User:Jerry Huth/Sandbox: Difference between revisions

Effect of Expansion on Light

I’m thinking about changing the Expansion of the Universe page to correct the misconception among some physicists that “E=hf” means light loses energy when the universe expands. In reality the “hf” term is only the Power of the light (the per-second energy), not the Total Energy. So while light does lose Power in the expansion of the universe, it does not lose energy. The giants of inflationary cosmology back me up on this. See my short paper with references to Prof Guth (MIT) and Prof Susskind (Stanford) and which includes an example textbook study problem for this:

Physicists Confused by their Own Mathematical Constructs

I wanted to run this past you first before changing it though, since you made a lot of edits to that page. Basically this means that light’s energy density drops in the same proportion as matter (${\displaystyle \rho \propto a^{-3}}$). So I was going to fix the section about energy density, and remove the part about ${\displaystyle \rho \propto a^{-3(1+w)}.}$

What do you think? Does my paper (and Prof Guth and Prof Susskind) convince you? Or do you still think that light loses energy in the expansion of the universe?

– Jerry Huth (talk) 03:21, 12 October 2025 (UTC)

the reply from Aseyhe

The scaling ${\displaystyle \rho \propto a^{-3(1+w)}}$ is correct. The usual derivation uses general relativity. You can also derive it just using thermodynamic principles. Note that none of the derivations (that I know of) involve E=hf. In any event, this scaling is in accordance with established physics, and if you were to change it, you would be going against established physics — which is not the purpose of this site. Aseyhe (talk) 17:17, 12 October 2025 (UTC)

Ok, thanks for looking at this. Do you have a textbook reference for this statement on that page: “For ultrarelativistic particles (“radiation”), the energy density drops more sharply, as ${\displaystyle \rho \propto a^{-4}}$“? Or do you know what kind of textbook would have it, what subject matter or section it would be in, etc? (I live near this university library: https://library.du.edu/)

Thanks,

Jerry Huth (talk) 20:50, 12 October 2025 (UTC)

For example, Dodelson & Schmidt (2nd ed.) section 2.3. I’d guess most cosmology textbooks should have it though.

later reply

Thank you for that reference, I am able to access that book. I can understand why you wanted to include it on the Wikipedia page since it’s taught by cosmology textbooks, but it’s not correct. Their math is OK for individual photons, but they don’t explain their reasoning in extending it to the energy density of all the radiation, except to imply that the number of photons after expansion is the same as the number before expansion. But that is false, as this simple thought problem illustrates:

Q: A light source emits light for exactly 2 seconds. While the light is traveling through space, the universe expands with a scale factor of 3. How long will it take to receive the light after the expansion?

Answer:

If you want to think about it then you can come back here later and scroll down to get the answer. Scroll || || || || || V Scroll || || || || || V Scroll || || || || || V Scroll || || || || || V Scroll || || || || || V A: The number of seconds it will take to receive the light is six, because the light is stretched out not only in space but also in time (because the speed of light is a constant). So although the energy of each “light particle” (photon) is lower, there are more seconds of light (more photons) after expansion than there were before, so the total energy of the light doesn’t change. (see article which includes an example textbook study problem) All of the other sciences that deal with light, such as optical engineering, computer switching, medical applications, etc, have moved way beyond the early confusion surrounding the Photon (the per-second energy of light). It is only the physicists (but not the giants of inflationary cosmology) who cling to the false belief that photons are essentially the same as regular (matter) particles, when in reality the Photon is just a mathematical construct for 1 second’s worth of light (as this thought experiment illustrates). So if the frequency of a traveling light wave changes it does not mean the total light energy has changed, and the Photon was originally only meant to be used in the case where the frequency is NOT changing. (see article which explains that if the frequency of a traveling light wave changes, it simply means the Power of the light has changed (the per-second energy), not the Total Energy)

Aseyhe’s reply:

> The number of seconds it will take to receive the light is six Yes, this is a trivial consequence of the cosmological redshift. > there are more seconds of light (more photons) This is wrong. The number of photons is the same. They are simply spaced farther apart in time. > the Photon is just a mathematical construct for 1 second’s worth of light Sorry but this is nonsensical. The second is a totally arbitrary unit from a fundamental physics point of view. Aseyhe (talk) 17:12, 18 November 2025 (UTC)

My possible reply:

