# A possible question concerning the photon

An instructor is a person who has answers for the questions rised by his students. Consider that one of them comes with the following one:
If I am co-moving with a tardyon then I measure its rest mass (energy) obtaining a zero value for its momentum.
Nobody can comove with a photon and so nobody can measure its rest mass and nobody can say that its momentum is equal to zero.
Can I conclude that the magnitude of a physical quantity that I am not able to measure is equal to zero.

I have not so far an answer with pedagogical benefits. Have you one?

## Answers and Replies

In relativity, a particle's rest mass is related to its energy and momentum by:

$$m^2 c^4 = E^2 - |\vec{p}|^2 c^2$$

This means that we can infer a particle's rest mass by measuring its energy and momentum. So, there is no need to co-move with an object to determine its rest mass.

In relativity, a particle's rest mass is related to its energy and momentum by:

$$m^2 c^4 = E^2 - |\vec{p}|^2 c^2$$

This means that we can infer a particle's rest mass by measuring its energy and momentum. So, there is no need to co-move with an object to determine its rest mass.
Thank you. I think the problem is still open. We know many cases of indirect measurement of a physical quantity (say velocity measurement by measuring frequencies). The problem of how do we measure the rest mass directly remains IMHO open.

I recently read that they’ve put an upper limit on the photon rest mass. In 1994, the Charge Composition Explorer spacecraft measured the Earth's magnetic field and physicists used this data to define an upper limit of 6 X 10 (-16) eV for the mass of photons, with a high certainty in the results.

I guess, most would call that energy-mass equivalence, though?

But, even if photons don't have "rest mass", photons are always moving, aren’t they? If they weren't it gives them the Newtonian mass of -0-, a frequency of -0-, and a wavelength that will blow your calculator's mind!

It looks like a matter of definition:

"The photon has zero invariant mass" The need to qualify the variety of mass a photon lacks as "invariant" implies that there's some other sort of mass (presumably variant) that a photon does have.

Having said that, though, I'm inclined to agree with the majority view (less opposition) Last edited:
Also,the energy of a photon is dependent on the frequency.If the photon comes to rest it wont have any frequency,thus it will not exist as a photon is just energy.So thus it will have zero mass(invariant)

Meir Achuz
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Can I conclude that the magnitude of a physical quantity that I am not able to measure is equal to zero.
No, but the way most experimental physicists measure the mass of a particle is to measure E and p in any frame, and then use a belief in SR to calculate
m^2=E^2-p^2. The fact that this gives the same answer at any speed confirms the measurement.

Try turning it around. If you could move with the photon you would measure the mass of everything else (moving at c) to be infinite. But you can't move with the photon.

Can you therefore conclude that that the magnitude of a physical quantity that cannot be measured is infinite?

photon problem

Try turning it around. If you could move with the photon you would measure the mass of everything else (moving at c) to be infinite. But you can't move with the photon.

Can you therefore conclude that that the magnitude of a physical quantity that cannot be measured is infinite?

History of physics has registered an interesting situation. Galileo using poor clocks was not able to measure the velocity of light concluding that it propagates with infinite velocity and that is why the LT become Galileo's transformations for c going to infinity.
Presenting all the information received from the participants on the Forum to my sophisticated student he could argue:
I was tought that mass is a basic physical quantity and so we measure it by comparison with another known mass. Would a system of units with no mass between its basic physical quanities (no MKSA) of help?
Thanks for your participation on the forum? For my statistics do you teach or use SR?

History of physics has registered an interesting situation. Galileo using poor clocks was not able to measure the velocity of light concluding that it propagates with infinite velocity and that is why the LT become Galileo's transformations for c going to infinity.
Presenting all the information received from the participants on the Forum to my sophisticated student he could argue:
I was tought that mass is a basic physical quantity and so we measure it by comparison with another known mass. Would a system of units with no mass between its basic physical quanities (no MKSA) of help?
Thanks for your participation on the forum? For my statistics do you teach or use SR?

Infinite velocity implies action at a distance. Nothing is Galileo's world made him doubt that was possible. But he was still far ahead of his time.

Is a separate unit of mass necessary? You could ask your student to check out general relativity, which puts mass in terms of length.

Thank you, too, for posing a great question. I recall that Einstein was led to special relativity by pondering what things would look like if he could travel at c .

For your statistics, I'm a physicist, but SR is a hobby.

HallsofIvy
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I'm not going to answer the physics question but respond to two points made:
An instructor is a person who has answers for the questions rised by his students.
Where did you get that idea? An instructor is a person who helps his students learn how to find answers themselves. And good students are quite capable of raising questions that have NO answers!

Can I conclude that the magnitude of a physical quantity that I am not able to measure is equal to zero.
Why would you think such a thing? If you can assert that a physical quantity has magnitude 0 then you have measured it! The only thing you can say about the magnitude of a physical quantity you cannot measure is "I don't know". That is a very good thing for an instructor to learn to say!

