If you’re reading Waves in an Impossible Sea and you have a question about something in the book, ask it here! No question is too basic or elementary; whatever question you have, no doubt ten other readers have the same one.
Although I can’t hope to answer all of your questions in a timely fashion, I will be taking note of them, and gathering them into a list of Frequently Asked Questions for each chapter. Please consider mentioning the chapter or even the page that inspires your question, if there is one.
If you question is inspired by the book but is on a subject that the book doesn’t cover, consider putting your question on this page instead; it will help me keep things organized.
120 Responses
Dr. Strassler,
I asked question on this web page back in April but for some reason it never got answered and it now does not even appear on the webpage. So, I decided to pose it again:
You mention in the book that mass does not slow things down but on the other hand you refer to the intransigence of massive objects. I regard the combination of these two statements as contradictory.
What is it, in your view, then the reason for objects not being able to reach the “cosmic speed limit”? The intransigence of mass or something else?
After doing some research, Einstein himself in his book addressed to lay readers, Relativity: The Special and the General Theory, attributes the phenomenon to “inertial mass”.
Any clarifications would be appreciated
Sorry, I don’t know why your question disappeared. Maybe a glitch as we were updating the website…?
In any case, your two paragraphs don’t really agree with each other, so I will address them separately.
1) “mass does not slow things down but on the other hand you refer to the intransigence of massive objects. I regard the combination of these two statements as contradictory.” I’m not sure why you would view these as contradictory. Both statements are true even in classical pre-relativistic physics; they follow from Newton’s law, F=ma. “m” does not slow things down, “F” does; even if “m” is huge, “a” is zero unless “F” is nonzero. And for a given “F”, a large “m” causes “a” to be small: that’s the nature of intransigence, an unwillingness to change. So the two statements are far from contradictory.
Both statements remains true in relativistic physics, where Newton’s law is replaced by equation (4d) in https://en.wikipedia.org/wiki/Acceleration_(special_relativity) . It is still true that “m” [which in the Wikipedia notation is “rest mass”] does not slow things down and “f” is necessary for there to be a change in motion. And it is still true that for fixed “f”, a large “m” leads to a smaller “a”.
2) Now separately: “What is it, in your view, then the reason for objects not being able to reach the “cosmic speed limit”? The intransigence of mass or something else?” It is equation (4d) in the Wikipedia article, which shows that for fixed “f” and “m”, both terms in the expression relating “f”, “m” and “a” have a factor of
or 
. Since 
goes to infinity as the object’s speed approaches the cosmic speed limit, “a” goes to zero even for finite “F” and finite “m”. And that is the explanation; it is not mass, but kinematic relations between force and acceleration that generalize Newton’s second law.
I believe that in your own thinking you have been implicitly assuming that F=ma is still true in relativity; but it is not. Moreover, you can’t save the situation by redefining mass to be some other quantity, such as “inertial mass”; the fact that there are two terms in (4d) makes it impossible to redefine mass so that F=ma. It simply isn’t, under any definition of mass.
As for what Einstein thought, it doesn’t really matter, since we don’t blindly follow leaders of the past. But if we must appeal to his authority, the issue is that Einstein went back and forth as to whether it is better to focus on rest mass, inertial mass, or something else. By the end of his life he had concluded that one should use rest mass, as seen in his letters to various people, such as this one: https://einstein.manhattanrarebooks.com/pages/books/112/albert-einstein/typed-letter-signed#:~:text=Addressed%20to%20Dale%20B.,provided%20the%20mass%20is%20finite.
Particle physicists have a principled reason for using rest mass and not relativistic mass, and explaining the impossibility of crossing the speed limit using equation (4d) of the Wikipedia article. I have discussed it here: https://profmattstrassler.com/waves-in-an-impossible-sea/waves-in-an-impossible-sea-commentary-and-discussion/chapter-7/chapter-7-endnote-7/
I have a question regarding gravitons. As far as I understand, they are only theoretical and gravity itself is not well defined?
Yet, in the book, gravitons are casually mentioned as quantum of gravitational field.
There are other things very well described with important disclaimers, why is this concept of gravitons just mentioned as a proven fact? Or maybe I am wrong?
Gravity is perfectly well defined. Gravitational waves are also well-measured. Nothing theoretical there.
What is not yet known experimentally is quantum gravity. This includes gravitons, which are to gravitational waves as photons are to light waves. We do not know experimentally that they exist.
The fact that gravitons are still only theoretical does seem to have gotten a bit buried in the book. It is explicitly mentioned on page 230 in footnote 6 of chapter 16. “Gravitons, wavicles of the gravitational field, may well exist, and I usually assume that they do. But it may be a long time before this can be confirmed experimentally.” But I can see that a person reading the book through might miss this caveat. Gravitons then explicitly appear on page 236 (and a couple of times after) without explicit reference back to that footnote.
If gravitons had been a more important part of the book, I would have made a bigger deal about this; but this isn’t a book about quantum gravity, after all, so I decided a footnote was enough.
Thanks a lot for this answer and clarification.
I’ve lived with an assumption that gravity is described, its behavior, but not yet fully explained. If it’s a field, like other fields. I need to fine some book (well written like yours) to get me up to speed with the latest understanding.
Einstein’s general relativity is a field theory, just like electromagnetism. You’ll find it in any standard list of classical (i.e. pre-quantum) field theories. For instance https://en.wikipedia.org/wiki/Classical_field_theory
It is sometimes said that there is no quantum field theory of gravity, but that’s not correct; there is no complete theory of quantum gravity without adding additional structure, as in string theory. Even without that additional structure, there is still an incomplete but useful theory of quantum gravity, which can be used to calculate some things precisely, some things imprecisely, and some things not at all. This is called an “effective quantum field theory”, widely used throughout particle physics. Again, you’ll see gravity appear in any list of effective quantum field theories, as in https://en.wikipedia.org/wiki/Effective_field_theory .
This is not in contradiction with your assumption that gravity is not fully explained; but electromagnetism isn’t either. If what you really mean is that we don’t have a complete calculable theory of gravity (which is different from an “explanation”), that is true, but that doesn’t mean we can’t calculate any of its quantum behavior at all. The big problem with studying even these aspects of quantum gravity is experimental; all the quantum effects we know of are very tiny and too hard to measure.
Matt
No question here, just an accolade for a tremendous book. I would have thought it the best “first”physics book for an enthusiast such as myself, preventing the raft of misconceptions that many other books promulgate. That is, until I saw all of the questions here. As a true enthusiast, I have read literally dozens of physics books, typically enjoying them all and gaining some new insights and understanding from each, if only by sheer repetition.
But your clear and matter of fact explanations put a lot of open questions in my mind to rest and really made me feel like I have an innate understanding- finally!
Just as helpful were your book tour appearances on Sean Carroll and Daniel & Jorge’s podcasts, both were amazingly informative.
Many thanks to you. Your book will be my gift of choice to my fellow enthusiasts.
Thanks, Mike, for these generous words. I’m so glad that even for someone as experienced as yourself, the book brings a new level of clarity.
Prof. Strassler,
Did you intend Figure 37 as the result of a thought experiment or of a possible laboratory experiment? That’s the one that shows E(t) for various light intensities. Is it possible to measure the electric and magnetic fields of a photon? I thought that if you detect a photon, you always get all of it or none of it, not something spread out in space and time as a small wave packet. Thanks.
Excellent question.
Figure 37 is impressionistic and intended to build intuition, rather than be precise about measurement of an electric field. Still, the point is to convey that a photon, despite being particulate, is still a wave. A photon can be extremely spread out… it can be a much wider wave packet than I had space to draw on the page. After all, a laser photon has a definite frequency and a wavelength; and how could it have these things if it were not spread out, with multiple crests? The math is absolutely clear about this.
It’s true that the detection of a photon is either all or none, and that this might seem inconsistent with the fact that the photon may be spread out across space and time as a wide wave packet. After all, if the photon is spread out over a million miles, or is going in multiple directions all at the same time, how can it be absorbed all at once in one location? Well, welcome to quantum physics. This is the kind of question that I did *not* address in the book, because it takes us into the morass of quantum observation and measurement which, while fascinating, would have served as a distraction from my main topics.
Thank you for your careful and helpful answer to my question.
Again with reference to Figure 37, I can imagine an antenna, say a dipole wire antenna, that detects the electric field as a function of time in the top of the figure. The signal arises from large numbers of photons streaming by and some hitting the antenna. Each photon that hits the wire gives all of its energy to a single conduction electron in the wire. How does this produce the time varying voltage difference between the wires of the antenna?
Suppose that you tried this with the electric field of a single photon’s wave packet shown in the lower part of the figure. It seems to me that the antenna would just get a single jolt of energy, not an oscillating electric field. Is it possible to measure the electromagnetic fields of a single photon?
(Ham radio and physics nerd here…) It’s important to distinguish the energy deposited by the photons and the momentum deposited by the photons. Energy doesn’t have a direction, but both the electric field carried by a photon and the momentum it imparts on an electron does have a direction.
Notice that photons carry a vector field. If you could see the individual photons streaming past the antenna, you would see that the direction(s) the vector(s) point varies with time (at the frequency of the radio wave detected by the antenna). If you are far from the source antenna, the vectors of all the photons at the antenna are (very nearly) parallel. (When one is close to the source, there are “near field effects” because the parallelism is far enough from simultaneous over the entire antenna that there are engineering-relevant effects.)
