Gravitational time dilation is a confirmed prediction of Einstein's general relativity where time passes at different rates depending on gravitational potential; near a sufficiently massive and compact object like a black hole, extreme curvature causes time to slow dramatically, with the ratio of 1 hour to 7 years being a specific quantitative example derived from the Kerr metric for a near-maximally rotating supermassive black hole, and this effect has been experimentally confirmed through GPS satellite corrections, atomic clock comparisons, and binary pulsar timing observations.
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The Terrifying Truth About How Slow Time Moves Near a Black Hole | Brian GreeneAdded:
1 hour equals 7 years. Let me be precise about what that sentence means because it's a sentence that sounds like the premise of a thought experiment. Like something a philosopher might propose to make a point about the nature of time.
Like a metaphor for how subjective experience differs from objective clock measurement. It's none of those things.
It is a specific quantitative experimentally confirmed prediction of the most precisely tested physical theory in the history of science. A prediction that falls directly out of Einstein's general theory of relativity when you apply its equations to the specific gravitational environment near a sufficiently massive and compact object. 1 hour on the surface of a specific type of black hole. A black hole with specific mass and specific rotation at a specific orbital distance from the event horizon corresponds to exactly 7 years of elapse time for someone watching from far away. Not approximately, not as a rough estimate to within the precision of the calculation which is extraordinary. The ratio 1-61, 321 hour to 7 years emerges from the specific mathematics of curved spacetime. When you set the numbers in this specific ratio, 1 hour to 7 years is not famous because it appears in any physics paper specifically. It is famous because it appears in a movie. The 2014 film Interstellar depicted an astronaut descending to a planet orbiting a super massive black hole and experiencing one hour of surface time while seven years elapsed for the crew of the spacecraft waiting in higher orbit. The science consultant for the film was Kip Thorne, one of the most distinguished relativists of the 20th century, a co-founder of LIGO, a Nobel Prize laurate, and the specific ratio 1 to 61,320 is one he calculated to be consistent with the film's black hole parameters.
The ratio is physically correct, not approximately, not as a loose illustration of a real effect that is much smaller in practice. As a specific application of the time dilation equations of general relativity to a specific set of physical parameters, parameters that are extreme but not impossible. parameters that correspond to a real class of astrophysical objects that we have now observed directly. Time dilation near a black hole is real. It is one of the most firmly established predictions of physics. It has been confirmed in weaker forms by every GPS satellite in orbit, by every precise atomic clock comparison between different altitudes, by every timing measurement of pulsars in binary systems with neutron star companions. The specific magnitude of the effect near a stellar mass black hole is beyond anything current technology could survive to measure directly. But the physics is confirmed at lower field strengths and extrapolated to the extreme with confidence. And the story of what time dilation near a black hole actually means, what it implies, about the specific nature of time, about the relationship between gravity and the geometry of spaceime, about the extraordinary counterintuitive reality of the universe we inhabit is one of the most profound and most consequential stories in the history of physics. Let me take you into it. Let me start with something that I think is almost never communicated clearly enough in popular explanations of time dilation. The specific reason why gravity affects the rate at which time passes at the deepest level of the physics. The intuitive picture that most people carry that clocks near a massive object tick more slowly because the gravitational field somehow physically slows down the mechanism of the clock is wrong. Not approximately wrong. Fundamentally wrong in a way that misses everything that is actually interesting about the phenomenon. Time dilation near a massive object is not an effect on clocks. It is an effect on time itself. The specific rate at which time passes, the specific rate at which all physical processes including the oscillations of atoms in a cesium atomic clock, the beating of a human heart, the aging of biological tissue, the decay of radioactive nuclei is genuinely physically different at different positions in a gravitational field. Not because clocks are being interfered with because time itself is geometrically different at different positions. To understand this, you need to understand what general relativity actually says about the relationship between gravity and geometry. Einstein's great insight, the specific conceptual leap that separates general relativity from everything that came before is that gravity is not a force. Not in the Newtonian sense of a force acting at a distance between masses. Gravity is the curvature of spacetime produced by the presence of mass and energy. In the absence of matter and energy, spacetime is flat. Its geometry is the specific flat four-dimensional geometry of special relativity in which the spatial and temporal relationships between events are described by a specific metric. The Manowski metric in the presence of matter and energy spaceime is curved. Its geometry is distorted from the flat Manowski geometry in a specific way that Einstein's field equations describe. The curvature of spacetime near a massive object is not just a curvature of space. It is a curvature of spacetime, a distortion that affects both the spatial and temporal dimensions of the geometry simultaneously.