I'm not going to answer the physics question but respond to two points made:

Where did you get that idea? An instructor is a person who helps his students learn how to find answers themselves. And good students are quite capable of raising questions that have NO answers!

Why would you think such a thing? If you can assert that a physical quantity has magnitude 0 then you have measured it! The only thing you can say about the magnitude of a physical quantity you cannot measure is "I don't know". That is a very good thing for an instructor to learn to say!

I do not understand your logic. I consider that an instructor has a lot of answers among them "I do not know", "No", "Yes"! and even step by step answers which can help the learner to find out the answer if he thinks that it exists?. I practiced that way for long time! Thank you for teaching me, but I like more polite ways for answering or questioning.

photon

Try turning it around. If you could move with the photon you would measure the mass of everything else (moving at c) to be infinite. But you can't move with the photon.

Can you therefore conclude that that the magnitude of a physical quantity that cannot be measured is infinite?

I and my "virtual" students we have taken into acount all the answers our thread has received. Thanks. We have tried to rephrase them as follows:
In order to detect a photon I should be located in an electromagnetic wave to which it is associated. Moving with velocity c in the direction in which the wave propagates my wrist watch is not of much use because I am not able to synchronize it with other clocks. I could use as clock the electromagnetic oscillations taking place in the wave. Consider that I receive a wave crest. The scenario makes that I will never receive a second one and so I conclude that the period of the oscillations is infinite, the frequency of the oscilaltions is zero and so is the proper mass and the proper energy of the photon. If I change the direction in which I move I receive only wave crests, I conclude that the period is zero, the frequency being infinite and so should be the mass (energy) of the photon. The formula that accounts for the Doppler Effect reflects the conclusions. Are we right?/I]

In relativity, a particle's rest mass is related to its energy and momentum by:

$$m^2 c^4 = E^2 - |\vec{p}|^2 c^2$$

This means that we can infer a particle's rest mass by measuring its energy and momentum. So, there is no need to co-move with an object to determine its rest mass.
That expression is derived upon the assumption that the particle is a tardyon. If the particle is actually a Luxon, such as a photon, the the derivation is invalid and so is its use in this condition.

Pete

Thank you. I think the problem is still open. We know many cases of indirect measurement of a physical quantity (say velocity measurement by measuring frequencies). The problem of how do we measure the rest mass directly remains IMHO open.
i'd say that you can't measure the rest mass of a particle unless the particle is moving. Momentum is defined as p = mv where m = gamma*m_0, where m_0 is the rest mass. The definition of rest mass is found by letting v -> 0 and then measuring its momentum (i.e. measure the particle's momentum when the speed is small compared to that of light, i.e. v << c). Then divide the momentum by its speed and that will give you its rest mass. This is one of those reasons why I dislike the term "rest mass." I prefer the term "proper mass" instead.

Pete

Meir Achuz
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Thank you. I think the problem is still open. We know many cases of indirect measurement of a physical quantity (say velocity measurement by measuring frequencies). The problem of how do we measure the rest mass directly remains IMHO open.
I don't think you understand the process of measurement in physics. Do you propose running along with an electron and putting it on a scale to measure its mass?

I don't think you understand the process of measurement in physics. Do you propose running along with an electron and putting it on a scale to measure its mass?
I recommend that you don't make such assumptions with Bernhard. He knows his stuff when it comes to physics and relativity.

The measurement of a property of something depends on what that something is. I can step on a weight scale and determine my weight and use that to determine my mass. But I can't exactly put the Earth on a weight scale.

Pete

photon

I don't think you understand the process of measurement in physics. Do you propose running along with an electron and putting it on a scale to measure its mass?

Thank you. That is the kind of answer I dislike and I have mentioned that fact responding to your answers. When I started the thread I mentioned that the problem could be raised by a student and I as a teacher I should answer it, of course in a civilized manner (sine ira et studio not puting in his mind things he never thought. Using your style I could say that you have not heard about "Gedanken experiments" I like so much, that you have no experience in teaching ... but I avoid it. Have in mind that our discussion is followed by many youngsters and we should teach them that there is some deontology in a scientific discussion. I am glad that Nakurusil is no longer present on the Forum, a master in offending the participants.

photon

i'd say that you can't measure the rest mass of a particle unless the particle is moving. Momentum is defined as p = mv where m = gamma*m_0, where m_0 is the rest mass. The definition of rest mass is found by letting v -> 0 and then measuring its momentum (i.e. measure the particle's momentum when the speed is small compared to that of light, i.e. v << c). Then divide the momentum by its speed and that will give you its rest mass. This is one of those reasons why I dislike the term "rest mass." I prefer the term "proper mass" instead.

Pete
Thanks for your answer. I will tell the measurement procedure you propose to my younger coleagues. I think that following it, it would be better to speak about Newtonian mass. Please have a look at a thread of mine, above, in which I present what an observer could do being immersed in an electromagntic wave. I intend to include it in a book. We are all here on the Forum to learn form each other in a civilized manner and to propagate that style to all who participate on it active or passive.