When an electron absorbs a photon, that electron responds to the vector carried by the photon. At that instant, the slab of photons passing through the antenna all have that vector, so all push the electrons in the same direction. If that vector points along the length of the antenna, all the electrons that absorb photons recoil along the antenna (anti-parallel to the photons electric field vector). One half-period of the wave later, the vectors on the currently arriving slab of photons will point in the opposite direction and electrons absorbing these photons will slosh in the opposite direction along the dipole. So, if your dipole is resonant at (or very near, because no dipole is actually a 1-dimensional resonator, so there is some width to the resonance) the frequency of the spinning of the vectors carried by the photons, the electrons will be driven to slosh in synchrony with the vectors.
This also explains why a source dipole that is tilted relative to the receiver dipole absorbs less energy — the vectors don’t point parallel to the receiver, so the projection of the vector onto the receiving antenna is the portion of the induced momentum that sloshes electrons along the antenna. The perpendicular component, moves electrons across, and attempts to move them outside the conductor of the antenna — so is eventually dissipated as heat. (Of course, the power received at antennas is tiny; there’s a reason this stuff is measured in dBs.)
Going a little further. Call the line segment between the two dipoles L. Notice that we can spin an antenna around, always perpendicular to L, like a propeller at the end of a stick. We can to this to both antennas. If we start parallel, we get the scenario in the second paragraph. Leaving one fixed but rotating the other one, we get the loss of received power described in the third paragraph. Finally, when the two antennas are skew perpendicular, the vectors carried by the photons emitted by one are, when they arrive at the receiving antenna, perpendicular to the pointing of the receiving antenna, so no power is deposited in the sloshing motion of the electrons, they’re just pushed against the surface of the conductor and dissipate this motion as heat. One would normally describe this as “cross polarized” and expect no transmission of power from one to the other.
I just finished your book. The further I got into the book, the slower I read because it became something of a tough slog, but that is due to the complexity of the subject. I thought you did a great job of trying to explain particle physics to a lay audience.
Even though I read the book quite closely, I never saw an explanation of what the Higgs boson actually does. You did a thorough job of explaining how the Higgs field works, but what exactly is the role of the Higgs boson?
I researched this online and know that it is produced by the quantum excitation of the Higgs field. I have also read that the Higgs boson is the “force carrier” of the Higgs field just as photons are the force carrier of the electromagnetic field. And, of course, the discovery of the Higgs boson proved the existence of the Higgs field. But does the Higgs boson actually do anything?
Thank you very much for providing this forum for answering questions about your book.
I’m glad you made it all the way through. And thanks for the kind words.
As far as we know, the Higgs boson really does nothing (and has done nothing) of significance, except provide physicists with a tool that allows them to study the Higgs field. This is a point I tried to emphasize in the book, and I’m sorry that this didn’t entirely come across. There are no Higgs bosons on Earth or anywhere in space except in the rare places, natural or artificial (i.e. inside the Large Hadron Collider), where enormously powerful particle collisions take place. Those Higgs bosons, once produced, decay away in one billionth of a trillionth of a second — not long enough for them to travel the width of an atom even if they were moving at half light-speed. Higgs bosons play no role in atoms, in subatomic particles, in the cosmos, or in our daily lives. The last time there were Higgs bosons in abundance was during the Hot Big Bang, for a tiny fraction of a second, and they were just one class of particles among the many that were swarming around.
I don’t think that one could say that bottom or top quarks, or tau leptons, play a role in our existence either. But their fields do, at least indirectly.
You might say there is a very loose conceptual analogy here to earthquake waves. Earthquakes are a sign of plate tectonics, the motion of thin plates upon the Earth’s mantle. Without plate tectonics, there would presumably now be a global ocean and no continents, and for this reason, our lives critically depend on these motions, which are always going on. Earthquakes, on the other hand, are sudden, relatively rare events. They don’t do us any good (and the big ones are destructive.) But earthquakes are enormously valuable for science, because they have allowed us to study the Earth’s interior and to discover and understand plate tectonics, on which our lives depend.
The Higgs boson is of even less value for daily human life than are earthquakes, and has much less impact. Nevertheless, Higgs bosons have allowed scientists to confirm the existence of and to study the Higgs field, which is of even greater importance for human life than plate tectonics.
I hope that answer is clear. Let me know if it is not.
Thanks very much. That was very clear: “As far as we know, the Higgs boson really does nothing (and has done nothing) of significance, except provide physicists with a tool that allows them to study the Higgs field.” I don’t think you came out and said that explicitly in the book, and I couldn’t find anything so stating in my online research. I’m relieved I didn’t miss an explanation saying what the Higgs boson does!
I think you do a great job of explaining very complicated concepts in a way that laymen can understand, even if it requires reading an entire book to be able to understand that explanation. I suspect you wonder how many of your readers make it all the way through!
I do wonder how many make it through, yes. I hope that the book is valuable even if one only makes it halfway, but I’m also working hard on this website to increase the fraction who can reach to the end. And I made sure there would be big rewards for those who do!
You did make me wonder about whether I did or didn’t state the Higgs boson’s non-role explicitly. But I checked, and indeed, I did — on page 5, no less! However, maybe it was too early, and maybe I should have reiterated it more strongly (there is some reiteration on page 255 but it is brief.) Here are the paragraphs in question:
“The media enjoys calling [the Higgs boson] the ‘God Particle.’ But most particle physicists, including Peter Higgs himself, think this name is a bit silly. Higgs bosons play no role in daily life or in the wider cosmos. You won’t find them lying on the ground or wandering between the stars, and they haven’t done anything of interest since the early moments of the universe. The reason is simple: a Higgs boson, once created, disintegrates in a billionth of a trillionth of a second.
“This is why physicists needed the LHC in the first place. In order to have any hope of discovering these elusive beasts, we humans had to try to make new ones from scratch. But why bother to make these ephemeral particles at all? This was an important question, since building the LHC and its predecessors took a great deal of money and time.
“The answer is that the search for Higgs bosons wasn’t an end in itself. Instead, it was a means to a far more important end. The rationale for the endeavor was that finding the Higgs boson would prove the existence of something of much greater significance: the Higgs field.”
I remember reading that on page 5, and I remember thinking how it didn’t make much sense because I thought I was going to have to read the entire book to figure out why the Higgs boson was so important and, specifically, how it “gives” mass to subatomic particles. Having read the entire book, I now know that it’s the Higgs field that is so important.
I think it would be a good idea to repeat or restate about the Higgs boson having no function near the end of the book where you finally explain the fundamental importance of the Higgs field. Specifically, I would have found it very helpful if you had stated that its only importance was proving that the Higgs field exists and that it otherwise has no role to play in the Simple Standard Model.
Thank you for taking the time to exchange ideas with me. I don’t think I have ever had that opportunity before with an author.
I appreciate your feedback on this point; in retrospect a clear review of this point would have been wise. If there’s a second edition, I’ll make sure to add that somewhere.
Part of the paradox of the 21st century is that, on the one hand, it marks the end of books and bookstores as we knew them, and on the other hand, it creates new opportunities for exchange between author and reader. In other words, a 21st century book is now an opening for a conversation, and remains a living document. I don’t consider the book done just because it is published; a whole wing of this website will be an extension of the book. Your questions and our discussion will be kept here as a record, and also, because I think you will not be the only one with this question, I will probably copy our converasation into the FAQ for Chapter 1.
Hi, I really appreciate your book. It puts Quantum physics altogether for me to get a picture of what physicists are talking about even though all the math is way beyond me.
To my question, why is the medium of quantum fields not energy?
I’m glad you enjoyed the book!
Energy, as defined in physics, is something that fields have, the way you have age and height and strength. Energy is not a thing. It is a property of things. Just as you cannot build a house out of strength (even though a well-built house will be strong), you cannot build or create a medium from energy (even though the medium will have energy.)
As such, energy cannot be a medium; it can only be a something that a medium can have.
Energy, in short, is not a substance from which a thing (including a medium) can be made. One sign of this is that energy is so often moving around from one form to another.
I hope that is clear… If not, feel free to re-ask the question.
Re. your mass/weight discussion, one place to see this clearly is at docks. It is easily possible to pull for a while to get a, say, 5 ton boat moving fairly well. But it is very easy to get injured if you get between said load that you started yourself with say a 10 or 15 second pull and a solid dock edge and attempt to stop it with a quick push. Stevedores have been severely injured this way and lost many limbs with larger loads over the years.
What would be your top list of misnomers in quantum physics that would in theory benefit from renaming.. like particle, wave ..etc
Sounds trivial but your book (as a physics hobbyist ) is helping me make conceptual leaps by recognizing these !
Well, renaming is both very difficult and potentially more confusing than not, so I tend to be very selective and wouldn’t rush into changing words. Many words in English have multiple definitions, and its okay to use a word with a standard definition as long as it is clear that a non-standard definition is used in physics; “wave” would be a good example of this. But the word “particle” is special because it really gives the wrong impression about the fundamental ingredients of the universe, and “wavicle” helps correct this.
Other examples: The word “force” is already often replaced with “interaction” by physicists. “Dark energy” isn’t very good but we’re not going to change it. “Dark matter” is fine for now; maybe when we figure out what it is we’ll rename it.
One of the biggest issues is “Higgs field” and “Higgs boson”; we usually try to avoid naming something after a person, especially since Higgs wasn’t the only one who suggested the idea of this field. “H field” and “H boson” has been tried; it’s hard to change this, but maybe someday it will happen.
