A pause from my quantum series to announce a new interview on YouTube, this one on the Blackbird Physics channel, hosted by UMichigan graduate student and experimental particle physicist Ibrahim Chahrour. Unlike my recent interview with Alan Alda, which is for a general audience, this one is geared toward physics undergraduate students and graduate students. A lot of the topics are related to my book, but at a somewhat more advanced level. If you’ve had a first-year university physics class, or have done a lot of reading about the subject, give it a shot! Ibrahim asked great questions, and you may find many of the answers intriguing.
Here’s the list of the topics we covered, with timestamps.
- 00:00 Intro
- 00:40 Why did you write “Waves in an Impossible Sea”?
- 03:50 What is mass?
- 09:03 What is Relativistic Mass? Is it a useful concept?
- 17:50 Why Quantum Field Theory (QFT) is necessary
- 23:50 Electromagnetic Field, Photons, and Quantum Electrodynamics (QED)
- 36:17 Particles are ripples in their Fields
- 38:47 Fields with zero-mass particles vs. ones whose particles have mass?
- 46:49 The Standard Model of Particle Physics
- 52:08 What was the motivation/history behind the Higgs field?
- 1:02:05 How the Higgs field works
- 1:05:33 The Higgs field’s “Vacuum Expectation Value”
- 1:12:02 The hierarchy problem
- 1:24:18 The current goals of the Large Hadron Collider
8 Responses
Hi Matt,
Good video, lots of interesting points.
Probably just a simple mechanics question but had this thought while watching.
If an electron, a muon and a proton walked into a bar … um … wrong question.
If an electron, a muon and a proton all had the same total energy, say 10x the rest energy of a proton, in a particle accelerator, does it take the same amount of force to deflect each of them by the same amount? Basically is there a difference in the force it takes to act sideways on rest mass vs “relativistic mass”?
The higher the energy, the more similar they will be. You can read something about this here, see especially equations 4b-4c. https://en.wikipedia.org/wiki/Acceleration_(special_relativity)#:~:text=Accelerations%20in%20special%20relativity%20(SR,complex%20definitions%20of%20%22acceleration%22. Relativistic mass (m gamma, where m is the rest mass and gamma is the usual boost factor) appears in the denominator of a in terms of f, but unless the force and velocity are strictly perpendicular, the acceleration depends on the relative angles.
A key moment in interview was a lessening of the connection between HIggs level to vacuum but the discussion as well in focusing on the recursive structure of Higgs to other fields prompts a view on the the vaccua as well mirroring a similar recursiveness which while in themselves not perhaps fields, do in hosting them begin find a semblance… looking back then at the Einstein effort at fifth dimensional analysis as a Unified Field Effort constraining extra dimensions to that fifth nevertheless the following efforts moving from the bosonic to fermion or d brane view on such barionic veritices as extendor graphs of a sort on relating dimensional bridges accross non holomorphic/ non cummutability but then again commutators… seems to leave open a kind of complex reconnection or unified field theory in a bridge over that mirroring in a tunnelling mode whereby the curvature of the Higgs is open to some such Sphaeron
dear Matt,
thanks for the elaborate answer.
Your (quote) “However, the logic does not run the other way. Even if a field’s particles have no mass, so that it has no restoring effect, it does not follow that changing the field’s value has no effect.” (unquote) clinches it.
But, how is the “value” of a field even defined?
Observable differences in value are measured in quanta, and the size of a quantum corresponds (somehow) to its particle’s rest mass (in eV). And at the same time, this also quantifies the ‘restoring effect’ (??). Feels like I’m mixing up concepts again.
But the field values need a reference value to measure it against, no?
This becomes problematic (for me) when I try to link it to the concept of a VEV for that field. That VEV is not related (??) to the restoring effect (and so to the particle mass via the energy involved in the restoring effect). Or is the VEV also given in mass-energy units? Are field amplitudes (squared) always translatable to mass-energy?
In the talk, you refer to a mean energy-density as a reference, and to the Planck scale as an absolute measuring stick. But I can’t help feeling woozy about the concept of (numerical) field value.
Btw, don’t take my pun on ‘private lecturing’ too seriously. If my feed-back is of any didactic use for you, ok. If not, feel (and be) free to ignore my ramblings.
Wouter.
The value of a field is not measured in its quanta. Consider electromagnetism. The value of the electric potential, or the value of the electric field, is about what the field is doing when it is not waving. The counting of quanta is about understanding what the field is doing when it is waving.