Thank you for your response, that is very interesting. I wasn’t expecting that, but it does seem to agree with the Modern Cosmology textbook. However that textbook doesn’t go into any detail about it, and simply implies that the number of photons is the same before and after expansion. Do you know of a textbook that has any supporting details about the assertion that the number of photons remains the same, or any details about the photon in general? My own 1st year physics textbook (the only physics textbook I have from college, “University Physics” by Sears, Zemansky and Young) only mentions the photon in a couple paragraphs (OSLT right?) and doesn’t go into any real detail about it. I have also looked at various textbooks at the DU Library (https://library.du.edu/) and haven’t found any details about it or why the number of photons would remain the same before and after expansion.

Or possible reply:

Thank you for your response, that is very interesting. I wasn’t expecting that, but it does seem to agree with the Modern Cosmology textbook, which implies that the number of photons is the same after expansion. But it’s not stated outright, and it also doesn’t include an equation for the Total Energy of light, and in fact I can’t find an equation for the Total Energy of light in any physics textbook. Do you know of a physics textbook that includes any details or supporting evidence for the assertion that the number of photons is the same before and after expansion? Or that has an equation for the Total Energy of light?

As my short article posits, the Photon is the Per-Second Energy of light, not the Total Energy, while the Total Energy of minimum power light is characterized by the equation “E=hft”:

The Photon (the E in “E=hf”) is not the total energy of the light, it is the per-second energy (which is the power (energy bandwidth), not the energy itself). The Total Energy of lowest power light is fundamentally described by “E=hft”, i.e. the energy of light is proportional to both the frequency and the time in which the light shines (where h in that last equation is 6.626e-34 J/cycle). And power is the total energy divided by the time, so “P=hf” is fundamentally true (and not confusing like the famous “E=hf”).

But probably don’t include the end of that paragraph:

So if the frequency of a light wave changes it simply means that the Power has changed, not the Energy. And the Photon was originally only meant to be used in the case where the frequency is NOT changing.

Instead maybe add this after it (but probably not):

Power and Energy are related, but they are not the same thing.

A real honest reply would be:

The Modern Cosmology textbook implies that the number of photons is the same before and after expansion, but it provides no explanation for it, and it doesn’t state it outright. Do you know of any physics textbook that provides any details or explanation for it, or do they all just assume it to be true?

The reason why the frequency of light goes down in an expanding universe is because the light wave is spread out in space and also in time because the speed of light is a constant. It doesn’t mean that the total light energy has changed, it simply means that it will take longer to receive the light (and the giants of inflationary cosmology agree with me, see references in my article).

Here is another thought problem that illustrates what I’m talking about: If a 1KHz light source emits light for 1 second, the energy of the light will be 1000 times the Planck energy. But if a 1KHz light source emits light for 1.5 seconds, what will be the energy of the light?

A: It will be 1.5 times 1000 times the Planck energy, i.e. 1.5 photons. This proves that the “photon” is just an abstraction (i.e. it is the per-second energy of light), it’s not a real particle. All of the other sciences understand this, it is only physicists (but not the giants of inflationary cosmology) who cling to the false belief that the photon is a real particle.

Another possible part of the honest reply:

This is exactly what’s wrong with the “established physics” formulation of light: In the mathematically constructed universe of the standard model everything is made of virtual particles including light, and the Photon is the virtual particle of light. But in the real world light is a continuous wave in the EM field, although the energy of light is quantized. But in the real world the energy quantization of light is the same for all frequencies and it is the Planck energy 6.262e-34 J, which Einstein referred to as hv-naught (see my article which includes a quote from one of Einstein’s papers about it). The Photon is just an abstraction whose original purpose was simply to formulate the equations of light for use in the per-second realm which is necessary for engineering applications. Because the Photon is the per-second energy of light it depends on time so it does not apply in an expanding universe where space and time are changing (unless you are very careful, as explained in my article, and you understand that the number of photons goes up as the frequency goes down so the total energy remains the same).

