Gravitational time dilation implies energy change?

In summary, according to Einstein's Gravitational Time Dilation, an oscillating physical system at height H above the Earth will have a higher frequency than the same system at ground level. This is due to Planck's relation between energy and frequency, which states that the oscillator at height H must have more energy than it does on the ground. As a result, any photons emitted by the oscillator at height H will have more energy than those emitted by the same oscillator on the ground. Contrary to popular belief, this extra energy in the blue-shifted photons is not due to their "fall" from height H, but rather they were emitted at a higher energy/frequency at height H in the first place. There are different ways to interpret
  • #36
PAllen said:
[..] Why, actually, is light different from all other oscillators? If I have perfectly reflecting mirrors, and a beam bouncing between them, and fall with this apparatus from the tower, the light in the beam gets blue shifted? That can't be right either, then you can distinguish free fall from other inertial motion. So light directly received from higher source is blue shifted, but not if reflected back and forth between falling mirrors? I've gotten myself confused about this.]

I reflected :-p a little more on that question... and I now suspect that the question may be faulty! A proper clock (also in a double sense of the word) generates its proper time, and the "clock" of your thought experiment doesn't do that - it uses a fast dying, non-proper signal from another gravitational potential. Note also that there is a difference between free fall and an apparatus at rest at another potential - but that aspect I did not work out.
 
<h2> What is gravitational time dilation?</h2><p>Gravitational time dilation is a phenomenon in which time appears to pass at different rates in different gravitational fields. This means that time moves slower in stronger gravitational fields, such as those near massive objects like planets or black holes.</p><h2> How does gravitational time dilation relate to energy change?</h2><p>Gravitational time dilation is caused by the curvature of spacetime, which is influenced by the presence of mass and energy. As an object moves closer to a massive object, its energy increases due to its increased velocity and gravitational potential energy. This increase in energy causes time to appear to pass slower for the object.</p><h2> What are some real-world examples of gravitational time dilation?</h2><p>One example of gravitational time dilation is the time difference between clocks on Earth's surface and clocks on GPS satellites in orbit. The clocks on the satellites run slightly faster due to their higher velocity and weaker gravitational field. Another example is the time dilation experienced by astronauts in orbit around Earth, as their spacecraft is traveling at high speeds and in a weaker gravitational field.</p><h2> How is gravitational time dilation calculated?</h2><p>The amount of time dilation due to gravity can be calculated using the formula Δt' = Δt √(1 - 2GM/rc^2), where Δt is the time interval measured by an observer in a weak gravitational field, Δt' is the time interval measured by an observer in a strong gravitational field, G is the gravitational constant, M is the mass of the massive object, r is the distance from the object's center of mass, and c is the speed of light.</p><h2> Can gravitational time dilation be observed on a large scale?</h2><p>Yes, gravitational time dilation has been observed on a large scale in the form of gravitational redshift. This is when light from distant galaxies is redshifted due to the effects of gravity as it travels through the universe. This phenomenon is one of the key pieces of evidence for the theory of general relativity.</p>

FAQ: Gravitational time dilation implies energy change?

What is gravitational time dilation?

Gravitational time dilation is a phenomenon in which time appears to pass at different rates in different gravitational fields. This means that time moves slower in stronger gravitational fields, such as those near massive objects like planets or black holes.

How does gravitational time dilation relate to energy change?

Gravitational time dilation is caused by the curvature of spacetime, which is influenced by the presence of mass and energy. As an object moves closer to a massive object, its energy increases due to its increased velocity and gravitational potential energy. This increase in energy causes time to appear to pass slower for the object.

What are some real-world examples of gravitational time dilation?

One example of gravitational time dilation is the time difference between clocks on Earth's surface and clocks on GPS satellites in orbit. The clocks on the satellites run slightly faster due to their higher velocity and weaker gravitational field. Another example is the time dilation experienced by astronauts in orbit around Earth, as their spacecraft is traveling at high speeds and in a weaker gravitational field.

How is gravitational time dilation calculated?

The amount of time dilation due to gravity can be calculated using the formula Δt' = Δt √(1 - 2GM/rc^2), where Δt is the time interval measured by an observer in a weak gravitational field, Δt' is the time interval measured by an observer in a strong gravitational field, G is the gravitational constant, M is the mass of the massive object, r is the distance from the object's center of mass, and c is the speed of light.

Can gravitational time dilation be observed on a large scale?

Yes, gravitational time dilation has been observed on a large scale in the form of gravitational redshift. This is when light from distant galaxies is redshifted due to the effects of gravity as it travels through the universe. This phenomenon is one of the key pieces of evidence for the theory of general relativity.

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