- Momentum and energy are intricately connected to the concept of force. The terms energy and force are not interchangeable; they are not synonymous. The formula for energy vs. momentum is CONNECTION to E= mc2..
- The energy–momentum relation is consistent with the
- familiar mass–energy relation in both its interpretations: E = mc2 relates total energy E to the (total) relativistic mass m (alternatively denoted mrel or mtot), while E0 = m0c2 relates rest energy E0 to (invariant) rest mass m0.
- Energy is not made of anything. It’s a fundamental concept closely related to time. That’s because energy just represents change in a system. Ultimately, we observe systems to change in time. We’ve developed a concept called energy to account for the amount of change. This is clearly a very convenient and useful concept. For example, the amount of energy in the fuel of your car determines how far you can drive. That is the chemical potential energy in the fuel. Similarly with batteries, the stored energy (also chemical energy) allows a certain amount of things to happen, like powering your phone for a day. There are three underlying concepts in physics: forces, momentum, and energy. Electrodynamics and quantum electrodynamics. Electromagnetism is a classical field theory that is described by Maxwell’s equations. Electrodynamics then includes the Lorentz force law that includes the interaction of the field with charge particles. Such particles also provide the source terms in Maxwell’s equations. In this model, most people would be familiar with the electromagnetic field as a phenomenon that has some value throughout all space. Forces cause change in a system.
An ever-changing array of force fields comes together to build our perceived reality. This field array is ever changing/Momentum is the property that is changed. Energy accounts for how much change. Force fields bind atoms together. These three concepts are axioms from which you build physics, so you can’t actually reduce these concepts any further.
- trictly necessary, it is just useful as an accounting tool; just as accountants themselves are not needed, but can be very useful ;-)Ultimately, with relativity, both energy and momentum become part of the 4-momentum vector, but that’s another story…
- Why is the speed of light so small relative to the size of the universe?The speed of light plays a fundamental role in the structure of our universe and in how we perceive and understand it. It is a universal constant that appears in many important physical theories, such as Einstein’s theory of relativity. According to this theory, the speed of light is the maximum speed at which information or matter can travel in the universe.
When we consider the immense size of the universe, the speed of light may seem small in comparison. However, the vast distances in the universe are precisely why the speed of light is so significant. Light travels at a finite speed, so when we look at distant objects in the universe, we are actually seeing them as they were in the past, because of the time it takes for light to travel across those vast distances.
- When we add electromagnetic interactions to quantum mechanics, we introduce fields. This is done via the so-called minimal coupling Hamiltonian, where the momentum of a particle, p, is now expressed as p → p-eA, where A is the vector potential and is also an operator. So now we have quantum mechanics that includes a field and therefore the wave function now has to include the field. That’s just a straightforward extension of the Hilbert space, which means it’s still a quantum theory.
- In summary, while the speed of light may seem small relative to the size of the universe, it is a fundamental constant that shapes our understanding of the cosmos and plays a crucial role in
- If an observer is moving relative to the light source, they will measure the speed of light to be the same [math]c[/math], but the wavelength and frequency of the light will appear different because of the Doppler effect. The time intervals between events, as measured by different observers in different reference frames, will also differ. This is known as time dilation. Distances between objects, as measured by different observers, will also differ. This is known as length contraction. So in summary, while the speed of light is a universal constant within a reference frame, it is not an absolute constant that is the same for all observers in relative motion. The measurements of space and time can vary between different inertial reference frames.
- What experiments support the principles of special relativity?ompareThe answer to this is the absence of planetary atmosphere which scatters light. There’s no atmosphere out there in the space. The Earth’s atmosphere scatters mainly blue light, so that is why you see a blue sky during the day.
- When Bob returns to Earth after his high-speed journey, he will be younger than Alice. The difference in their ages is because of the time dilation effect experienced by Bob during his high-speed trip. This practical example illustrates how time can pass at different rates for two observers in relative motion, as predicted by Einstein’s theory of special relativity.
- t’s unfathomable how ridiculously enormous that star is! It’s so huge that its radius is comparable to that of the orbit of Jupiter. The orbit of Jupiter.
- If this big beautiful bastard replaced Uranus (heh), not only would we be destroyed,
- What happens with the photons when an atom absorbs them? Are they destroyed? They are gone once they’re absorbed. The energy isn’t gone – it leaves the photon field and enters the electron/positron field. And when it leaves the photon field, that photon no longer exists – the presence of the energy in the photon field literally was the photon.
- Eventually that electron will fall back to a lower energy state – that corresponds to energy leaving the electron/positron field. And it goes into the photon field, and what I regard as a new photon is thereby created. But whether you regard it as the same photon might be a matter of convention – to me it makes sense to think of it as a new one, precisely so you don’t have to ask yourself what the situation with “that” photon was while the energy was off in another field.
- The only real existence a photon has is the energy in the photon field. We sometimes perceive that as something localized in some particular region of space, but that’s just a way of looking at it. It’s best to think directly in terms of the quantum fields and the energy in the modes of those fields.