Maybe I’ll think of some others…
Prof: I was reading your book and on page 64 you state that the “our planet circles the Sun at 20 miles per second”.
Question: So do our precise measurements confirm that there is absolutely NO reduction in this speed at all even at the billionth or trillionth of seconds level? Just wanted to confirm that there is absolutely no drag in outer space. Also the other way around, that there is no increase.
This is a great question, and one whose answer emphasizes how difficult and often counter-productive it is to be absolutely precise.
First, the Earth’s speed is not constant in its orbit. Its orbit is elliptical and its distance from the Sun varies, and therefore, so does its speed on a yearly basis, between 18.8 and 18.2 miles per second. [I was being judiciously imprecise when I said “20”; the details were not important.] Moreover, the Moon and the Earth co-orbit each other, which causes the Earth’s orbit around the Sun to look like a sinuous ellipse, rather than a perfectly smooth one; its speed varies monthly. Furthermore, its orbit is not perfectly this sinuous ellipse either, because the pull of Venus, Mars, Jupiter and the other planets distorts the shape of the orbit and even makes the Sun’s location wobble as the Earth goes round it. At the level of the tiny effects you’re thinking about, even comets and distant stars affect the Earth in tiny ways.
None of this is drag, however. This is just gravity.
But on top of all this, the Earth travels in *outer* space, which, as the book emphasizes, is not quite the same as *empty* space! First, there are atoms and subatomic particles floating around in the solar system, as well as particles from the solar wind, and as the Earth sweeps them up, its orbit is affected. In addition, all across the universe, there are photons (the “cosmic microwave background”) leftover from the Big Bang, and as they collide with the Earth, they do gently affect its orbit. Measuring these effects would be virtually impossible, because of all the much larger gravitational effects that I mentioned in the previous paragraphs. But they are there.
In principle, I could have explained all of this in the book. But a book has to flow. It’s better to explain this kind of detail in a footnote, or here on a blog. So thanks for asking!
Hi Matt, in classical electromagnetism we’re taught that the mass of a point charge isn’t affected by electromagnetic fields. I’ve always found this to be a mathematical assumption that conflicts with my physical expectation from thinking about how charged spheres affect one another’s mass: they polarize one another’s charge leading to a change in one another’s intrinsic electric field, intrinsic energy and therefore mass. Hence:
How is the rest energy/mass via E = hf of a wavicle, such as an electron etc, affected by polarization effects etc from other wavicles?
Just finished your amazing thought provoking book.
I really like the image of a stationary electron as a high-frequency low-amplitude extended standing wave.
If string theory turned out to be true, would that image have to drastically change ? I’m having difficulty picturing the combination of a small vibrating string with the extended standing wave ( in the electron field ).
I also liked the way you explained the difference between the waves and the medium, with the waves almost having a separate existence.
In fig 41, the vertical axis seems to represent a real value of the electron field at a location, but elsewhere you explain that for a fermionic field one plus one is zero. With such alien maths I find it hard to imagine the what the wave would look like. Should I think that the fermionic nature of the electron field really a property of the underlying medium, and (real-valued) waves sit on top of that strange medium.
I was also wondering if the quantum nature of the electron field was something similar, maybe some strange property of the underlying medium, whereas what we experience are the waves sitting on top of that peculiar medium.
Yes, you are absolutely right that Figure 41 is really more correct for a bosonic field’s wavicle, such as for the Higgs boson itself. It is much harder to imagine drawing a fermionic wave. But drawing any of this is suspect; after all, I can draw a wave with any amount of energy, but these are wavicles, and so, for a definite frequency, should only have special amplitudes. I can’t draw that.
You should not think of any of these waves as “on top” of a medium. They are inside it, like sound waves inside air, or seismic waves inside rock. This is hard to draw, but maybe not so hard to imagine in one’s head.
The quantum nature of the fields is probably a property of the universe as a whole, or of the rules that govern it. Whether that can be thought of as a property of the universal medium is far from clear. But that quantum property already assures that the waves in this system, whatever it is, will come in wavicles.
Good question. In the end, the image doesn’t change, but to understand why it doesn’t change is hard.
In a way, we’re lucky that an electron as a standing wave is still something I can draw. When we get to string theory, it’s harder to draw the full picture. Part of the issue is that the massless (or very low-mass) particles corresponding to strings are very hard to draw anyway; they aren’t the little wiggly strings that people (admittedly including me) naturally use in images.
The problem is that one needs to understand the idea of a string field, whose vibrations are strings; that’s no simple matter. Then one has to understand why string theory includes massless (or very low-mass) particles such as photons or electrons; the picture of little wiggly strings that people naturally draw doesn’t actually apply to them. Finally one has to understand why a string field contains an infinite number of fields. In the end it all boils down to my picture, but it would take several chapters and a lot of mental gymnastics to see how it works.
So it’s no surprise that you’re having difficulty picturing this. Again, your image of a “small vibrating string” is not really what an electron is, even in string theory. Any string that really can be pictured in this way has a mass that is much larger than that of any known particles, up at the string mass scale.
Hi Matt , you managed to find the right middle between philosophy and physics writing a book to convey something profound with competence and passion. Now a question: are we wavicles or are we describable through wavicles?( are wavicles the map or the territory? ) Thanks again
Thanks for the very kind words!
Wavicles are ingredients, just as we would expect particles to be. They are the simple objects out of which complex objects, like us, are formed. We do not satisfy basic features of wavicles. For instances, wavicles satisfy the Planck/Einstein relation E = f [h], and all wavicles of the same type are exactly identical (in that you could exchange one for another and no experiment could tell that you had done so.)
In the last chapter I gave some criteria that separate simple things like atoms from complex things like snowflakes. We’re definitely on the far side of those criteria, which is why each of us is unique (and ever-changing.)
You say the energy vs. Higgs field value is shaped like the bottom of a wine bottle, with an unstable point at the center of the bottle. I have read elsewhere that this wine bottle was more parabolically shaped, with a stable point at the center of the bottle, in the very early universe when the temperature of the universe was very high. This is considered part of Spontaneous Symmetry Breaking. Why and how does the Higgs energy curve depend on the temperature of the universe?
These statements are often made loosely. The Higgs field’s potential energy is the potential energy; it doesn’t change with temperature. But what determines the Higgs field’s behavior at finite-temperature is not the potential energy; it is a thermodynamic free energy. This is not special to the Higgs field but is true of any field in a finite-temperature system; one must consider the entropy of the system as well as its energy.
Physically, what this means is that at high temperatures, thermal fluctuations make the Higgs field jiggle (even more than quantum fluctuations) and prevent it from settling down at the minimum of the energy. Computing the free-energy is a way of comparing the effect of these thermal fluctuations compared to the effects of the potential energy. One can write the free-energy as a “finite-temperature effective potential”, and that is the object that is parabolically shaped at high temperatures and turns into the true potential energy at very low temperatures.
The same issue applies for the magnetization of an iron magnet. There is a potential energy for the magnetization that has a minimum at a non-zero value inside a magnet. That minimum is what the magnet chooses when it is at zero temperature. But at finite temperatures, the iron atoms jiggle, and if they jiggle enough, the magnetization switches off — a phase transition. The free energy of the magnetization is used to calculate this, and one can phrase it as an effective potential for the magnetization field; it qualitatively resembles the Higgs field’s effective potential.
Prof Strassler, I very much enjoyed your book. However, I’m struggling a bit on how to visualize photons as they travel through the cosmos. As I understand the book, each photon is a wavicle consisting of a traveling wave in a discrete energy packet at value E=hf. But does the wavicle itself travel as a wave as it goes from point A to point B, or more like in a straight line? Also, in chapter 16 you say that a single photon wavicle can spread out to occupy a room-sized space. But how does it do this and still maintain its specific frequency?
These are basic questions, I know, but I would much appreciate your insights.
These questions may be “basic”, but they are not “basic” in the sense of “elementary” or “easy”. They go to the heart of what makes quantum physics so hard to understand and to explain. I can’t give you simple answers — they don’t exist — nor can I give you an intuitive answer — they don’t exist either. Experiments that try to address such questions give highly counterintuitive results.
First, an easy point. A photon doesn’t *necessarily* have a fixed frequency. If it does, then it is a spread-out traveling wave (like a sound wave at a definite musical note) with E=hf. But it can also have a more complex shape, in which case it has no definite frequency — it is built from a combination of traveling waves at a variety of frequencies (for instance, like a sound wave that makes a “clunk” sound). In the latter case, it is possible to make it somewhat localized. (And in this case it will not have a definite energy.)
A little more difficult is this: a photon does not go from point A to point B. As a wave, it is never “at point A.” It’s not a point object, and to squeeze it (for a moment) to a point would require a substantial artificial effort, requiring a huge amount of energy. [See Figure 40.] Even a photon emitted from an atom is not at a point — after all, an atom is not a point. In subatomic terms, an atom is huge, even though it seems small to us. Also, the photon takes time to emerge from the atom, also, during which time it is spreading out. So your question “does the wavicle itself travel as a wave as it goes from point A to point B, or more like in a straight line?” should be unasked; it’s not a meaningful question.
More meaningful would be: if the photon is emitted by one atom and is detected through absorption by a second atom, what was it doing in between? It is no longer a point-A-to-point-B question, but it is a region-A-to-region-B question — so the photon is certainly not a point traveling in a straight line, and most definitely is behaving as a traveling wave, and typically (in atomic emission) a fairly simple traveling wave with a definite frequency and energy.
