Is there an analytical explanation for Einstein's famous equation E=mc^2?

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Discussion Overview

The discussion centers on the analytical explanation of Einstein's equation E=mc², exploring whether a derivation exists and how it relates to concepts like time dilation, length contraction, and conservation of momentum. Participants also consider thought experiments that illustrate mass-energy equivalence.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant mentions an analytical description of time dilation and length contraction but questions the existence of a similar analysis for E=mc².
  • Another participant points out that the linked webpage does provide an analytical derivation of E=mc², noting the broader equation E² = m²c⁴ + p²c².
  • Some participants propose that mass-energy equivalence is related to the conservation of momentum and the momentum of photons.
  • A participant describes a thought experiment involving an object emitting photons and discusses how this relates to changes in mass and momentum conservation.
  • Another participant suggests that Einstein's insights may have stemmed from the Doppler effect and conservation laws, while noting the lack of a direct derivation from these principles.
  • One participant expresses skepticism about the understanding of space and time, emphasizing the mystery surrounding their nature despite established relationships like the Lorentz transformations.

Areas of Agreement / Disagreement

Participants express differing views on the existence and nature of analytical derivations for E=mc², with some asserting that such derivations exist while others remain uncertain. The discussion reflects multiple competing perspectives on the relationship between mass-energy equivalence and conservation laws.

Contextual Notes

Some claims rely on specific interpretations of momentum conservation and the behavior of photons, which may not be universally accepted. The discussion also highlights the complexity of deriving E=mc² from fundamental principles, indicating potential gaps in understanding.

Urmi Roy
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I obtained an analytical description of time dilation and length contraction which describes why these occur at high speeds. However there was no such analysis of Einstein's famous equation E=m(c squared).
Instead, a derivation that I found in http://www.karlscalculus.org/einstein.html starts off with

m =

m0
√1 - v2/c2

Then they derive the formula using calculus.

Is an analytical treatment for E=m(c squared) possible? Is there any thought experiment which helps us to realize the applicability of the mass-energy equivalence?
 
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Um... the web page you linked to does give an analytical derivation of E=mc^2 (although technically the equation is E^2 = m^2c^4 + p^2c^2). I'm not sure what else you're looking for...
 
I think the mass energy equivalence stems from the conservation of momentum and the fact that photons have momentum.
 
I think DaleSpam provided me with what I wanted to know,though it would be better if it was elaborated a bit,(meaning how we can derive the formula from the very basic theory of conservation of momentum (applied to photons)).
 
OK, it has been a while so I am a little sketchy on the details, but it is something like this:

Suppose an object at rest of mass M emits a pair of photons each of energy E/2 and one to the left and the other to the right. Those photons carry equal and opposite momentum so the object remains at rest. Now, consider the same situation in a frame moving to the right, the right photon is blueshifted and the left photon is redshifted, so the photons carry some net momentum to the right, and we know the object's velocity, so by conservation of momentum the object's mass must have changed. When you work out the amount of the change you find that it changed by an amount m=E/c².

I am sure that is missing some important details, but it is something to that effect.
 
Okay,so I guess that through this very revolutionary experiment,which is based upon the doppler effect of electromagnetic waves and the law of conservation of momentum gave Einstein the whole idea.
At the same time there seems to be no derivation as such for the formula which originates from the law of conservation of momentum --it was something that Einstein found to fit in perfectly with the other rules of nature,that's why we can arrive at it fom other sources like the one I found on that webpage I mentioned earlier,right?
 
I obtained an analytical description of time dilation and length contraction which describes why these occur at high speeds.

If true, this would be BIG news!. BIG<BIG news and pulitizer, emmy and Nobel worthy.

Not to nitpick, but nobody knows why these occur, why space and time are dynamic; nobody even knows what space and time are. But we do have the Lorentz relationships.

Interesting derivation at the Virgina website, Thanks!
 

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