The specific way that time is embedded in the curved space-time geometry near a massive object is different from the way time is embedded in flat empty spaceime far from any mass. This difference, the specific change in the temporal geometry of spacetime as a function of position in a gravitational field is what we call gravitational time dilation. And it is not an illusion, not an apparent effect, not a consequence of the finite speed of light or of signal travel times. It is a genuine physical geometric difference in the rate at which time passes at different positions in the curve spaceime. Let me now take you to the specific mathematics not in the form of equations which I'll translate into the specific physical meaning but in the form of the specific physical picture that the mathematics describes. The geometry of spacetime near a non-rotating spherically symmetric mass, a static black hole or a star or any other spherical mass is described by a specific metric called the Schwarz metric named for the German physicist Carl Schwarzchild who found the first exact solution to Einstein's field equations in 1916 within weeks of the equations publication while serving on the Eastern Front in World War One, the Schwarz metric describes how distances and time intervals are related in the curved spaceime around a spherical mass and its specific content in the temporal direction is this. The rate at which time passes at a given position measured by a clock sitting at rest at that position depends on how deep in the gravitational field that position is.
The deeper in the gravitational field, the slower time passes relative to a clock far from the mass. The specific formula involves the ratio of the Schwarzild radius, the specific radius of the event horizon to the position of the clock. The Schwarz shaw radius is defined by the mass of the object. For a non-rotating black hole, it is 2gm c^², where g is Newton's gravitational constant, m is the mass of the black hole, and c is the speed of light. For the sun, this works out to approximately 3 km. For a black hole of 10 solar masses, approximately 30 kilometers. For the super massive black holes at the centers of galaxies, millions to billions of kilome, the rate at which time passes at a distance r from a non-rotating black hole compared to far from the black hole is proportional to the square root of 1 minus the schwarz shield radius / r. At large r, far from the black hole, this factor approaches one and time passes at its normal rate.
As r approaches the Schwarz shield radius as you descend toward the event horizon and this factor approaches zero time passes more and more slowly relative to the distant observer at the Schwarz chilled radius itself at the event horizon the factor is exactly zero from the perspective of a distant observer time at the event horizon has stopped completely. This is the extreme of gravitational time dilation. Not just 1 hour equals 7 years. From the perspective of a distant observer, an infinite amount of time passes before any clock at the event horizon advances by even one tick. The event horizon is in this sense a horizon in time as well as in space. A boundary beyond which time from the perspective of the outside universe has ceased to flow. Now, let me take you to something that requires very careful thinking. The distinction between what a distant observer sees and what the infalling observer actually experiences.
The distant observer watches a clock falling toward a black hole and sees it ticking more and more slowly as it approaches the horizon. At the horizon itself, the distant observer never sees the clock reach it. The time dilation is infinite and the clock appears to freeze asmmptoically at the horizon. But the infalling observer, the person carrying the clock does not experience this. They experience nothing unusual as they cross the horizon. Their clock continues to tick at its normal rate. Their heartbeat continues. Their thoughts proceed at their normal speed. From their perspective, there is no dramatic event at the horizon. They cross it without noticing anything special. The local physics is perfectly normal because the equivalence principle guarantees that in a sufficiently small region of spacetime, the effects of gravity are locally indistinguishable from flat spacetime. This distinction, the difference between what the distant observer sees and what the infalling observer experiences is one of the most conceptually challenging aspects of black hole physics. Both descriptions are correct. Both are physically real.
They are simply different coordinate descriptions of the same physical reality. The curved space-time geometry of the black hole. The distant observer never sees anything fall into the black hole. From the distant observer's perspective, everything that has ever fallen toward a black hole is still there hovering asmmptoically close to the horizon, frozen in the infinite time dilation. The black hole's horizon is littered from the outside perspective with the frozen images of everything that has ever fallen into it. The infalling observer crosses the horizon, continues falling toward the singularity, and depending on the mass of the black hole, reaches the singularity within a finite and possibly very short proper time after crossing the horizon. Both of these descriptions are consistent with general relativity.
