one value at any point.
Temperature can be represented using a scalar field. There is only one temperature at any point in our universe.
Theories like Quantum Field Theory describe our universe as a series of interacting fields that are everywhere. The Higgs field gives us mass, a single number at any point in space.
In this sense, the space around us is permeated by many fields.
Space itself is not a single scalar field because space contains many properties at every point that cannot be represented using a single number — for that one might use a matrix of values.
Temperature seems like a bad example because its an average of energy in particles in a volume of space. The temperature at any finite point will always be zero. Like what's the temperature on the inside a neutron? Is that even mean anything?
Wait, why would the temperature at any finite point will always be zero? Because I’m quite confident it would be non zero as emptying space is stupid expensive.
And there is temperature inside a neutron, since it’s not a fundamental particle but composed of quarks: The neutron temperature T, on the Kelvin scale, is given by T = 2E/3k, where E is average neutron energy and k the Boltzmann constant.
> why would the temperature at any finite point will always be zero
Based on your answer of the temperature inside a neutron then maybe it won't be zero everywhere. Any finite point is going to either be inside a particle or outside of a particle. And since most of space is empty, and atoms are also mostly empty, the vast majority of finite points will be where there is nothing, and hence have no temperature.
> emptying space is stupid expensive
I don't what this means. Most of space is already empty.
If space is “empty”, then how come we can measure the temperature of the microwave background radiation?
Think about it…any direction we point an apparatus, we will get a reading — the static of a radio IS the CMB, and if you could take that radio into space, and have the ability to travel anywhere, that radio would still have static. As such, space cannot be “empty”, it’s filled with photons, electrons, and quarks, amongst other things.
To reach 0 Kelvin would take an infinite amount of energy (infinite is not exactly accurate but might as well be), hence “stupid expensive”. It would also create holes in the CMB. CMB has no holes, as such, there is stuff everywhere.
> how come we can measure the temperature of the microwave background radiation
Because that's the average temperature over an region not the temperature of a finite point. It's kind of like pressure; it really only makes sense at a macro level where you are averaging over a volume or region. The pressure at a singular finite point will also be zero because that singular infinitely small point will likely be in the empty space that makes up an atom.
The original comment was about scalar fields in which there is a value at every finite point. Temperature and pressure are not good examples of these. A better example would be like a magnetic or gravitational field which would have a specific value at every point in space.
Isn't the hypothesis that dark matter is composed of primordial black holes quite old and established.
The attributes "old" and "established" do not describe the accuracy of a thing.
Humans believed that the earth was flat for thousands of years in various cultures - old, established, and wrong.
The geocentric model of the cosmos prevailed for about fourteen centuries until the emergence of heliocentric theories - old, established, and again, wrong.
To be clear, I'm not arguing one way or the other about the accuracy of the hypothesis you mentioned, but simply that the age and popularity of any hypothesis has little to do with whether or not it will eventually be disproven.
Is the space around us (and that we occupy) a scalar field?
A scalar field is a field with one value at any point.
Temperature can be represented using a scalar field. There is only one temperature at any point in our universe.
Theories like Quantum Field Theory describe our universe as a series of interacting fields that are everywhere. The Higgs field gives us mass, a single number at any point in space.
In this sense, the space around us is permeated by many fields.
Space itself is not a single scalar field because space contains many properties at every point that cannot be represented using a single number — for that one might use a matrix of values.
https://en.wikipedia.org/wiki/Scalar_field
Temperature seems like a bad example because its an average of energy in particles in a volume of space. The temperature at any finite point will always be zero. Like what's the temperature on the inside a neutron? Is that even mean anything?
Wait, why would the temperature at any finite point will always be zero? Because I’m quite confident it would be non zero as emptying space is stupid expensive.
And there is temperature inside a neutron, since it’s not a fundamental particle but composed of quarks: The neutron temperature T, on the Kelvin scale, is given by T = 2E/3k, where E is average neutron energy and k the Boltzmann constant.
Source: https://www.oxfordreference.com/display/10.1093/oi/authority....
> why would the temperature at any finite point will always be zero
Based on your answer of the temperature inside a neutron then maybe it won't be zero everywhere. Any finite point is going to either be inside a particle or outside of a particle. And since most of space is empty, and atoms are also mostly empty, the vast majority of finite points will be where there is nothing, and hence have no temperature.
> emptying space is stupid expensive
I don't what this means. Most of space is already empty.
If space is “empty”, then how come we can measure the temperature of the microwave background radiation?
Think about it…any direction we point an apparatus, we will get a reading — the static of a radio IS the CMB, and if you could take that radio into space, and have the ability to travel anywhere, that radio would still have static. As such, space cannot be “empty”, it’s filled with photons, electrons, and quarks, amongst other things.
To reach 0 Kelvin would take an infinite amount of energy (infinite is not exactly accurate but might as well be), hence “stupid expensive”. It would also create holes in the CMB. CMB has no holes, as such, there is stuff everywhere.
Does that track?
> how come we can measure the temperature of the microwave background radiation
Because that's the average temperature over an region not the temperature of a finite point. It's kind of like pressure; it really only makes sense at a macro level where you are averaging over a volume or region. The pressure at a singular finite point will also be zero because that singular infinitely small point will likely be in the empty space that makes up an atom.
The original comment was about scalar fields in which there is a value at every finite point. Temperature and pressure are not good examples of these. A better example would be like a magnetic or gravitational field which would have a specific value at every point in space.
> since most of space is empty
Empty space is still busy fucking around with itself [1].
[1] https://en.m.wikipedia.org/wiki/Vacuum_energy