Most subtle: My (near-throwaway) comment in chapter 16 about a single spreading wavicle. I did not intend it to be clear; it was intended only as a nod toward those aspects of quantum physics that my book does not cover. I’ll give you an example of what I had in mind, but really, a hundred pages are required to do this justice. (I may address this on the blog in coming weeks, to some extent, but can’t really answer properly in a comment.) I’ll give you one example to illustrate the issue.
The example is the decay of a stationary Higgs boson to two photons. The two photons have definite energy; each has half the Higgs boson’s internal energy. To conserve momentum, the two photons must travel, as waves, in opposite directions. But we do not and cannot know which directions they will take. One photon could go north, the other south. Or one could go southeast, the other northwest. Any direction will do, as long as one photon goes one way and the other goes the other way. So what are the two photons doing? It depends what you mean. If we detect neither one, then quantum physics says that they they are going in all possible directions — and in this sense, they are going everywhere around the room. [This despite the fact that their energy and frequency are known.] And yet, if we detect them, only one atom will absorb each one, and whatever atom absorbs the first one, an atom on the opposite side of the room will absorb the second one. This shows, in a sense, that neither photon can be treated as independent of the other… they are correlated… and so to ask about what one of the photons does without talking about what the other does is to make an unjustifiable assumption that each photon has an independent reality.
You can perhaps see why I chose to carefully skirt these incredibly confusing issues in this book; one can understand the Higgs field’s role in nature without getting lost in them. But one cannot understand nature as a whole without diving deeply into them — and people have written many volumes without a consensus having emerged on how to think about them.
Thank you for your detailed reply. It is very helpful.
However, I’m still wrestling with what a photon looks like as it travels from “region” (which as you say is a more accurate word than “point”) A to region B; for example, through the cosmos, from some distant star to my retina.
I think I understand the fuzziness of its path caused by its wave nature as is shown in Figure 40. However, I am hung up – perhaps erroneously – on the old Maxwell model of electromagnetic waves traveling through space (or the luminiferous aether) much like sound waves do through air. I also note your comment to gsakhardande where you describe a cell phone signal as traveling in large amplitude waves of photons.
Therefore, clarifying my original question: Do photons (singularly or in groups), in addition to being discreet wavicles, generally also travel through space as large amplitude waves (e.g., as Maxwell waves)?
Sorry to belabor this point. I’m just trying to get a more accurate mental picture of the wave / particle duality of photons.
The old Maxwell model of waves traveling through space is not changed, as long as the photons that make up the Maxwell wave are produced in a sufficiently straightforward fashion. Of course, Maxwell waves need not be simple waves with a definite frequency… sunlight is hardly simple, as it extends across all frequencies. So to keep the answer to your question short, let’s take an artificially simple case.
Imagine we had an astrophysical object that creates a beam of Maxwell waves at a definite frequency f and moving in a definite direction. (Roughly speaking, such things exist: they are called “astrophysical masers”.) Each second, the beam carries energy E_beam/sec. Then the number of photons emitted each second in the beam is n_photons/sec = (E_beam/sec) / f h , where h is Planck’s constant.
Maxwell’s equations also tell you that the energy in the beam is proportional to the square of the amplitude of the wave. Therefore the number of photons per second is proportional to the square of the amplitude of the beam. If the beam has cross-sectional area L^2, then
E_beam/sec/L^2 = 1/2 epsilon_0 c A^2
where epsilon_0 is the “permittivity constant” of nature, c is the speed of light, and A is the amplitude of the electric field. In short:
A^2 = 2 E_beam/sec / (L^2 epsilon_0 c) = 2 n_photons/sec / (f h L^2 epsilon_0 c)
Therefore, if you know the amplitude and the shape and energy flow of the beam, you know the number of photons per second in the beam, and vice versa. Smaller amplitude means fewer photons. Changing the number of photons directly changes the amplitude of the Maxwell wave; they are inextricably linked. You can think of the Maxwell wave, therefore, as a piling up of photon wavicles, each with the same frequency.
You can conversely think of as a photon as the limit of a Maxwell wave with a very small amplitude and a finite (but not very short) duration. For instance, if the beam turns on at time 0 and turns off again at time T (where T * f >> 1, so this is still a wave with many crests and troughs) then the total energy emitted is E_total = (E_beam/sec)*T. If we choose E_total to be equal to f h, so that the brief beam consists of only one photon (still with many crests and troughs), then the wave’s amplitude is
A^2 = 2 / (f h L^2 T epsilon_0 c)
That is the smallest amplitude this brief beam of light can have; if you try to take the amplitude smaller, you’ll get no light at all.
Now, when you take a more complex, realistic wave, containing many frequencies and moving in many directions outward, for instance from a star, then the story of the energies, amplitudes and photons is infinitely more complicated. But it boils down to the above story, using much more complex mathematics.
You may also find this series of articles useful: https://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/ , especially the 5th in the series.
Prof. Strassler, Thank you again for providing such a detailed reply, and especially the included math. It was very helpful and gave me a more accurate mental picture of how photons travel through space.
Please forgive this simplistic question but is the increasing amplitude with number of photons analogous to constructive interference?
This isn’t simplistic at all! It’s a very good question.
Normally, what is meant by “constructive interference” (and “destructive interference”, too) occurs when waves traveling in different directions intersect, causing a complex pattern; in some locations the waving is enhanced, and in others reduced. See https://www.youtube.com/watch?v=PCYv0_qPk-4 for a nice video of this effect.
But when I’m writing about the increasing amplitude of a wave with the number of photons, I’m referring to photons traveling in exactly the same direction, absolutely in synchrony. The effect can indeed be viewed as an extreme example of constructive interference — but in this case, in contrast to the case of intersecting waves shown in the above-mentioned video, there are no corresponding areas of destructive interference. So you might want to call this “perfectly constructive interference.”
This effect occurs when we dial up the brightness of a laser beam. The photons of a laser are perfectly in synch, and the brighter the beam, the more photons per second are emitted from the laser.
Is it correct to say that quantum/wavicle moves thru spacetime? First, since we only collect information about quantum photon-by-photon we can only say that that quantum is here-now and there-then but with no continuous information about between. Second, since quantum has no identity (“hair”), there is no “this” quantum to trace a continuous trajectory from here-now to there-then.
The second point is a red herring in the sense that it’s always true; you can never say which photon is which, nor which electron is which, but often there is only one particle candidate which is physically capable of going from A to B… for instance, when a muon decays and an electron comes flying out, the probability that the high-energy electron wasn’t from the muon decay is tiny.
The first issue is too tricky to address in a comment, but I’ll make one remark. A lot of what we know has to do with whether non-destructive measurements are possible — for example, a bubble chamber measures a set of positions that an electron has over time without dramatically affecting its motion. It is then natural to draw a line through the bubbles, and say “that’s where the particle went” — and in fact that is correct, when we remember that the bubbles are nearly macroscopic and so our knowledge of the particle’s trajectory is extremely fuzzy. In other words, it’s perfectly fine to say that the particle went from A to B, and in many cases you can even show it is true, as long as you remember that you typically don’t have microscopic knowledge of where A is, where B is, or where the trajectory is. To say it another way: the answer to your question is that it is not a black-and-white situation; it’s grey, and it depends on the details of the experimental situation.
Thanks a lot Prof your reply. That was very helpful.
I had settled into the discursive targeting of the book, but a line on p. 85 (second paragraph of section 6.2) dropped me out of it: “For instance, if a beam of electrons is pointed at a thin surface, one can measure the impact of the individual atoms on the beam as it passes through the surface.” The use of “impact” here seemed very backwards — it’s the electrons that are impacting the atoms, not the other way around. (“Did I misunderstand? Are we were throwing gold atoms at a thin foil of electrons?” — “gold” because at the time I was fairly confident you were referencing Rutherford’s experiment(s).) Maybe this isn’t super important, but it dropped me completely out of the rhythm and had me puzzled for most of a minute.
Top-of-my-head alternatives for “impact”: “effect”, “push-back”, “deflection caused by” (minus the “of” in the original). Given the excellence of the text, I expect you’ve thought of something better already.
Thanks for noting the issue with “impact”. Although I only meant it metaphorically rather than literally, I can see that it could be read otherwise.
“Effect” is over-used in the text as it is, so that won’t do. Perhaps “influence” would have been best… the individual atoms influence the beam, and we can look at the changes in the beam caused by the atoms to learn where the atoms are located.
It’s not quite Rutherford’s experiment — the goal of that experiment was to study nuclei inside of atoms, not the location of atoms in a crystal. Moreover, Geiger and Marsden used Helium nuclei (i.e. “alpha particles”), not electrons. Nothing special about gold, either; any set of atoms will do, and indeed different crystals will affect the electron beam differently (with an example given in Figure 13). What I’m really referring to is Transmission Electron Microscopy (TEM) https://en.wikipedia.org/wiki/Transmission_electron_microscopy
Ref Chapter 9, if relativistic energy is given by the old formula E=1/2mv^2, and if m is intrinsic mass, that would imply that an object cannot have relativistic mass if it has no intrinsic (inertial) mass. Obviously I’m not understanding something here. Thanks!
Indeed, that’s not the right formula. The whole story is quite complicated.
Total energy is related to relativistic mass by E_total = m_relativistic c^2 .
Total energy is related to rest mass by E_total = m_rest c^2 / (1 – v^2/c^2)^(1/2) = Sqrt[ p^2 c^2 + (m_rest c^2)^2], where p is the object’s momentum.
