Time is relative, not absolute, as both gravity and motion cause time dilation. The head and feet, therefore, do not age at the same rate.
There is no absolute time. It doesn’t matter where you are, how fast you’re moving, or how strong the gravitational field is around you. Whatever watch you have on you will always record time passing at the same rate: one second per second. But if you have two different clocks, you can compare how time flows in conditions different. If one clock remains stationary while the other travels fast, the fast-moving clock will experience an amount of time inferior with respect to the stopped clock: this is the time dilation rule in special relativity (or restricted).
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What’s even more counterintuitive, however, is that the relative flow of time also depends on the difference between how curved the space is between two locations. , this corresponds to the force of gravity in your specific location, meaning that your feet actually age at a different rate than your head, when you’re standing. Here’s how we know.
Because feet “age” at a different speed than the head
One of the things we rely on is that the laws of physics. While the properties of the Universe might change with time, energy, or position, the fundamental rules and constants that govern it remain the same. The same goes for ionic, molecular, or even nuclear transitions: the laws of physics remain the same at all times and in all places, and therefore these transitions that emit or absorb photons always occur at the same energy. However, if the emitter of a photon and the absorber (potential) of a photon are not found at the same time and in the same location as each other, there is a good chance that they will not agree on the energies they observe.
The Doppler effect
When objects are in relative motion relative to each other, we know this effect as . Most of us experience the Doppler effect whenever we hear an emergency vehicle (an ambulance, for example) approaching or moving away from us: we can hear the pitch of the siren changing. If the vehicle is approaching you, its waves will appear to have gotten closer and you will hear a higher pitch. If he is moving away from you, you will hear a lower tone.
What about the light?
Just as you can have redshifts and blueshifts for sound, you can also have redshifts and blueshifts gravitational. For example, if you send a photon from the Sun to the Earth, since the Sun’s gravitational field dominates the Solar System and is strongest near the Sun, that photon will lose energy (and become “redder”). If it were to go in the opposite direction, from Earth to the Sun, the photon would gain energy and become “bluer”.
There were many skeptics in the physics community who thought this idea, of a shift, was completely unphysical. It is closely related to the speed of clocks: the number of wave “crests” that pass by your location in any time interval determines the frequency of the light you receive, and if gravitational redshifts are real, then sending a photon higher or lower in a gravitational field should lead to consequences observable. This means that, as is the case with most predictions in physics, there is a way to test it.
The Pound-Rebka experiment on the passage of time
Let’s say we induce a quantum transition. Either an electron changes energy levels or an excited nucleus reconfigures itself, releasing an energetic photon. If you have such an atom (or atomic nucleus) nearby, it should be able to absorb that photon, since the same physics that drives the emission of a photon can also lead to the reverse process: the absorption of that photon.
If, however, you move the photon to longer or shorter wavelengths, no matter how you do it, you will no longer be able to absorb it. The laws of the quantum Universe are quite strict, and if a photon arrives with slightly too much or too little energy, it will not trigger the correct excitation.
This led to a remarkable experiment, the Pound-Rebka experimentwho sought to demonstrate and quantify the existence of gravitational redshift and to prove that time does indeed flow faster at the head than at the feet.
From failure to success: why time changes based on where we are
The experimenters had installed a photon emitting source inside a small vertical tower, and then placed the same material at the other end of the tower. If there hadn’t been any redshift gravitational, that is, if time continued to flow at the same speed for everyone, then the material at the other end of the tower would have to absorb the photons emitted from the first end.
Of course it didn’t, because they had the wrong energy and therefore the wrong wavelength.
But what Pound and Rebka did was install an oscillator (basically the inside of a loudspeaker) which allowed them to “enhance” the photon-emitting material at one end of the tower. If they boosted it by the right amount, they reasoned, they could tune this induced Doppler shift to exactly cancel out the predicted gravitational redshift. As for time, you basically add extra motion (and a bit of extra time dilation) to compensate for the effects introduced by gravity.
Yes, the head ages faster than the feet
Suddenly, when the right frequencies were reached, the (iron) atoms began to absorb those photons emitted from the other end. The experiment confirmed and was subsequently improved by Pound and Snider during the 1960s.
The lesson is this: for every meter of height you gain, you need a Doppler shift of ~33 nanometers per second to compensate for it. It’s like you’re lower on the surface of the Earthyou would have to be moving at a certain speed for time to pass at the same rate as if you were higher up. In other words, without a small increase in velocity at your feet, without an extra amount of time dilation added, time passes faster at higher altitudes in the Earth’s gravitational field. To put it bluntly, the head ages faster than the feet.
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