# Higgs field

hi,

i'm reading brian greene's "the fabric of the cosmos" and in it he explains what a higgs field is. he says the potential energy of the field is shaped like a bowl with a raised peak at the center of the bowl. further he says the vertical height above the bottom of the bowl represents the energy of the field, and the horizontal distance from the center/peak of the bowl is the 'value' of the field. so, if the field(?) rests on the bottom of the bowl, the energy of the field is 0, but the 'value' is not zero. what does it mean for a field to have 0 energy but a non-zero 'value'?

likewise if the field(?) is trapped on the peak in the center of the bowl, it has a 0 'value', but positive energy. what does it mean for a field to have a 0 'value' but still contain energy?

please assume your audience is a 10-12 year old, so that i have a chance to understand.

He man;

check out this site and you will recognize the figure you are referring to.

http://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking

The x-axis gives field-values. The y-axis gives potential energy-values corresponding to a certain field value.

These fields are just a way of describing particles, ok? So a certain fieldvalue corresponds to a particle with specific energy and so on. These fiels can also describe interactions between particles which is the case in this example. The figure represents the potential energy of some interaction between particles.

The lowest value of the potential energy is on the bottom of the mexican hat. You see that when you pick one lowest value, you can go around the hat. This means that there are multiple lowest-potential energy-values. This means that the vacuum (=the groundstate, corresponding to the lowest potential energy) is degenerate (more than one possible value).

Now we can pick just 1 vacuum-state out of all the possible ones and forget about all the rest. In physiscs this loss is said to be a loss of symmetry (the circle at the bottom is gone since we forgot about all the other possible minimal values of the potential energy). This loss of symmetry gives mass to elementary particles.

And basically the Higgs-field is there to make sure that there are MORE THEN ONE states with minimal potential energy. In this case we can always apply to above system in order to get this loss of symmetry and gain mass for elemantary particles.

regards
marlon

hi,

These fields are just a way of describing particles, ok?

this particular description had to do with the bang in the 'big bang'. i don't comprehend how a field can have 0 energy and a positive 'value', (which I guess is the current state of the 'higgs ocean' and gives rise to the mass of elementary particles as they move through it). what is the meaning of the 'value' of a field?

right before the big bang, i think he says the higgs field was momentarily trapped at the center of the mexican hat--in a high energy configuration but with a 0 'value' (once again i don't understand what a 0 'value' means). with the higgs field trapped in a high energy configuration, it caused an immense burst of repulsive gravity and a massive inflation of the universe over a miniscule amount of time. then the higgs field dropped down into its 0 (low?) energy state, and massive amounts of energy were released causing something equivalent to a 'big bang'. he said that the one-two punch of immense repulsive gravity and the subsequent release of massive amounts of energy is a theory called 'inflationary cosmology', and the massive amount of inflation right before the big bang explains many things that the 'big bang' alone cannot.

i thought one of the most interesting things in the book is how he says einstein had to redo his general theory of relativity equations because they showed that the universe either had to be expanding or contracting and not constant in size--yet everyone including einstein just 'knew' the universe was a constant size. so einstein added a 'cosmological constant' to the equations to make them produce a stable universe.

then astronomers made observations that showed the universe was expanding which was hailed as one of the most important cosmological discoveries--had einstein trusted his equations he would have gotten credit for first recognizing that possibility.

then everyone thought the expansion of the universe should be slowing because gravity is an attractive force pulling everything back together again. however, again astornomers discovered that not only is the universe expanding, but that it is expanding at an every increasing rate. that finding gave birth to the theory of inflationary cosmology to explain how that could be possible.

Last edited:
nrqed
Homework Helper
Gold Member
aliendoom said:
hi,

i'm reading brian greene's "the fabric of the cosmos" and in it he explains what a higgs field is. he says the potential energy of the field is shaped like a bowl with a raised peak at the center of the bowl. further he says the vertical height above the bottom of the bowl represents the energy of the field, and the horizontal distance from the center/peak of the bowl is the 'value' of the field. so, if the field(?) rests on the bottom of the bowl, the energy of the field is 0, but the 'value' is not zero. what does it mean for a field to have 0 energy but a non-zero 'value'?

likewise if the field(?) is trapped on the peak in the center of the bowl, it has a 0 'value', but positive energy. what does it mean for a field to have a 0 'value' but still contain energy?

please assume your audience is a 10-12 year old, so that i have a chance to understand.

Hi there. Very good questions.

In short, the value of the Higgs field they talk about is a certain property of the field (in physics jargon, it's related to something called the vacuum expectation value). That this value is zero does not mean that the field itself is zero. As for the energy, it is always defined with respect to some reference value, in physics. That something has zero energy in a certain state does not lead to contradiction.

The best way to understand the Higgs field is to go back to bowl raised at the center but now think of a marble which you would place in the bowl. The marble will play the role of the Higgs fields in some sense. To be more precise, the *distance* of the marble from the center of the bowl will play the role of the "value of the Higgs field" they talk about. So the marble can have a "value" equal to zero without this implying that the marble is not there.

And the height of the marble will play the role of the energy of the Higgs field (that makes sense, the higher the marble, the more gravitational potential energy it has).

So the marble may be at the center (with a zero value of distance) and have a large energy (large height). And it could be in one of the two minima at a sizeable distance from the center (so large distance) and have no energy.

Again, I think the keep point is that the "value" of the field is a property of the Higgs field. That this is zero does not imply that there is no Field.

Let us know if this still does not help.

Pat

...the "value" of the field is a property of the Higgs field. That this is zero does not imply that there is no Field.

ok, thanks. very interesting book. physicists and cosmologists are very smart people, and they/you understand more about stuff than most people could ever imagine.

one other thing. when a higgs field gets trapped in the high energy state, is that necessarily associated with a "cooling" of the field? from what i could gather, the field has to want to descend to the low energy state for it to get stuck and cause the burst of negative gravity.

then the question is what caused that cooling? the author says, neither inflationary cosmology nor the big bang can explain why prior to those events there was a higgs field in the first place or where it came from, nor why space-time even existed for those processes to take place in.

Last edited:
vanesch
Staff Emeritus
Gold Member
aliendoom said:
physicists and cosmologists are very smart people, and they/you understand more about stuff than most people could ever imagine.

:rofl: :rofl: :rofl:

That's in fact the biggest difficulty they are confronted with !!

cheers,
Patrick.

nrqed
Homework Helper
Gold Member
vanesch said:
:rofl: :rofl: :rofl:

That's in fact the biggest difficulty they are confronted with !!

cheers,
Patrick.

I wonder what you mean here, Patrick ?!?

vanesch
Staff Emeritus