Notice that the last formula makes sense even if m_rest = 0; even without rest mass, a photon can have both momentum and total energy, and thus, by the first formula, it can have relativistic mass.
Intrinsic mass is not the same as inertial mass. Intrinsic mass is what I called “rest mass” and is also called “invariant mass”; it is constant and independent of speed. Inertial mass and gravitational mass are the same, but they do depend on speed, or more generally, upon momentum. Photons have momentum, total energy, and gravitational/inertial mass, even though they have no rest mass (no intrinsic mass.)
The formula E = 1/2 m v^2 only applies to motion-energy, not total energy, and it does not survive into Einstein’s relativity. The formula for motion energy is
E_motion = E_total – E_intrinsic = m_relativistic c^2 – m_rest c^2 = Sqrt[ p^2 c^2 + (m_rest c^2)^2] – mc^2
If m_rest = 0, as for a photon, then E_motion = E_total = p c.
If speeds are slow, then p = m v and the square root can be approximated, and so E_motion is approximately p^2/(2 m_rest) = 1/2 m v^2 .
I think that covers all the issues raised by your question. Feel free to follow up.
In the third sentence of your reply, I get the first equation for the total energy but I’m having trouble understanding how the second equation in that sentence can be anything but 0 if rest mass is 0. If p equals the relativistic mass times velocity (is that right?), and relativistic mass is proportional to intrinsic mass at any given velocity (is that right?), then how can p be anything other than 0 if intrinsic mass is 0?….. Thanks for bearing with me!!
The second and third sentences both give formulas for E_total, and if you look at them carefully, they say that m_relativistic = m_rest / sqrt[1-(v/c)^2]. But this formula becomes ill-defined for m_rest –>0, v–> c, which is the case for a photon. In particular, as you take a particle’s rest mass to zero holding its energy fixed, which requires that you take its velocity to c, its relativistic mass remains finite. In other words, your mistake is that while it is true that “relativistic mass is proportional to intrinsic mass at any given velocity”, the proportionality constant goes to infinity as v –> c, and so your conclusion does not follow. Does that make things clearer?
Thanks, Dr. Strassler. That helps!
I have read that the reason that the tide occurs on the opposite side of the earth from the moon is that the earth is being pulled away from the water on the far side. Would you consider that a phib? It seems to me that that is a reasonable interpretation of what is happening.
It’s not entirely wrong, but I find it confusing, as it gives the wrong intuition.
The point is that the gravity on the Earth’s center is greater than the gravity on the part of the Earth farthest from the Moon, and less than the gravity on the part of the Earth closest to the Moon. This change in gravity from one side to the other tends to want to stretch the Earth into an oval pointing at the Moon. However, the Earth is stiff enough that it resists this effect. Meanwhile, however, the ocean is less stiff, and flows in respose to this stretching effect. It’s the fact that the ocean flows while the Earth does not deform that leads to the two bulges in the sea.
I’ve explained this in detail here: https://profmattstrassler.com/2023/10/27/what-really-causes-our-twice-daily-ocean-tides/
I found this part somewhat confusing. “ It’s because Bostonians view Miami as moving in a daily circle, one that leaves the distance between the two cities always unchanged—and vice versa. You can get a hint of this from Fig. 2; if you turn the picture in a circle centered on any one of the black dots, you’ll see that dot as stationary while the other two dots move around it.”
If you were standing on the dot wouldn’t your line of sight rotate with it and therefore you wouldn’t perceive any motion of the dots rotating at the same angular velocity as yourself?
What you say is true, and yet not quite.
If you were to believe that the Earth is fixed in space and the Sun and stars rotate around it daily, you’d indeed think your line of sight is fixed and the location of other cities does not change.
But if you accept that the Earth rotates, then you also would view the apparent motion of the Sun and stars as an indication that your line of sight is rotating, and knowing that, you’d indeed infer that the direction to other cities rotates daily.
Galileo’s principle explains why it’s not instantly obvious which perspective is correct. Of course most people do accept that the Earth rotates. And yet, they often don’t realize how rapidly we all move relative to our cousins in other cities, even when we’re all sitting down. To emphasize the ubiquity and speed of this secret motion was the point of the discussion.
Does that clarify the issue?
Thanks, perfectly clear. It’s just in my view the passage makes it sound as if a naive measurement is possible hence my confusion.
Note that you can measure rotation inside a laboratory, using the Sagnac effect (the difference in the time it takes for photons to undergo a closed path if they are traveling with the rotation or opposed to it). The Sagnac effect is used routinely in ring laser gyros in inertial navigation systems, and (if scaled up a bit) can be used to monitor the Earth’s rotation. (For example, there is a 4 x 4 meter ring laser gyroscope in Germany that keeps track of Earth rotation changes.)
Your point is well taken…
Hi Matt, thank for an excellent book that covers field theory. It’s unique.
How does a wavicle, like an electron wavicle, travel as a standing wave, say in a wire or as a beta particle? Is an electron wavicle a stable entity or constantly regenerating? Does it matter if they are identicle?
How does a boson exchange take place to mediate a force? How does it know where to go to make the exchange?
Thanks again!
Thanks! Glad you liked it.
Well, if an electron is traveling, it is *not* a standing wave. It’s only a standing wave if it is stationary (relative to you). If it travels past you, you will see it as having a different shape, more energy, and a higher frequency.
An electron is a stable entity, in the sense that it never spontaneously decays away and need not regenerate. That’s because (a) it has energy and charge, both of which are conserved, and (b) because there is nothing into which it could spontaneously be transformed via the process known as “decay”. This is discussed in Chapter 21 or 22.
Yes, it matters a lot that all electrons are identical. All of atomic physics depends on it. But maybe you mean something else by “does it matter”?
The idea that forces come from “boson exchange” is one of the phibs I hate the most, because it leads to questions such as yours that are perfectly sensible, but have no answer. The notion of “boson exchange” is math that has been misrepresented as physics. Forces do not come from “boson exchange”, because the bosons involved are “virtual particles”, which are not particles (i.e. wavicles). No objects are being “exchanged”. Instead, what is happening does not involve wavicles, but rather the same general behavior of bosonic fields that one learns in first-year physics class — where one sees that electric forces come from electric fields. To express those fields in terms of virtual bosons is sometimes useful mathematically, but obscures the physics.
The history of this notion arises from Feynman diagrams, a math technique for doing calculations that was once the most efficient method. But the amount of real physics behind Feynman diagrams is limited, to the point that the method is used less and less every year, having been superseded by more efficient and general techniques.
Thank you,
Steve
Hello, while reading chapter 5, when I got the discussion of photons having a zero rest I wondered; how do we know that the rest mass is zero? If a photon is always moving, there is never an instance where we can be said to be stationary relative to it, right?
I found the distinction between rest mass and other forms of mass especially interesting, for I remember reading years ago that ‘light can exert a pressure’ (I was probably reading this in the context of the idea of solar sails) and ‘photons have no mass’, statements that seemed contradictory as I know enough physics to know that common definitions for pressure is a force per unit area and force being defined as mass times acceleration, and so I couldn’t understand how something with zero mass could exert a force.
Good questions. I do address the issue of a photon’s rest mass briefly in chapter 17, but it’s reasonable to ask it now.
I’ll start with pressure because that is simpler. The problem is indeed that you are trying to use Newton’s laws in an Einsteinian world.
Pressure is a measure of the momentum carried by the objects pounding a surface. While in Newton’s world, momentum is mass times velocity, this is not true in Einstein’s world (or even in Maxwell’s world of electromagnetic waves.) For Newton, one can write the relation KE = p^2/2m , where E is kinetic energy, p is momentum and m is mass. But in Einstein’s one writes a formula for total energy: TE = Sqrt[(mc^2)^2 + (pc)^2], and kinetic energy is then KE = TE – mc^2, which one can show becomes Newton’s formula when speeds are slow and TE is just a bit larger than mc^2. You will see from Einstein’s formula, however, that total energy for a zero-mass particle is TE = pc. Thus a photon does carry momentum equal to its total energy divided by c, and so it can therefore exert pressure.
Now, how do we know a photon’s rest mass is zero? At the risk of being circular, one way we know is that photons travel at the cosmic speed limit, which is only possible for objects with zero rest mass. Another clue is that we do indeed measure that E = pc for photons.
But all measurements have uncertainties. You should therefore ask how precisely we know that a photon’s mass is zero, and through what means. The best technique is different from what you might guess, putting to use yet another relation between photons and the electromagnetic fields in which they are ripples.
There is a direct linkage between the rest mass of a photon and the range of the electromagnetic force (a point I do not discuss in the book, but I suppose I should add to the book’s supplemental material.) That is, instead of the force being the usual 1/r^2 that we learn in school, the force would instead be approximately e^(-mr)/r^2 if the photon had a mass m. Measurements of long range magnetic fields across large portions of the universe give a limit on the photon’s rest mass: planetary magnetic fields measured by space satellites show unambiguously that the photon’s rest mass can be no larger than 6 × 10^(−16) eV/c^2, and a 2007 argument puts the limit at 10^(-18) eV/c^2. (There are some less reliable methods which suggest it must be smaller than 10^(-26) eV/c^2.) These methods are much more powerful than trying to make precise measurements of a photon’s precise speed, energy and/or momentum.
Thank you! There is much more to this than I would have guessed.
I’m only on Chapter 7, and you have answered so many questions I didn’t even realize were questions.
A HUGE thank you for your careful and lucid explanations. Interweaving the vews from both ends of the telescope.
