Why does m*c*c not equal 0 in the theory of relativity?

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Discussion Overview

The discussion revolves around the relationship between energy, mass, and frequency in the context of the theory of relativity, particularly focusing on why the expression m*c*c does not equal zero under certain conditions. Participants explore concepts related to rest mass, energy equations, and the behavior of massless particles like photons.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that in the theory of relativity, energy is defined as E = m*c*c, while in the photoelectric effect, energy is given by E = h*f, leading to confusion when considering a particle at rest.
  • One participant suggests that E = hf applies only to massless particles, implying that m*c*c should equal zero for such particles.
  • Another participant clarifies that E = hf can also apply to massive particles, stating that the full energy equation is E^2 = p^2c^2 + m^2c^4, and that E = mc^2 is valid only when momentum p is zero.
  • Some participants discuss the concept of mass being related to the rest frequency of a wave, referencing De Broglie's hypothesis about the intrinsic periodicity of massive particles.
  • There are claims that when mc^2 is zero, the energy must be expressed through momentum, leading to discussions about the properties of massless particles and their energy-momentum relationship.
  • One participant argues against the idea that if mc^2 is zero, then momentum p must also be zero, citing that photons carry energy and momentum.
  • Another participant acknowledges a misunderstanding regarding the terms "rest mass" and "relativistic mass," indicating a need for clarification on these concepts.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the definitions and implications of mass, energy, and momentum in the context of relativity. There is no consensus on the interpretations of these relationships, particularly concerning massless particles and the conditions under which m*c*c may or may not equal zero.

Contextual Notes

Participants express uncertainty regarding the definitions of rest mass versus relativistic mass and how these relate to energy equations. There are references to external sources for further reading, indicating that some claims may depend on additional context or definitions.

Zong xiaobo
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f is the frequency of a particle.
In the theory of relativity, energy equals m*c*c.
In the theory of Photoelectric effect, energy equals h*f
If the particle keeps still.
m is the rest mass of the particle.
In this case the frequency is 0 and h*f is 0
However m*c*c isn't 0.
It's a little strange.
 
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I think E=hf is just for particles with 0 rest mass such as photons. So m*c*c is 0.
 
Well... actually, you can say [itex]E = hf[/itex] for massive particles too (although the formula is usually used for massless particles, true) The reason this works is that the formula for energy is actually
[tex]E^2 = p^2c^2 + m^2c^4[/tex]
If you set [itex]p=0[/itex], then you get [itex]E = mc^2[/itex] - but only then. The popular version of Einstein's formula applies only to particles at rest.

In this case [itex]E = hf[/itex] is used to define the frequency of a particle.

I refer you to Wikipedia: http://en.wikipedia.org/wiki/Matter_wave for more information.
 
Well, the mass can be alternatively defined as the rest frequency of a wave. [tex]f_0 = m c^2 / h[/tex]. De broglie postulated that every massive particle has an internal clock whose frequency is fixed by the mass, and actually this intrinsic periodicity of the particles has been observed in a recent experiment [ http://www.ensmp.fr/aflb/AFLB-301/aflb301m416.pdf ]
 
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From the full formula given by diazona you can see that when mc^2 is zero but the particle still has energy it must all be in E = pc.
Thus the particles with no rest mass have momentum, frequency, and energy. having no rest mass they must travel at c.
 
map19 said:
From the full formula given by diazona you can see that when mc^2 is zero but the particle still has energy it must all be in E = pc.
Thus the particles with no rest mass have momentum, frequency, and energy. having no rest mass they must travel at c.

I think when the mc^2 is zero, p must be zero. So the E=pc must be zero.
 
Halcyon-on said:
Well, the mass can be alternatively defined as the rest frequency of a wave. [tex]f_0 = m c^2 / h[/tex]. De broglie postulated that every massive particle has an internal clock whose frequency is fixed by the mass, and actually this intrinsic periodicity of the particles has been observed in a recent experiment [ http://www.ensmp.fr/aflb/AFLB-301/aflb301m416.pdf ]

It seemed have answered my question. I will read the paper first.
 
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  • #10
Zong Xiaobo -I think when the mc^2 is zero, p must be zero. So the E=pc must be zero.

No ! A photon transports energy, it has momentum p = hf/c
You know that light has momentum everytime you sit on the beach.
E = hfc/c = hf.
 
  • #11
map19 said:
Zong Xiaobo -I think when the mc^2 is zero, p must be zero. So the E=pc must be zero.

No ! A photon transports energy, it has momentum p = hf/c
You know that light has momentum everytime you sit on the beach.
E = hfc/c = hf.

I think when a photon travel at a speed of c. The invariant mass of a photon isn't zero.
So mc^2 isn't zero.
 
  • #12
That statement is not only not logical - if the invariant mass is able to vary, then it's not invariant - but it's just wrong in physics.
 
  • #13
map19 said:
That statement is not only not logical - if the invariant mass is able to vary, then it's not invariant - but it's just wrong in physics.

I'm sorry, I made a mistake, the invariant mass of a photon is zero, however the relativistic mass of a photon isn't zero.
I will give you a link:http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html
 
  • #14
map19 said:
That statement is not only not logical - if the invariant mass is able to vary, then it's not invariant - but it's just wrong in physics.

It seemed that I misunderstand what you said.
when you mentioned mc^2, m is the rest mass.
I always consider m as the relativistic mass.
 
  • #15
Zong xiaobo said:
It seemed that I misunderstand what you said.
when you mentioned mc^2, m is the rest mass.
I always consider m as the relativistic mass.

You might want to read an entry in the FAQ thread in the General Physics forum.

Zz.
 

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