Moving with velocity c in the direction in which the wave propagates my wrist watch is not of much use because I am not able to synchronize it with other clocks. I could use as clock the electromagnetic oscillations taking place in the wave. Consider that I receive a wave crest. The scenario makes that I will never receive a second one and so I conclude that the period of the oscillations is infinite, the frequency of the oscilaltions is zero and so is the proper mass and the proper energy of the photon.

Moving along with the light wave, you will not see crests moving by. But you will also not measure the passage of time (try to construct a light-clock). Therefore, the frequency will be indeterminate. The same consideration makes all experiments at the speed of light impossible, doesn't it?

physics in the electromagnetic wave

Moving along with the light wave, you will not see crests moving by. But you will also not measure the passage of time (try to construct a light-clock). Therefore, the frequency will be indeterminate. The same consideration makes all experiments at the speed of light impossible, doesn't it?
Thank you. Between our points of view there is no disagreement. If we call infinite and zero as indeterminate then frequency is indeterminate as well. Light clocks as well as wristwatches are not of use as long we move with c mainly because we are not able to synchronize them. Let bring our statements of the problem in accordance.
Your name on the forum suggests to change my name in country oldboy. Thanks for your answer. I will tell the measurement procedure you propose to my younger coleagues. I think that following it, it would be better to speak about Newtonian mass. Please have a look at a thread of mine, above, in which I present what an observer could do being immersed in an electromagntic wave. I intend to include it in a book. We are all here on the Forum to learn form each other in a civilized manner and to propagate that style to all who participate on it active or passive.
I've been tossing around an idea on this. Let there be a massive particle, of known rest mass, at rest in the inertial frame S. Let the mass be such that when the photon strikes and is absorbed by it the final speed of the particle is v << c. You could then measure the momentum of this particle and deduce the momentum of the photon. That lets you determine p. The energy of a similar photon can be determine otherwise such as in the photo electric effect. Then defined the invariant mass m_0 as the magnitude of the 4-momentum of the photon. The measurements should show that m_0 = 0.

Pete

Please have a look at a thread of mine, above, in which I present what an observer could do being immersed in an electromagntic wave.
I can't seem to find the thread. What is the title of the thread?

Pete

Meir Achuz
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I've been tossing around an idea on this. Let there be a massive particle, of known rest mass, at rest in the inertial frame S. Let the mass be such that when the photon strikes and is absorbed by it the final speed of the particle is v << c. You could then measure the momentum of this particle and deduce the momentum of the photon. That lets you determine p. The energy of a similar photon can be determine otherwise such as in the photo electric effect. Then defined the invariant mass m_0 as the magnitude of the 4-momentum of the photon. The measurements should show that m_0 = 0.

Pete
That is the right track, but E and p conervation do not allow a single photon to be absorbed by a particle. A more realistic case is pi0 decay into two photons. The decay distribution confirms zero mass for the photons.
The most accurate measurement of the zero mass of the photon (if you believe QED) is the 1/r^2 dependence of Coulomb's law as determined using Gauss's law. That is the basis for m<2X10^-16 eV by the PDG.

Thank you. Between our points of view there is no disagreement. If we call infinite and zero as indeterminate then frequency is indeterminate as well. Light clocks as well as wristwatches are not of use as long we move with c mainly because we are not able to synchronize them. Let bring our statements of the problem in accordance.

I agree. The question revolves around the infinities and zeros that occur at the speed of light. It's not so much that the speed-of-light observer "can't" synchronize his clocks, but that it takes an infinite amount of time to do so. That difficulty is "compensated" by the fact that his clock is not changing time, so it doesn't matter how long it takes. He, of course cannot be aware of any of this, because he is also not able to "observe" or even "think."

Here's another way to look at the problem: A conventional observer can get the energy and momentum of a light wave by measuring the phase change per unit time at a fixed location (frequency) or the simultaneous phase difference between two locations (wavelength). But the observer co-moving with the light wave has a problem. For him the phase is not changing, and he can't get information from any other location. That is why he can't do the measurement of energy or momentum.

This has been an enjoyable thread.

Meir Achuz
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Thank you. That is the kind of answer I dislike and I have mentioned that fact responding to your answers. When I started the thread I mentioned that the problem could be raised by a student and I as a teacher I should answer it, of course in a civilized manner (sine ira et studio not puting in his mind things he never thought. Using your style I could say that you have not heard about "Gedanken experiments" I like so much, that you have no experience in teaching ... but I avoid it. Have in mind that our discussion is followed by many youngsters and we should teach them that there is some deontology in a scientific discussion. I am glad that Nakurusil is no longer present on the Forum, a master in offending the participants.
I don't mean my comments to be taken as insults. I based my statement on your statement: "If I am co-moving with a tardyon then I measure its rest mass (energy) obtaining a zero value for its momentum." There are a huge number of particle masses in the PDG tables. Not one is measured that way. I just meant to suggest that you look at the PDG to see how mass is actually measured. Just one other question. Were other participants insulted by Nakurusil?