And your insistence on precise use of language– So Very Important these days.
Those phibs in sound bytes never sound right to me, even without much science background.
Thanks for writing! I’m gratified that my approach is helpful to you.
A question. Note 2 of Chapter 22 says “there’ s no precise, unambiguous definition of the up, down, and strange quark rest masses. That’ s because the powerful forces keeping these quarks trapped never allow them to be stationary and isolated.” Is it an experimental or theoretical problem, i.e. whether the quark trapping makes precise measurement of their masses very hard, or the trapping makes the quark immediate surrounding very messy, and they can’t be described as well-defined ripples in their respective fields?
It’s more the latter than the former. Since we never find these quarks isolated, they are always surrounded by and interacting with other particles, so we don’t get a chance to isolate one of them and do a crisp measurement of its energy and momentum. But even more profoundly, the mass of a particle which is never isolated turns out to be ill-defined mathematically. So in a way, the problem exists is at all levels, and the reasons at the different levels are closely related.
Just from the symmetry argument Fig.34 can’t depict a travelling wave as the wind field is mirror-symmetric relative to the pressure crests/troughs there and could describe the wave travelling in the opposite direction as well, while they must definitely be different. And really, the figure and its explanation relate to the standing wave at half the amplitude. To find the correct wind field let’s consider the sound generator plane. It starts moving to the right followed by harmonic oscillations around the origin. For the sound wave moving to the right, the max right-wise plate speed which is reached at the origin corresponds to the max sound pressure (due to its ram pressure), and simultaneously to the max right-wise wind speed. In the same manner, max left-wise plate speed at the origin – min sound pressure – max left-wise wind speed. Therefore, the max wind arrows should be placed at the crests pointing right, and at troughs pointing left.
Again, correct. (Similarly, spins precess in a magnetic field, rather than rocking back and forth.) But here the issue was to get the point across that the wind is a field and that sound is a wave in the wind. Putting in the correct figure would have required another layer of explanation, lengthening the discussion and provoking additional confusion for more readers. Instead, I decided I would give the correct explanation (and the figure) here on this website (to be added soon); this seems the best compromise between being clear about the points that matter and being 100% accurate about the points that don’t matter.
Classic travelling wave is a core concept for a book on waves and fields. Yes, it requires some thinking, but I believe that good understanding of simple cases will help readers to grasp more complex concepts later. For example, here we encounter not three, but five interconnected entities – air, pressure field / wave, wind field / wave, and sound is equally a pressure and a wind wave. Pressure and wind wave influence and support each other during the wave propagation, here’s just one step from an electromagnetic wave. I think it’s possible to explain it not going to technical details (I have it for myself). And I would have avoided “At the center of a trough or crest, the wind field drops to zero” which is outright wrong.
On your last point, fair enough. On the rest of it, I disagree. You have made a very simple point into a highly complex one, and I’m likely to delete it from here because you are again straying into things that the book does not cover. The purpose of this page is for people to ask about things they don’t understand, not for highly trained physicists to teach me that I should have done things differently, which only is more confusing for those who are not highly trained physicists. This page has an intended use, and I can’t let it be taken over for a completely different use.
Sure delete it, sorry if I went too far. I’m not a trained physicist, just an engineer with math/physics background and an eye for details. I really enjoy reading your book and will post at Going Beyond thereafter.
You’re trained enough! 🙂 Of course I’m glad you’re enjoying the book and I’m happy to discuss it. Maybe I should add a page to “Got a Question” and “Beyond the Book” that specifically allows us to discuss the pedagogical choices made. I’m having trouble thinking of a good name for it…
At Fig.33 what you describe as “leaning” is actually shearing. Leaning implies rotating as a whole, like The Leaning Tower of Pisa, while shearing involves sliding layers as in the shifting stack of cards. I’m not aware of using the leaning and shearing terms interchangeably.
This is not a technical book, and I did everything to avoid technical jargon. “Shear” does not mean in English what it means in physics, and so it is yet another word that would put a unnecessary barrier between reader and subject.
Oh, sure. I learned shear from physics textbooks only. But may be sliding or shifting would work better? Their English meanings are closer to the actual process.
I’m sticking with this decision.
Beautiful wind field at Fig.31. And the original animated map at hint.fm/wind is mesmerizing! For the figure, it would be great to have full directionality info, such as by adding small arrows to the lines. Without that info we need an additional input to fully decipher the map. Here we have two storms “draining” counter-clockwise – the larger over Pennsylvania and the smaller over Kansas. From them we can trace the wind field to other areas, and the pattern of the wind blowing from thinner end of the lines emerges. However, some areas are still hard, for example my initial guess for Arizona-Utah border area was wrong.
In chapter 11 (The Waves of Knowing) you say: “This is also why you cannot surf a wave crest that isn’t breaking; it won’t take you with it”. Here by “surf” you mean “float freely along” I think. However, surfing usually means “riding a surfboard”. Riding a crest (“going into wave”) starts before it’s breaking. A surfer slides her surfboard down a coasting crest obliquely such as her forward speed is equal the crest’s coasting speed, staying roughly halfway down the crest.
Great book. I learned a lot. Found a couple of typographical errors :
(1) Chapter 19 (page 257) : “millibarns” should be millibars
(2) “Library of Congress Cataloging-in-Publication Data” (no page number) says the author is Karl Sigmund” and the title is “The waltz of reason…”
My hardcopy is “Printing 1, 2023”.
Probably you made those errors on purpose, to see if people are reading carefully 🙂
Keep up the good work.
Oops! millibarns –> millibars, I’ve done that twice this year. Hah! The Library of Congress error is entirely the publisher’s, of course, and was noticed some time back; they are fixing it in future printings. Maybe your copy will someday be worth more than you paid for it 😉
(1) FYI, my motivation to acquire your your book came from reading Don Lincoln’s review in Science (February 22). Unlike Lincoln, I like the way you used end notes. (2) My daughter is a geologist. She loved that, on page 3, you compared human existence to seismic waves in rock. She may never finish the book, but she will always be inspired by that metaphor.
If the metaphor sticks, that’s a huge win! And yeah, endnotes are always an issue — I don’t like them much either, and in any case it was the publisher’s decision.
I had always hoped this would be a 21st century book, with clickable endnotes, but publishers are still in the 19th century. But I’m going to put all the endnotes on a webpage, when I get a free minute, so one can have them available on one’s phone while reading the book.
The general problem is the cutoff in energy/momentum.
It’s easy to imagine a world that is the same in all directions and in all locations because it is somehow full of tiny particles moving in all directions that bombard us from all sides. Of course this is already an infinite number of particles, and you have to wonder where all their energy comes from, but set that aside.
To make a world that appears the same for all observers in steady motion (i.e. Lorentz-invariant), using a clould of particles coming from all directions, is much, much harder… especially since there is no limit on the amount of energy that the individual particles in the cloud must carry. So now not only do you have an huge number of particles everywhere, most of them individually carry enormous energy … and any cutoff on that energy is easily detectable, since that cutoff will be easily noticeable and will be different for different observers.
If it were easy to model Lorentz-invariant systems, you can bet it would have been done. There are some cases where Lorentz-invariance emerges in systems that don’t obviously have it — the “gauge-string” or “AdS-CFT” correspondence gives an example. But the emergence is a quantum effect, far from the simple classical idea you’re playing with.
Concerning the vacuum energy and induced vs suppressed zero-point excitations. On intergalactic scale the suppressed zero-point excitations might still dominate as the space there is mostly empty. Then this model predicts the vacuum equation of state value as close to but still larger than minus one (due to dilution of the induced excitations during the expansion), which is vaguely consistent with the observed value.
Serge, this is all fun, but if you wouldn’t mind, please move it to this page: https://profmattstrassler.com/waves-in-an-impossible-sea/waves-in-an-impossible-sea-commentary-and-discussion/going-beyond-the-book/ The current page is for people asking questions about the book itself, and I don’t want these kinds of speculations to get in the way of people trying to find answers to their personal questions.
Duplicated the thread in “Going Beyond the Book”
Thanks, I appreciate it. I removed the older thread.
You were such a courageous boy jumping while flying in a jet. You might have expected that if you’d jumped high enough, you would have tackled by the jet’s wall rushing at 500 mph! Here’s an exercise which I came up with many years ago during my long subway commutes, and which also plays with relativity principle. In a subway car take a seat for you to look sideways. Suppose the train goes to the left of you, and you’re in a long steady hop between two stations. Close your eyes. Without visual clues, feeling just steady bumps and shaking, it’s rather easy to trick you mind thinking that the train goes to the right of you, in opposite direction, as by relativity principle they’re indistinguishable. And when the train starts braking, you’ll feel – quite opposite – rather intense speeding up! The feeling lasts until you realize that instead of intensifying, bumps and shaking subside.
🙂 I will try that when I am next in New York City.
Oh, please remove that post, wrong thread.
Hi Matt,
Not sure if this is the place to post this question but it is related to the book and the “Sea”.
On you recent interview with Sean Carroll you were talking about the Luminiferous Aether.
Matt: “this magical substance which was called The luminiferous aether a name which has got lovely resonances”
Sean: “it’s a great name compared to a lot of other dumb Names physicist came up with, Too bad it doesn’t exist”
Matt: “or maybe it is, we’ll come back to that”
But the conversation never returned to whether or not that aether exists.
Can you give a little overview of what your comments on the subject would have been if you got back to it?
