Relativity, Quantum Mechanics, & the Link Between Energy & Time

In summary, there is an explanation for why energy is related to time and momentum is related to space in both relativity and quantum mechanics. This is due to Noether's theorem, which states that energy is the quantity left invariant under time translations and momentum is the quantity left invariant under space translations, given the corresponding symmetries in the laws of physics. This explanation is based on the action principle and can be further explored through research or resources such as the provided link.
  • #1
daniel_i_l
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Is there an intuitive explanation for the fact that in both relativity (time part of 4vector) and qm (frequency) energy is related to time and momentum to space?
Thanks.
 
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  • #2
Well by counter examples you can find some intuition:

if the interaction changes with time, energy will change
(switching on slowly some high voltage for example)

if the interaction changes with position in space, the momentum will change
(a piece attached by a spring cannot maintain its momentum)
 
  • #3
daniel_i_l said:
Is there an intuitive explanation for the fact that in both relativity (time part of 4vector) and qm (frequency) energy is related to time and momentum to space?
Thanks.

There is an explanation, but it may not be "intuitive". Momentum can be defined as space translation symmetry, and energy as time translation symmetry. This happens because of "Noether's theorem".

You can google a bit for this, or check out http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html and maybe even the Wikpedia.

Noerther's theorem requires that the laws of physics be expressed in terms of an action principle, but this requirement is generally met (Newtonian physics with or without gravity and General Relativity are both expressible in terms of an action principle, for instance).
 
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  • #4
pervect said:
Momentum can be defined as space translation symmetry, and energy as time translation symmetry. This happens because of "Noether's theorem".

Perhaps you mean "momentum can be defined as the quantity that is left invariant under space translations (given the space translation symmetry of the Lagrangian)," and similarly with energy and time, respectively.
 

1. What is the theory of relativity?

The theory of relativity, developed by Albert Einstein in the early 20th century, is a set of two theories that describe the relationship between space, time, and gravity. The first theory, Special Relativity, deals with objects in constant motion, while the second theory, General Relativity, includes the effects of gravity on space and time.

2. How does relativity relate to energy and time?

According to Einstein's famous equation, E=mc², energy and mass are equivalent and can be converted into each other. This means that time and space are also intertwined with energy, as they are affected by the presence of matter and energy. Additionally, the theory of relativity shows that time is not constant, but rather relative to the observer's frame of reference.

3. What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior of particles on a very small scale, such as atoms and subatomic particles. It describes how these particles behave and interact with each other through principles such as superposition, uncertainty, and entanglement.

4. How does quantum mechanics relate to relativity?

Quantum mechanics and relativity are two of the most successful theories in physics, but they have different domains of applicability. While relativity deals with large objects and gravity, quantum mechanics is used to explain the behavior of particles on a small scale. However, efforts have been made to combine these theories into a theory of quantum gravity that can explain the behavior of particles on all scales.

5. What is the link between energy and time according to quantum mechanics?

In quantum mechanics, time is considered to be a continuous and linear variable, but it can also be affected by the presence of energy. The Heisenberg uncertainty principle states that the more accurately we know the energy of a particle, the less accurately we can measure its time. This shows that energy and time are intricately linked in the quantum world.

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