Neither contradicts the other. They are simply different observers in different positions in the curved spaceime with different relationships to the temporal geometry of the geometry around the black hole. Let me now take you to the specific case of a rotating black hole, the curr black hole, because this is the type of black hole that the interstellar calculation applies to. And the rotating case is dramatically more complex and dramatically more interesting than the non-rotating Schwarz case. Roy Kerr, a New Zealand mathematician, solved Einstein's field equations for a rotating mass in 1963, 47 years after Schwarzild's solution.
The Kur solution was one of the most important solutions in the history of general relativity because all astrophysical black holes formed from the collapse of rotating stellar material are rotating black holes. The Schwarzild solution is an idealization.
The KUR solution is the realistic case.
The specific features of the Kerr metric that differ from Schwarzchild are extraordinary.
First, the Kerr black hole has not one but two special surfaces. The outer event horizon, the surface of no return, is still present at a radius that depends on both the mass and the spin.
But there is an additional surface outside the event horizon called the argosphere. a region where the rotation of the black hole drags space-time itself around with it so strongly that nothing not even light can remain stationary. Everything in the erosphere must rotate with the black hole whether it wants to or not. The frame dragging effect, the specific pulling of spaceime into rotation by the rotating mass is so extreme in the ergosphere that the very concept of remaining stationary is physically impossible. Second, the time dilation in the Kurr geometry is dramatically more extreme than in the Schwarz shield geometry for the same mass when you approach specific orbits near the maximally spinning black hole.
The specific orbit in the interstellar scenario, the innermost stable circular orbit around a near maximally rotating super massive black hole can be dramatically deeper in the gravitational potential than the corresponding orbit around a non-rotating black hole of the same mass. The time dilation factor is correspondingly more extreme. For a maximally rotating black hole, one spinning at the maximum possible rate allowed by the cur solution, the innermost stable circular orbit is right at the event horizon. A clock on this orbit experiences time dilation that is essentially infinite. It ticks infinitely slowly relative to a distant observer. The ratio 1 hour equals 7 years requires a black hole that is spinning at approximately 0.998 to 0.999 of the maximum possible spin. Extremely close to but not quite at the maximum.
At this spin, the innermost stable orbit is close enough to the horizon that the time dilation factor is approximately 61,320 to1. This is the specific physics that Kip Thorne calculated for Interstellar, a super massive black hole gargantua in the film with a mass of approximately 100 million solar masses spinning at 0.998 of maximum the planet Miller orbiting at the innermost stable orbit.
Time dilation factor 61,320 one hour on the planet 7 years for the distant observer. The numbers are real.
The physics is real. And the specific experience of a human being on that planet one hour passing while seven years pass for their crew mates in higher orbit is one of the most specific and most viscerally comprehensible illustrations of what curved spaceime actually means for human experience. Let me now take you to the experimental evidence because time dilation near massive objects is not just a theoretical prediction. It is a measured, confirmed, daily relied upon physical reality. The most immediately relevant and most routinely verified form of gravitational time dilation is the correction applied to the GPS satellite system. The global positioning system consists of 31 operational satellites orbiting Earth at an altitude of approximately 20,200 km. At this altitude, the satellites are higher in Earth's gravitational field than the GPS receivers on the ground.
And therefore, by gravitational time dilation, their clocks tick faster than identical clocks on the ground. The specific magnitude of this gravitational time dilation effect at GPS satellite altitude is approximately 45 microsconds per day. Each GPS satellites clock gains 45 micros secondsonds relative to a groundbased clock every day purely because of the difference in gravitational potential. This sounds tiny but GPS positioning depends on timing signals with nanocond precision.
An uncorrected error of 45 micros secondsonds per day would accumulate to approximately 13 kilometers of positioning error per day. GPS would be useless for navigation within a matter of days if the gravitational time dilation were not corrected. It is corrected. The GPS satellites atomic clocks are specifically adjusted to compensate for the gravitational time dilation. and they are deliberately run slightly slow on the ground to tick at the same rate as a groundbased clock once they are in orbit at altitude. The correction is based directly on Einstein's general theory of relativity.
Every time you use GPS navigation, you are relying on a correction that would not exist if gravitational time dilation were not a real physical effect. The specific terrestrial experiments that have confirmed gravitational time dilation, most precisely are atomic clock comparisons at different altitudes.
In 2010, the NIST group led by Chia and colleagues compared two optical atomic clocks, the most precise timekeepers ever built, separated by a height difference of just 33 cm. 33 cm less than the length of a ruler. And the experiment confirmed the gravitational time dilation predicted by general relativity for this tiny height difference, a fractional frequency difference of approximately 4 * 10 -17 at a signal to noise ratio of more than four sigma. Time dilation is not exotic.