I am a little over half way through the book and you seem to like the idea of a ‘space medium’ but so far don’t seem to committed.
Thanks
Peter Becher
p.s. I did ask the same question of Sean for his AMA April ’24 on why he seemed so sure that it does not exist. Not sure if he will answer it.
My answer to this question appears in Chapter 14, you may be almost there yet. Circle back if you don’t understand my answer.
On pg 212 of WiaIS you write:
“In short, we have a remarkably clear (if incomplete) picture of what the known elementary fields _do_. Despite this, we have barely any concept of what they _are_ —assuming that’s even a question we should be trying to answer.”
My question is, should we be concerned that this seems to sound curiously similar to the debate over the “Copenhagen Interpretation of QM” [CI/QM]. That is, (to simplify the issue enormously) that those who support the CI/QM argue that QM is basically “merely” a highly-successful set of tools for calculating the outcome of experiments/measurements, and that asking “what’s really going on” is a fundamentally meaningless question.
(Similarly, those who are uncomfortable with CI/QM argue that this approach is deeply unsatisfactory, in no small part because it deliberately ignores the underlying “Reality” —in the EPR sense— of the situation.)
Now, I would never accuse you of being in the “Shut up and Calculate” camp 😉 . But does this seem like a reasonable characterization of the (current?) situation? And again, should we be concerned?
I don’t think there’s reason (yet) for that level of conceptual concern. Quantum mechanics is inherently confusing to the human brain, and that’s why weird interpretations have emerged for it. By contrast, the issues on page 212 might be much simpler than that.
If you didn’t understand what air was, you might have trouble interpreting what a barometer actually measures; “pressure” would be just a name, not an underlying concept. Once you had a better grasp of the nature of air, that would change. It’s possible that we can’t interpret what the electron field is because we don’t understand the full internal structure of the cosmos; once we learn that structure, perhaps the electron field’s nature will become clear. In some string theory constructions of imaginary universes, this is what would happen.
Alternatively, it might turn out that space doesn’t exist after all, and both space and its fields will be interpreted in terms of, say, emergent phenomena in a completely different physical system.
It’s true, though, that space and the relativity principle are sufficiently puzzling that we might end up with unresolvable confusions and the need for debateable interpretations. Too early to say, I think.
Thanks for the detailed walk through of the basic concepts professor
I am trying to understand how the gravitational mass varies with position/velocity of the observer.
What is the formula for the same ? It seems different from relativistic mass obtained by relativistic version of E = mc^2.
I also saw terms such as metric tensor & energy momentum tensor (in Wikipedia). How would they differ based on relative velocity ?
Basically I am trying to visualize how space curves & influences motion based observer’s relative velocity/position.
There is, in fact, no unambiguous definition of gravitational mass. In general relativity, the concept doesn’t really arise unless you force it to. This is why it is hard to find a clear definition of it on-line; there’s no clear definition in physics. Instead, in general relativity the question is subsumed into the equivalence principle: https://en.wikipedia.org/wiki/Equivalence_principle .
The one thing that we can say is that if you are in a situation where Newton’s laws almost work, then it is clear that gravitational effects depend on motion in ways that Newton would not have expected, and that they grow as an object’s energy grows. But I haven’t been able to find any expert in general relativity who has been able to give me a reference in which it is shown that, in some limited situations, there’s a definition of gravitational mass that is clearly useful and widely agreed upon.
I hope I’ll soon be able to understand this messy situation well enough that I can explain better why there’s no good answer. But up to this point, my efforts to resolve my own questions have run up against the fact that experts seem to disagree.
When I read your discussion about the wave speed method of detection of motion, I was wishing you included an explanation about redshift. It seems like it should be related somehow.
This is a bit intricate. There are different causes for redshift, which can be due both to relative velocity and to gravity. Let me just focus on the relative velocity case, as that’s more closely related to the wave-speed method.
There is a “redshift” and “blueshift” in sound, too; that’s the Doppler effect. If the observer and the object emitting the sound wave are receding from each other, then the sound frequency drops. But the amount of the drop depends *both* on the speed of the object relative to the air *and* the speed of the observer relative to the air.
The redshift for light is similar, yet different. If the observer and the object emitting the light wave are receding from each other, then the light-wave’s frequency drops. In this case, however, the amount of the drop depends *only* on the speed of the object relative to the observer.
In short, as is the case over and over again, light resembles sound, yet differs from it in a crucial subtle way. The Doppler-like effect for light is arranged just so that it is independent of any motion relative to light’s medium — allowing it to be consistent with Galileo’s relativity. For sound, this is not the case; one can use the details of the Doppler effect to measure one’s motion relative to the air.
This is the key conceptual point. I could go into more detail, but such details can be found in many places, such as Wikipedia. https://en.wikipedia.org/wiki/Doppler_effect https://en.wikipedia.org/wiki/Relativistic_Doppler_effect Let me know if my answer and the information on Wikipedia still leaves you wanting more information.
I’ve seen it described something like this: light maintains its speed regardless of its frequency or wavelength, but an observer moving toward encounters the crests sooner and in a way more compacted, and therefore at an effectively higher frequency (blueshift); and the opposite for redshift. It’s not that the frequency actually changes, it’s the relative motion that makes it appear differently.
So it seemed kind of similar to the wave speed method where you described watching the water waves pass by the boat — to determine if you’re moving, possibly how quickly, and in which relative direction.
I’m a non-expert. In reading your book, I really appreciated your methodical examples throughout and consistent wording without relying on the usual seemingly inaccurate metaphors (Mrs Thatcher at a party).
On the one hand, you are right, these issues are related. But you are imagining that there is a “true” — i.e., intrinsic — frequency. And this is a tricky point. Frequencies are generally relative, since they depend on speed, and speed is relative. For light waves, there is no intrinsic notion of frequency.
This is already true in Sound. First, there is the wave frequency as seen by the sound emitter — for example, a violin plays a note on its G string, and that G is the note, right? Well, not so fast. If the violin is moving rapidly through the air, then the sound wave as seen by someone stationary with respect to the *air* may hear it as an F, not a G. There is no “true” frequency of the sound wave, unless you define truth in an arbitrary way… why should the violin’s perspective be truer than the air’s perspective? Meanwhile, someone else, moving throug the air in a different direction, may hear it as an A, or an F-sharp. Who is right? Everyone is right.
In Light, it is even more true. Observers moving relative to one another see the light’s frequency as different. The light-emitter’s perspective is just that of one more observer; indeed, if the light scatters off some moving mirrors, the light-emitter may not even see the reflected light as having its original frequency. Again, everyone is correct. There is no true, intrinsic freuqency for a light wave. This is Einstein’s point.
For an electron, things are otherwise. Observers moving relative to one another see the electron’s frequency as different; that’s all relative. But in this case there is a special perspective — the perspective of the electron, which an observer stationary with respect to the electron will share. In this case, we can define an intrinsic notion of frequency… that of the observer at rest with respect to the electron.
By contrast, no one can ever be at rest with respect to a light wave, and so no light wave (and, more specifically, no photon) can have an intrinsic frequency. This lack of an intrinsic frequency is characteristic of any object with rest mass equal to zero.
And so, yes, redshift and blueshift are relative. If you are moving toward me, and light is approaching us from the other direction, then, yes, you will encounter the light waves’ crests more often than I do — and so, yes, you will see the light as blueshifted relative to the way I see it. But we could say it the other way round; from your perspective, I am moving toward you, and the light approaches from behind me, and so I see the light as redshifted relative to the way you see it. Both viewpoints are correct. There is no “true” perspective. And so your statement “It’s not that the frequency actually changes, it’s the relative motion that makes it appear differently.”, which presupposes that there is a true frequency, is not correct, even though the picture for why redshift and blueshift occurs is correct.
Gravitational blue- and red-shift are even more subtle. I don’t dare go into that today!
Sincere thanks for this brilliant (and brilliantly written) book.
I have a question about figure 37. I believe that this represents what happens for a laser beam, which makes sense given that a laser is coherent and all the photons are in phase with each other?
But that raises the question of what happens if the photons aren’t coherent. If two photons are emitted from a light bulb out of phase with each other do they destructively interfere? It’s got me wondering how many non-coherent photons combine to create a high intensity light beam at all without cancelling each other out (they clearly don’t do so, but I can’t see how!).
I’m glad you enjoyed the book!
Each photon has energy E = h f, where f is its frequency and h is Planck’s constant. The energy of the two photons is 2 h f, and that cannot disappear.
Locally there can be interference effects, but two incoherently emitted photons cannot be arranged to destructively interfere everywhere. There can only be an interference pattern which rearranges where the energy goes, but does not reduce it. The details depend on exactly how, when and where the photons are emitted.
Thanks! The conservation of energy makes perfect sense. I’m not sure what stops two photons from destructively interfering everywhere though? What’s to stop two photons from being identical to each other apart from one being exactly the opposite phase of the other?
I know I’m missing something, I’m just not sure what it is?
🙂 I don’t blame you for not being satisfied with my answer, even though it is correct.
To resolve what’s puzzling you, I think I would need to take you into a bit of the math of the quantum field theory. You are thinking classically, in which electric fields from two waves are ordinary numbers and simply add, whereas in quantum physics we deal with states. Also there are subtle effects from the fact that a single photon emitted from a light bulb is not an infinite sine wave, and must instead be treated as a wave packet — a sine wave inside a finite envelope. At the moment I am not sure of the simplest way to show how this would work, but I will think about it and try to come up with a simple argument. It may not, in fact, be simple…
[An example of something even more important, but not at all simple, involves the claim (even in classical physics) that no information travels faster than light-speed even though phase velocities, for certain types of fields, are generally faster than light-speed. Sometimes facts about waves really are subtle.]
