Does Time Really Run Faster At Your Head Than Your Feet?

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There’s no such factor as absolute time. No matter the place you might be, how briskly you’re shifting, or how sturdy the gravitational discipline is round you, any clock you have got on you’ll at all times report time as passing on the identical fee: one second per second. For any solitary observer, time merely flows.

But in case you have two totally different clocks, you possibly can evaluate how time flows underneath totally different circumstances. If one clock stays stationary whereas the opposite travels rapidly, the fast-moving clock will expertise a smaller period of time passing than the stationary clock: that’s the rule of time dilation in particular relativity.

What’s much more counterintuitive, nonetheless, is that the relative movement of time additionally is determined by the distinction between how severely area is curved between two places. In General Relativity, this corresponds to the power of gravity at your specific location, which signifies that your ft really age at a distinct fee than your head whenever you’re standing up. Here’s the physics of how we all know.

One of the issues we depend on is that the legal guidelines of physics are common. While the properties of the Universe would possibly change with time, with vitality, or together with your location, the principles and the elemental constants that govern it stay the identical. A hydrogen atom situated wherever within the Universe will at all times have electron transitions occurring on the identical energies, and the quanta of sunshine they emit will likely be indistinguishable from every other hydrogen atom within the Universe.

The identical factor is true for ionic, molecular, and even nuclear transitions: the legal guidelines of physics stay the identical always and all locations, and so these transitions that emit or take up photons at all times happen on the identical vitality. However, if the emitter of a photon and the (potential) absorber of a photon aren’t situated on the identical time and place as each other, there’s a superb probability that they received’t agree on the energies they observe.

When it’s as a result of the objects are in relative movement with respect to 1 one other, we all know this impact as a Doppler shift. Most of us expertise the Doppler shift each time we hear an emergency car (or an ice cream truck) both approaching us or shifting away from us: we are able to hear the pitch of the siren change. If the car is approaching you, its waves will seem like shifted nearer collectively, and also you’ll hear a better pitch; if it’s shifting away from you, its waves will likely be shifted to reach spaced farther aside, and also you hear a decrease pitch.

For mild, it’s a virtually similar situation: if the supply and observer are shifting away from each other, the sunshine will get shifted in direction of longer (redder) wavelengths, whereas in the event that they’re shifting in direction of each other, the sunshine will get shifted in direction of shorter (bluer) wavelengths.

Now, right here’s the place issues get bizarre: this identical kind of shift must also happen — even when everyone seems to be stationary — when your gravitational discipline power adjustments from one location to a different.

Just as you possibly can have Doppler redshifts and blueshifts for mild, you can even have gravitational redshifts and blueshifts. For instance, for those who ship a photon from the Sun to the Earth, as a result of the Sun’s gravitational discipline dominates the Solar System and is stronger close to the Sun than farther away, that photon will lose vitality (and develop into “redder”) because it travels from the Sun to the Earth. If it have been to go in the wrong way, from the Earth to the Sun, the photon would achieve vitality and develop into “bluer” in shade.

There have been plenty of doubters within the physics group who thought that this concept — of a gravitational redshift — was fully unphysical. It’s intricately associated to the speed at which clocks run: the variety of wave “crests” that go by your location over any time interval decide the frequency of the sunshine you obtain, and if gravitational redshifts are actual, then sending a photon increased or decrease in a gravitational discipline ought to result in observable penalties. That means, as is the case for many physics predictions, there’s a approach to check it.

Let’s say you induce a quantum transition. Either an electron shifts in vitality ranges or an excited nucleus reconfigures itself, releasing an lively photon. If you have got an analogous atom (or atomic nucleus) close by, it ought to have the ability to take up that photon, as the identical physics that leads to the emission of a photon can even result in the reverse course of: the absorption of that photon.

If, nonetheless, you shift the photon to both longer or shorter wavelengths — no matter the way you do it — you received’t have the ability to take up it anymore. The legal guidelines of the quantum Universe are fairly inflexible, and if a photon is available in with barely an excessive amount of or too little vitality, it received’t set off the right excitation.

