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.*

## 92 Responses

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.

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.

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.

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 redshiftedrelative 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

dois very different from knowing what theyare, and from knowingwhythey 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.