It is not confined to black holes or to extreme gravitational environments. It is present everywhere there is a gravitational field including in the room you are currently in between the floor and the ceiling between the ground and the satellite. It is a real measured technologically exploited physical effect that is built into the infrastructure of modern civilization.
Now let me take you to the most important and most profound implication of gravitational time dilation. The specific thing that it tells us about the nature of time itself. Time dilation both gravitational which we've been discussing and velocity based from special relativity forces a specific and irreversible conclusion about what time is. Time is not absolute. Time is not a a universal objective backdrop against which events unfold at the same rate for all observers in all locations. Time is relative. Its rate depends on the gravitational potential of the position where it is measured and on the velocity of the measuring system. This is not a comfortable conclusion. It violates the deepest intuitive conviction about the nature of time. The conviction that there is a single objective now that is the same for everyone everywhere. The physicist technical term for this intuitive belief is the absolute simultaneity. The idea that two events that are simultaneous for one observer are simultaneous for all observers.
Special relativity showed in 1905 that this is not true. Simultaneity is relative to the reference frame. General relativity extended this to show that the very rate of time flow is relative to the position in a gravitational field. What these results collectively establish is that time is not a thing out there in the world. Time is a relationship, a specific geometrical relationship between events in spaceime that is determined by the local curvature of the geometry. Different positions in a gravitational field have different local geometries and therefore different local relationships between events. The rate at which time passes is a property of the local space-time geometry, not of some universal background clock. This is what is truly extraordinary about the 1 hour equals 7 years calculation. It is not telling you that something unusual is happening to the clocks near the black hole. It is telling you that the geometry of spacetime near the black hole is genuinely physically different from the geometry far from it. The 1 hour and the seven years are both real, both correct.
Both genuine measurements of time, but made in regions of different geometry where time itself is structured differently. Two people, one on the planet Miller near Gargantua, one on the distant spacecraft, live in the same physical universe, are both following the laws of physics correctly, are both experiencing time at its local rate, and are nevertheless aging at dramatically different rates, not because one of them is doing something wrong, because the geometry of spaceime, the specific distribution of curvature produced by the massive rotating black hole is different at their different positions.
and therefore time itself has a different structure at those positions.
Let me now tell you about something that I think is the most important physical insight that time dilation near black holes provides an insight that goes beyond the specific numbers and connects to the deepest questions about the nature of spacetime. The equivalence principle, Einstein's specific realization that gravity and acceleration are locally indistinguishable is the foundation of general relativity and it provides a specific and illuminating way to understand why gravity affects time.
Consider an accelerating rocket in empty space. No gravitational fields, no planets or stars, just a rocket accelerating upward at a constant rate.
Inside the rocket, the person at the top of the rocket and the person at the bottom of the rocket are both accelerating. But because the rocket has finite length, the person at the top had to have been given a slightly higher velocity than the person at the bottom when the acceleration started.
Otherwise, the rocket would be stretched or compressed as it accelerates.
Now consider what happens to light signals sent from the bottom of the rocket to the top. The signal travels upward, but during the time the light is in flight, the top of the rocket is accelerating away from it. The signal has to travel farther to reach the top than it would if the rocket weren't accelerating. The signal arrives at the top with a slightly lower frequency than it was emitted with. It's been gravitationally redshifted by the acceleration.
And here is the critical insight.
Frequency is the inverse of period. If the frequency of a signal decreases, the period the time between wave crests increases. The clock at the bottom of the rocket emitting light signals at one frequency is being read by the person at the top as ticking at a lower rate. The person at the top concludes that the clock at the bottom is running slow. But by the equivalence principle, this is physically identical to the situation of a rocket sitting at rest on the surface of a planet with a gravitational field pulling downward. The light red shift and the time dilation produced by acceleration are exactly the same as those produced by gravity because gravity and acceleration are the same thing locally. This is how time dilation and gravity are connected at the deepest level. Not through some mysterious influence of gravitational fields on the mechanisms of clocks. Through the specific geometric structure of curved spacetime that gravity as the curvature of spacetime produces. The frequency shift of light climbing out of a gravitational potential is the same as the frequency shift produced by acceleration because they are the same phenomenon. And that frequency shift is the same as the time dilation because frequency is the rate of oscillation which is the rate of time flow. Gravity bends light because gravity curves spacetime. Gravity slows time because gravity curves spacetime. They are not separate effects. They are the same effect seen from different perspectives.
