E2 - p2c2 = m2c4 - Meaning of symbols

  • Context: Undergrad 
  • Thread starter Thread starter particlemania
  • Start date Start date
  • Tags Tags
    Symbols
Click For Summary

Discussion Overview

The discussion centers around the equation E2 - p2c2 = m2c4, focusing on the meanings of the symbols involved, particularly in the context of relativistic physics. Participants explore the roles of rest mass, momentum, and energy, as well as the implications of Lorentz factors in these relationships.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants identify the symbols in the equation, noting that E represents total energy, m is rest mass, p is momentum, and c is the speed of light.
  • There is a discussion about whether only momentum (p) involves the Lorentz factor, with some asserting that energy (E) also incorporates it.
  • One participant mentions that the equation holds for both massive and massless particles, introducing alternative expressions for momentum in the context of massless particles.
  • Another participant elaborates on the conceptual implications of the equation, suggesting that it reflects a duality of positive and negative energies in nature.
  • Some participants challenge the notion of negative energy, questioning its relevance to the equation and discussing the implications of Dirac's ideas on negative energies and antiparticles.
  • There are speculative ideas presented regarding the nature of energy and spacetime, including references to four-dimensional oceans of energy and their relationship to physical reality.
  • Questions arise about the terminology used, such as "ocean," and its validity in a physics context.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the equation, particularly regarding the existence and interpretation of negative energy. While some agree on the basic meanings of the symbols, the discussion remains unresolved on the broader implications and interpretations of energy in relation to spacetime.

Contextual Notes

Some claims rely on specific interpretations of theoretical concepts, and there are unresolved questions about the definitions and implications of terms like "ocean" in a physics context. The discussion includes speculative ideas that are not universally accepted.

  • #31


aeon.rs said:
From that quotation we can draw the conlusion that the solutions of the relativistic energy equation E2 = m2c4+p2c2 are as follows: (1) in classical physics we could keep the positive values separate from the negative ones, (2) in quantum mechanics the positive and negative values do not tend to separate neatly; each of the two roots has to be considered as a possibility, so even an “unphysical negative energy” has to be considered as a physical possibility (3) in relativity we do not have a clear cut procedure for ruling out negative square root.
(3) should say that in relativistic quantum mechanics we do not have a clear-cut procedure. In the non-quantum version of relativity we do--that's what he meant by "classical physics" here.
aeon.rs said:
Even Dirac when he took antiparticle to solve the problem, he obliged to introduce the concept of “the ocean of occupied negative energy states” which is now referred to as the Dirac Sea (the same book p. 624-625).
My understanding is that the modern version of quantum field theory basically gets rid of the whole "Dirac Sea" idea, antiparticles are no longer viewed as "holes" but as particles in their own right. See this section of the wikipedia article, or this thread from physicsforums, or the last paragraph before "Free Space Solutions" in this google books result.
 
Physics news on Phys.org
  • #32


JesseM said:
(3) should say that in relativistic quantum mechanics we do not have a clear-cut procedure. In the non-quantum version of relativity we do--that's what he meant by "classical physics" here.

My understanding is that the modern version of quantum field theory basically gets rid of the whole "Dirac Sea" idea, antiparticles are no longer viewed as "holes" but as particles in their own right. See this section of the wikipedia article, or this thread from physicsforums, or the last paragraph before "Free Space Solutions" in this google books result.

Thank you, you are right. The original text of the quotation was written within the context of quantum mechanics. But the bottom line I would like to express is that we can not take the possibility of the existence of such negative energies very lightly. For me the presence of this symmetry, the pairing of these opposite energies and their interplay will substantially enrich the relativity theory and empower it to resolve the troubles we have both at the cosmic and quantum levels.
 

Similar threads

Graduate On the order of indices of the Christoffel symbol of the 1st kind
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad ##\epsilon_{ijk}## in terms of ##\delta's##
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Effects of magnetism on spacetime curvature, and implications
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Understanding Christoffel symbol in GR context
  • · Replies 19 ·
Replies
19
Views
6K
Undergrad Calculating Covariant Derivative of Riemann Tensor in Riemann Normal Coordinates
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Trying To Calculate Christoffel Symbols
  • · Replies 16 ·
Replies
16
Views
4K
Undergrad The wave equation interpretation of special relativity
  • · Replies 10 ·
Replies
10
Views
1K
Undergrad Inertial Gravity in Relativistic Geodesics - Forum Discussion
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Simultaneity of Events: Understanding Observer Perspectives on Time
  • · Replies 18 ·
Replies
18
Views
3K
Undergrad Issues with the variation of Christoffel symbols
  • · Replies 10 ·
Replies
10
Views
4K