If I encounter the Higgs field that locally (i.e. nearby me) has the form
H(x,y,z,t) = v + A cos(2 pi [f t – x / lambda]),
where v, f and lambda are constants, then v is the “vev” and “|A|^2” represents a number of Higgs bosons traveling together with energy E = f h, momentum p / lambda, and mass equal to sqrt[E^2 – p^2 c^2]/c^2 ; here “h” is Planck’s constant. Normally A is zero and v is not, but I can change A at the Large Hadron Collider. The restoring effect ensures that the Higgs mass isn’t zero *and* that it is very difficult to change v; we need Big Bang levels of energy density to change it over any appreciable reason.
Given the level of your questions, I think you might want to read my two series of articles on fields and particles and the Higgs field:
https://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/
https://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-the-higgs-field-works-with-math/
hi Matt, a big thanks for what feels like ‘private tutoring’.
It ties in nicely with the book and the blog. You allow me to catch up to stuff I was never taught.
As usual, a (silly) question :
when you describe the massless fields, you point out that they suffer no restoring effect, no preferred field value. That goes with the notion that only differences in field values have observable effects. (If my entire house were at 10 kVolt above neutral, I wouldn’t notice any effect inside). But then, you introduce the VEV of the Higgs field. And without even blinking, that field DOES have an absolute reference value. It has a zero reference value (that other fields lack) and prefers to sit at a value above zero. Where did I miss the point here? Can we assign an energy ‘label’ to other fields (electromagnetic- or electron-) dependent on its value, and if so, measured from what reference? I’m, again, confused.
Not silly at all. You are mixing up two issues, but in a very reasonable way.
The two issues are
(1) if I change the field’s value from its current value, is there a restoring effect which tends to pull it back to its current value (in which case the corresponding particle will have a mass), and
(2) if there is no restoring effect, then does changing the field’s value have any physical impact?
The case you refer too — where you change the electric potential of your house — is about case (2). You correctly note that since changing the overall electric potential of the universe has no consequences, there can be no restoring effect for the electric potential, and therefore its corresponding particles should have no mass.
However, the logic does not run the other way. Even if a field’s particles have no mass, so that it has no restoring effect, it does not follow that changing the field’s value has no effect.
Indeed, Higgs-like fields whose vacuum expectation value can be anything, but which do have a measurable effect, are theoretically possible, and are often called “moduli” or “moduli fields”. Supersymmetric theories are replete with them.
But the electric potential is not a moduli field, because it does not exist alone. The electric and magnetic potentials together form the electromagnetic potential, which is a spin-1 field, not a spin-0 field like the Higgs field or a modulus field. It has a property known as gauge invariance, which implies (among many other things) that a constant vacuum expectation value is unphysical; it has literally no effect at all. Changing the electromagnetic potential’s constant vacuum expectation value is like changing a coordinate system; it does nothing. Gauge invariance thus implies that there can be no restoring force for the electromagnetic potential, and therefore implies that its particle — the photon — must have zero mass. [Note: this argument could be violated if its gauge invariance were disguised by a Higgs-like field. In fact, that’s exactly what happens for the W and Z fields, leading their particles to have mass after all.]
Now, back to the real-world Higgs field. The Higgs field has some gauge invariance, but not the kind that would allow you to shift its vacuum expectation value without any effect on the world. Therefore (a) its vacuum expectation value can indeed have a physical effect on the world, including changing other particles’ masses, and (b) nothing prevents the Higgs field from being subject to a restoring effect.
Thus, if there were no restoring effect on the Higgs field, it would be a modulus field, unlike the electromagnetic field; its vev matters. But in any case, in our universe there is a restoring effect. It is quite a complicated effect. In principle, effects like this could be zero and stable when the Higgs field’s vacuum expectation value is itself zero; or it could be zero when the Higgs field’s vev is non-zero. Our universe happens to be stable, with the restoring effect balanced out, when the Higgs field’s expectation value is the 246 GeV (up to constants) measured in experiments. We don’t know why the universe turned out that way, but those are the experimental facts.
It is not a trivial matter to get this all straight! I finessed it in the book, because it would have taken us far afield, and I finessed it in the video because it is really usually limited to graduate school, not undergrad.
Enjoyed watching the video especially the section around self organized criticality.
And it’s yet another great youtube channel to subscribe to.