Another possible reply:

Yes I agree, the second is a totally arbitrary unit from a fundamental physics point of view. That is proof that the Photon (the per-second energy) is just a mathematical construct, not a real particle (or any kind of real fundamental quantity). In the real world, all light – regardless of frequency – has the same fundamental energy quantum size: the Planck Energy, 6.626e-34 J, which Einstein referred to as hv-naught, and which is independent of time. My article includes this quote from Einstein about it:

To arrive at a usable radiation formula, Planck had to treat the energy of the system of resonators as if it consisted of discrete energy quanta of the magnitude hv-naught

The Photon (the per-second energy) was used by the early physicists like Einstein because they had to formulate the equations of light energy in the per-second realm which is used by engineers. It was originally only intended to be used in the case where the frequency is not changing, i.e. in the simplified case of practical engineering applications. It doesn’t apply in the case of an expanding universe where space and time are changing unless you are very careful about how you use it (as my article explains).

It’s ironic that now 100 years later physicists have ended up confused about the Photon, which they created for engineers, while engineers today realize that the Photon is just a mathematical construct not a real fundamental quantity (my degree is Electrical Engineering). Each cycle of light contains one or more light quanta (of magnitude hv-naught), and when the universe expands those light quanta are spread out in space and time. The frequency goes down because light is a wave that is spread out in space, but the number of cycles of light – and the number of hv-naught light quanta – doesn’t change, it simply takes longer to receive the light. So the Power of the light (the per-second energy) goes down but the Total Light Energy remains the same.

The Modern Cosmology textbook implies (as you have stated) that the number of photons is the same before and after expansion, but it doesn’t state it outright, and it offers no reasoning or details of any kind to support it. So I can’t accept it particularly since the giants of inflationary cosmology agree with me about this (my article includes direct quotes from Professors Guth (MIT) and Susskind (Stanford)).

Do you at least agree with me that light is an electromagnetic wave and the number of cycles of light is the same before and after expansion?

msg to authors

Subject: Important Thought Problem missing from the Modern Cosmology textbook

Hello Dr Dodelson and Dr Schmidt,

I wanted to alert you to a serious issue in your textbook “Modern Cosmology”. This very important thought problem / exercise is not included in the textbook:

Question: A light source emits light for exactly 2 seconds. While the light is traveling through space, the universe expands with a scale factor of 3. How long will it take to receive the light after the expansion?

Answer: see https://en.wikipedia.org/wiki/User:Jerry_Huth/LightProblem1

This thought problem helps explain why the following equation about the energy density of radiation is not correct: ${\displaystyle \rho _{r}\propto a^{-4}}$

(on page 37 in the 2nd edition)

To calculate the energy density of light, you first have to correctly calculate the Total Energy of the light (see example exercise included in this article, which also includes references to the giants of inflationary cosmology who agree with me about this).

Ripple effects of this mistake include that equation 2.61 is incorrect: ${\displaystyle \rho _{s}(a)\propto a^{-3(1+w_{s})}}$

Please let me know if you have any questions or would like to discuss it. Are you convinced about this? i.e. do you think you will change this in the next edition of your textbook?

Thank you,

Other stuff / OLD

Thank you for that reference, I was able to get that book. All of their math is fine up to where they show that the momentum and energy of a photon decreases as the frequency goes down. But then they make the final leap (without evidence) and say that the energy density of radiation goes down by an extra scale factor, which is false (and the giants of inflationary cosmology agree with me on this – see references in article). The textbook authors don’t “show their work” on that final leap, i.e. they don’t even attempt to calculate the total energy of the light. So they make the same mistake as explained in the article. Here’s a simple thought problem that illustrates what they’re missing:

Did you intend those equations to apply to the Total Energy Density of the radiation? If so then they are incorrect, for instance the author of the Wikipedia article about Expansion of the Universe points to your textbook to support this statement:

The Photoelectric Fiction

There are other places where confusion about the Photon has led physicists to incorrect conclusions. For instance the classic textbook problem about the Photoelectric Effect (where the student calculates the speed of an ejected electron) is a total fiction/oversimplification. It could only be true if the electron absorbed exactly 1 second’s worth of light before being ejected (because the Photon is the per-second energy of light). Obviously that is an oversimplification, and as the following video I found on YouTube shows, once the experiment reaches steady state it takes many seconds for the electrons to absorb enough energy to be ejected (and there are multiple plateaus): https://www.youtube.com/watch?v=oYnp0WZDhYQ&t=270s

(at time 4:30)

(BTW I like this YouTuber’s enthusiasm for this experiment, but I don’t agree with his explanation of the underlying physical processes (it is the classic explanation, which is a gross oversimplification))