Thank you. I will take it on trust for now.
It’s worth mentioning that the list of things I’m taking on trust is significantly smaller today than it was a week ago, entirely thanks to your book. I’m deeply grateful for all the hard work that clearly went into it.
Big fan of yours and Lenny S’s classes. This refers to the kindle edition, chapter 15, no table 5. Not on iPad and not on pixel. Blank page on iPad, missing page number on pixel. Great book!!
Thanks, I will let the publisher know immediately. You said Table 5; but Table 4 is on the same page. Is it also missing?!
Tables 4 and 5 are now posted here: https://profmattstrassler.com/waves-in-an-impossible-sea/waves-in-an-impossible-sea-tables/
Update: The publisher says: “If the table is missing, the most likely explanation is that his download got corrupted. He should contact Amazon and send them a screenshot to see if they can help him. The problem is not on our end.” Let me know if you get this resolved, or if you can’t.
A question concerning note 4 of Chapt 7 in WiaIS (i.e. where you note that are “drastically abridging the complex prehistory I’d Einstein’s idea [concerning Special Relativy]):
Rather than ask you to expand on that history here, can you suggest a good history-of-science reference that discusses this history?
(For example, I know Pais’s excellent technical biography of the life and work of Einstein [“Subtle is the Lord”] and although the book gives an overview of these issues, it would be nice to find a book-length that covers this topic in depth.)
Thank you
Great question; I’ll have to put a good answer together and add it to the FAQ for chapter 7.
Unfortunately, much of what I know has been cobbled together from many sources, including primary sources and historical research articles, and I can’t just now recall a source that goes into the depth you are asking for. (Moreover, I didn’t keep careful records since I never planned to cover this in the book.) One person who would probably know would be Peter Galison, and you might start with his books/articles (which I highly recommend) and the sources that he uses. It’s really worth learning a lot about the thinking of Lorentz and of Poincare’, who were close to the right ideas about relativity of space and time but never fully understood or accepted Einstein’s novel perspectives; also there are many interesting side stories involving people like Max Abraham and Fritz Hasenöhrl, who were able to recognize that there was probably something important about mc^2 but didn’t think big enough. Compared to the efforts of most others at the time, Einstein’s two remarkably short papers are blindingly clear and to the point; reading them is like drinking cool, fresh water.
One article worth reading, based on a longer and more technical paper by Steve Boughn and Tony Rothman, is this summary by Rothman in Scientific American. I am not sure its claims all stand up to scrutiny, (and by “mass” Rothman always means “relativistic mass”, not “rest mass”, so be aware of that) but it does give some idea of how close the community was to figuring out relativity by 1905. If Einstein hadn’t existed, I suspect the main ideas of special relativity would probably have come together within ten years of 1905. Einstein short-circuited the process and moved everything along much faster. He wasn’t working in a vacuum, despite his relative isolation; he read a lot of the contemporary scientific papers, and so he probably encountered many of these confused ideas with little pieces of the truth. Nevertheless, the vision that what was involved was not limited to electrostatics, or electrons, or black body radiation, and instead was about literally everything — space, time, matter and motion — was bold and breathtaking, as well as correct.
I will try to find you a couple of my sources and post them here, so please check back now and then, and let me know if you happen to find something particularly good.
Thanks. I look forward to reading any further information when it’s available.
(BTW, I knew Tony (way) back in grad school.)
[Not a question, but I’ve often wondered about the follow-up question:
That is, the general consensus concerning the origins of Special Relativity seems to be that while, as you say, Einstein pulled everything together in a crisp, elegant manner, it’s also true that lots of folks were flirting around the edges of SR and it’s likely it wouldn’t have been too long before it had come together.
OTOH, it’s interesting to speculate that, if Einstein hadn’t lived, how long would it have been before we had _General_ Relativity. That’s certainly a whole different kettle of fish.]
Just before I buy your book, will it help me (B.Sc. Eng with two years of physics in the late 70s) to understand what forces are – how do repulsion and attraction work?
If you’re asking about forces in general, then that’s a tough question with a book-long answer, because forces come in great variety and can cause attraction and repulsion in a wide variety of ways.
But if you’re asking specifically about the elementary forces — gravity, electromagnetism, strong nuclear, weak nuclear, and Higgs — then the book gives some insights. It does not give a complete answer, however, and that’s for a very simple reason: we don’t have one yet.
What you learned in first-year university physics about electric forces has grown to become the universal story: across all known physics, there are elementary fields and particles, and these particles interact with each other via the fields, causing repulsion and attraction depending on the specific properties of the fields and the particles involved. In the case of gravity, we have a more complete story, thanks to Einstein, of how the gravitational field creates what we view as an attractive force; that’s through the notion of curved space, which I do describe in the book. But in the case of the other forces, there are many possible stories, none of which has been addressed by experiment, and the true story may be something we haven’t thought of yet. The most honest way to answer your question, then, is “we don’t fully know how repulsion and attraction work for the elementary forces of our universe.”
This isn’t to say that physicists are completely at sea when it comes to these forces; far from it. We have various methods to calculate precisely the energy of two particles a certain distance apart. (Among them are the famous Feynman diagrams, which are often over-interpreted as explanatory, whereas in fact they are simply a method for calculation.) If that energy increases as the two particles approach each other, then there will be a repulsive force between them; if it decreases, there will be an attractive force.
In other words, we physicsts have a very clear idea of what particles and fields do; we know the rules by which they operate. We can predict when a force will be attractive and when it will be repulsive, along with many other more subtle details, such as how the force changes with distance (which always differs from the 1/r^2 laws learned in first-year university physics).
But knowing what fields do is very different from knowing what they are, and from knowing why they do what they do. My sense is that the latter questions are the ones you want to know the answers to. I want to know the answers too, but these are still open questions for coming generations to tackle.
In short, the book won’t answer the question, but no scientist or author alive today could hope to do so. What the book does is explain what we know and delineate clearly what we don’t. I hope that will be, if not satisfying, at least profoundly clarifying.
Hi Matt: The electromagnetic field is present throughout the universe. When we send an email it is converted into light and send across as particles 1 & 0 via the electromagnetic field. Do the same particles travel through the field or the disturbance is passed on from 1 particle to other of the field and reaches the final destination?
Just wanted to understand how the actual electronic signal (chat or email or call etc.) moves through the electromagnetic field.
If an email or call is converted into light (specifically, into radio waves or into microwaves), this does not involve particles, in the sense of photons, the particles of light.
Yes, nowadays that information is converted into 1’s and 0’s — that is the digitization process. But the digitized information is not sent in particles — not in quantum-physics form.
Instead, it is sent in large-amplitude waves, made of huge numbers of photons, in much the same way that early cell-phone calls were sent in the days before digitization. This in turn resembled how radio waves were always sent for conventional analog radio. There’s nothing fundamentally different now. The only thing different is that the information stored in the waves is packaged more efficiently.
The precise way that the digitized information is stored in the electromagnetic waves will differ between one wireless system and another. That is a question that each set of engineers will decide; it’s not a physics issue, as it is a matter of strategy and efficiency, not principles. Some information about this is given in this person’s blog post: https://www.cwnp.com/transmitinfoblog/
Might you have been confusing digital technology with quantum technology? These are quite different…
Thank you Prof for the reply.
You said “Instead, it is sent in large-amplitude waves, made of huge numbers of photons” – So a simple “Hi” is converted into a n number of photons which travel though the electromagnetic field like a wave of “Hi”. So this will be a digital technology transmission. I am correct on this?
So my next question would be how would I convert this “Hi” into a quantum technology transmission?
It’s not that “Hi” is converted to some fixed number of photons via a simple math formula. It’s more likely that the sound wave pattern corresponding to the sound “Hi” in a cell-phone microphone is converted to a pattern of binary 1’s and 0’s [or the two letters “H” and “i” in an email are converted to ASCII numbers and from there to 1s and 0s.] and then the pattern of 1’s and 0’s is compressed using an math algorithm, after which the compressed information is sent as a complicated large wave that represents that information in some way that depends on what the engineers decide to do. It’s not n photons. It’s a large wave, like this one https://qph.cf2.quoracdn.net/main-qimg-f0eef0b0c69220c23036566d4e9da69f-lq, or this one https://upload.wikimedia.org/wikipedia/commons/b/b9/Frequenzumtastung.jpg; see also https://en.wikipedia.org/wiki/Digital_signal
To convert “Hi” to a quantum technology transmission, the transition to 1’s and 0’s would be the same. Then this would have to be encoded in a quantum signal. This could be done in many ways, but one of the simplest is to use the fact that photons can be polarized. For example, you could arrange to use photons that are linearly polarized — some of them vertically, some of them horizontally. You could decide that you will use vertically-polarized photons to stand for 1s and horizontally-polarized photons to stand for zeros.
However, this makes the message easily subject to errors, so you may want, for instance, to send three vertically polarized photons for every “1” and three horizontally polarized photons for every “zero” to make the message more robust.
Electrons can be polarized too, so you could use them instead.
There are many other possible methods.
Then, to really make it quantum, you may want to put the particles you are sending into more complicated quantum states that have forms of entanglement. But you haven’t given me a reason to do that, so I won’t get into that here.
Thank you so much Prof. for your reply. It was very helpful.