What Limits Does a Supernova Observation Set on Photon Mass?

In summary, the conversation discusses how to solve a problem involving the relationship between energy and momentum for a photon. It suggests starting by writing down the equation E=pc and rearranging it to solve for mass. The given values for energy and the speed of light can then be used to find the mass of the photon.
  • #1
no_brainer
3
0
I'll have struggle on how to get started on this problem. I don't have a clue on how to start, somebody give me some tips on how to figure this problem out. Thanks

Experiments has shown that for the quantum of radiation(a photon), the energy and momentum are related by E=pc, corresponding to a particle with mass m=0. Suppose that in the observation of a supernova 170,000 light-years away, the first bursts of photons with an energy range of E= 10 eV to 10^4 eV arrive within 10^-8 s of each other. What limits does this set on the mass of the photon?

Anybody have a clue on how to do this?
 
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  • #2
Start by writing down the equation linking energy and momentum, E=pc. Then rearrange the equation to solve for mass, m=E/c. From there, plug in the given values for energy and c, the speed of light (3 x 10^8 m/s). You should now have an equation that looks like m = E/(3 x 10^8 m/s). With this equation, you can now find the mass of the photon given the energy range provided in the problem.
 
  • #3


To start, we can use the relationship between energy and mass for a photon, which is given by E=pc, where E is the energy, p is the momentum, and c is the speed of light. Since we know that the speed of light is constant, we can rearrange the equation to solve for the momentum: p=E/c.

Next, we can use the fact that the first bursts of photons arrive within 10^-8 s of each other to set a limit on the distance traveled by each photon. This distance can be calculated using the formula d=ct, where d is the distance, c is the speed of light, and t is the time. In this case, we can substitute in the given values to get d= 170,000 light-years = (3 x 10^8 m/s)(10^-8 s) = 3 x 10^3 m.

Now, we can use the relationship between momentum and distance, which is given by p=hf/c, where h is the Planck's constant and f is the frequency of the photon. Substituting in the calculated distance and rearranging the equation, we get f=pc/hd.

Finally, we can use the energy range given in the problem, E= 10 eV to 10^4 eV, to calculate the corresponding frequencies using the formula E=hf. This gives us a range of frequencies from 10^15 Hz to 10^18 Hz.

Now, we can combine all of these equations to find the limits on the mass of the photon. Using the fact that c=3 x 10^8 m/s and h= 6.63 x 10^-34 J*s, we get the following equation: m = pf/c = (hf/c)/c = f/c^2 = (10^15 Hz)/(3 x 10^8 m/s)^2 to (10^18 Hz)/(3 x 10^8 m/s)^2. This gives us a range of masses from 10^-36 kg to 10^-39 kg.

Therefore, the limits on the mass of the photon, based on the given information, are between 10^-36 kg and 10^-39 kg. I hope this helps you get started on solving this problem!
 

Related to What Limits Does a Supernova Observation Set on Photon Mass?

1. What is the current accepted limit on the mass of a photon?

The current accepted limit on the mass of a photon is 1.2 x 10^-18 electron volts (eV), which is equivalent to approximately 2.2 x 10^-35 kilograms.

2. How is the limit on the mass of a photon determined?

The limit on the mass of a photon is determined through experiments and observations of the properties of light, such as its speed and wavelength, which provide evidence that photons are massless particles. Additionally, theoretical calculations based on the principles of special relativity and quantum mechanics also support the notion that photons have zero mass.

3. What would be the implications if a photon was found to have a non-zero mass?

If a photon was found to have a non-zero mass, it would challenge our current understanding of physics and have significant implications for the Standard Model of particle physics. It could potentially lead to the discovery of new fundamental particles and force carriers, and could also impact our understanding of the universe's expansion and the behavior of light in different environments.

4. Has there been any evidence or experiments that suggest a non-zero mass for photons?

So far, there has been no conclusive evidence or experiments that suggest a non-zero mass for photons. However, there have been some theories and hypotheses proposed, such as the idea of a "fifth force" that could affect the behavior of photons and give them a small mass. These theories are still being investigated and have not been proven.

5. Are there any potential technological applications for a photon with a non-zero mass?

If a photon was found to have a non-zero mass, it could potentially have practical applications in technologies such as quantum computing, where the properties of particles like photons are utilized. However, the implications of a non-zero mass for photons are still largely theoretical, and further research would be needed to fully understand any potential technological applications.

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