This led to a outstanding experiment, the Pound-Rebka experiment, that sought to reveal and quantify the existence of gravitational redshift, and to show that point actually does run sooner at your head than at your ft.

What the experimenters did was arrange a photon-emitting supply inside a vertical tower, after which put that very same materials on the different finish of the tower. If there have been no gravitational redshift — i.e., if time ran on the identical fee for everybody — then the fabric on the different finish of the tower ought to take up the photons emitted from the primary finish.

They didn’t, after all, as a result of they’d the incorrect vitality, and therefore, the incorrect wavelength.

But what Pound and Rebka did was arrange an oscillator (principally the inside of a speaker) that allowed them to “boost” the photon-emitting materials at one finish of the tower. If they boosted it by simply the correct amount, they reasoned, they may tune this induced Doppler shift to precisely cancel out the anticipated gravitational redshift. As far as time goes, it principally added an additional movement (and an additional little bit of time dilation) to compensate for the results that gravity introduces.

All of a sudden, when the precise frequencies have been reached, the (iron) atoms started absorbing these emitted photons from the opposite finish. The preliminary experiment confirmed General Relativity’s predictions, and was subsequently improved upon by Pound and Snider all through the Sixties.

The general lesson is that this: for each meter of top that you simply achieve, you want a Doppler shift of ~33 nanometers-per-second to compensate for it. It’s like being decrease on the floor of the Earth requires you to be in movement at a sure fee simply to have time go on the identical fee as it could for those who have been increased. In different phrases, with out an additional little velocity increase at your ft — with out an additional period of time dilation added in — time passes extra rapidly at increased elevations in Earth’s gravitational discipline.

Your head, to be blunt, ages extra rapidly than your ft do.

But you are able to do even higher than these unique experiments: by measuring the passage of time instantly utilizing atomic clock know-how. The means we outline time has developed over the centuries; what used to rely upon the movement of the Earth rotating on its axis or revolving across the Sun has now been changed by an atomic definition. A second, as we all know it, is outlined by the cesium-133 atom.

In that atom, there’s a hyperfine transition that’s extremely exact, emitting a photon of a really specific wavelength. That wave, for those who take 9,192,631,770 cycles of it, is our trendy definition of the second.

And but, for those who took an atomic clock — whether or not primarily based on cesium, mercury, aluminum, or every other factor — and moved it to a distinct elevation, that clock would run at a distinct fee from its unique elevation: sooner at increased elevations (in a weaker gravitational discipline), slower at decrease elevations (in stronger gravitational fields).

This has been experimentally verified to astonishing precision, as we’ve detected these predicted shifts for top variations as small as 0.33 meters (1 foot). In Earth’s comparatively weak gravitational discipline, this can be a outstanding achievement, demonstrating simply how correct timekeeping with atomic clocks has develop into.

But if we took this to a extra excessive setting, the results would develop into huge. No setting within the Universe is extra gravitationally excessive than a black gap. If you approached its occasion horizon, time would go so slowly for you that, in a single second (for you), centuries, millennia, and even eons may go for somebody distant.

It’s sufficient to make one fear that even when we may efficiently construct a wormhole, the extreme curvature of area may trigger the whole significant a part of the Universe — the place we now have stars, galaxies, and fascinating chemistry occurring — to go by whereas the traveler handed via it.

In our Universe, time will go the quickest for the observer who minimizes their movement via area and is situated the place the curvature of area is as little as potential. If you would journey to the area between galaxies, the place you’re distant from any sources of mass, you’ll age extra rapidly than anybody else. Here on Earth, the farther you might be from the middle, the sooner time runs for you. The results are extraordinarily slight, however measurable, quantifiable, and sturdy.

This means, for those who ever wished to time journey to the longer term, your greatest guess may not be to take a protracted, round-trip journey at practically the velocity of sunshine, however relatively to hang around the place there’s plenty of spatial curvature: close to a black gap or neutron star, as an illustration. The deeper right into a gravitational discipline you go, the slower time will run for you in comparison with those that are farther out. It would possibly solely grant you a number of additional nanoseconds over your complete life, however standing up — and protecting your head farther from Earth’s heart — actually gives you a bit bit extra time than laying down.

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