Let me close this first part with something that connects the black hole time dilation story to the specific personal experience of what these numbers mean. 1 hour equals 7 years.
Imagine experiencing this directly. You descend toward a black hole in a spacecraft. Land on a planet in a stable orbit extremely close to the event horizon. Conduct your research for 1 hour 60 minutes 3,600 seconds and ascend back to the waiting mother ship. Your crew mates have aged 7 years not apparently not from the perspective of some abstract coordinate system but genuinely physically biochemically seven years of cellular aging. Seven years of experiences you were not part of. 7 years of history of births and deaths and events in the wider universe that occurred while you were spending 60 minutes on the surface. You return 60 minutes older. They are 7 years older and nothing violated any law of physics.
No time travel occurred in any paradoxical sense. No causality was violated. The mathematics of general relativity predicted exactly this outcome. And if the technology existed to execute the experiment, this is precisely what would happen. The specific numbers are extraordinary. But what they are pointing at is something even more extraordinary. The universe we inhabit is not organized around a single objective universal time. It is organized around the specific geometry of spaceime. a geometry that is curved by the presence of mass and energy that has a different structure at different positions and that therefore has a different relationship between events a different time at different positions.
We don't experience this in everyday life because the gravitational fields we encounter earth's surface the vicinity of the solar system produce time dilation effects that are tiny by the standards of everyday experience. The difference in clock rate between the floor and the ceiling of a room is phmpto seconds per day. The difference between earth's surface and GPS orbit is 45 micros seconds per day. Enormous in the context of precision navigation imperceptible in the context of human aging. But near a black hole near a sufficiently massive and compact object that the curvature of spaceime becomes extreme the difference is not phento seconds. It is hours against years. It is the full visceral personally experienced reality of the geometric structure of spaceime expressing itself in the specific differential aging of two people who were once the same age separated by nothing more than their positions in the gravitational field.
One hour equals 7 years. and the story of why that sentence is true. The specific physics of curved spaceime, the geometry of the curved black hole, the experimental confirmations from GPS and atomic clocks and pulsar timing is the story of one of the most profound and most counterintuitive truths about the universe that physics has ever established. In part two, I want to go deeper into what the experience of time near a real astrophysical black hole would actually be like, into the specific phenomenon of gravitational red shift and how it connects to time dilation and into something that I find genuinely extraordinary. The specific way that time dilation near black holes is no longer purely theoretical. Now that we have direct images of real black holes from the event horizon telescope and specific timing measurements from pulsars in extreme gravitational fields that are beginning to probe exactly this regime of physics, 1 hour equals 7 years. The numbers are real. The physics is confirmed. And what the physics is telling us about the nature of time about the universe's deepest structure is more extraordinary than the numbers alone suggest. So we'd arrived at this place where the specific ratio 1 hour equals 7 years derived from Kip Thorne's calculations for the interstellar film based on a super massive black hole spinning at 99.8% 8% of maximum and an orbit at the innermost stable circular orbit of that near maximally rotating curve black hole is not Hollywood fantasy but specific correct general relativistic physics where gravitational time dilation is not just a theoretical prediction but an experimentally confirmed daily exploited physical effect built into the GPS correction algorithm measured between clock height separated by 33 cm detectable in the timing of pulsars in binary systems and where the deep explanation for why gravity affects the rate of time is the equivalence principle. The specific profound fact that gravity and acceleration are the same thing locally and that the curvature of spaceime produces both the bending of light and the slowing of time as manifestations of the same underlying geometric reality.
Now I want to go deeper into what the experience of being near a real astrophysical black hole would actually be like the specific physical phenomena that an observer near the horizon would encounter beyond the time dilation itself into the specific phenomenon of gravitational redshift. How light climbing out of a gravitational field loses energy, changes frequency, and how this is directly connected to time dilation through the equivalence principle and into something I find genuinely extraordinary. the specific way that the Event Horizon Telescope's direct images of real black holes are beginning to test aspects of the physics that Thorne calculated and what the pulsar timing observations in extreme gravitational environments are revealing about time dilation in real astrophysical systems. Let me start with the experience because I think the specific phenomenology of what it would be like to approach a real super massive black hole is one of the most extraordinary thought experiments in all of physics. Imagine you are in a spacecraft approaching gargantua, the specific super massive black hole of the interstellar calculation.
100 million solar masses spinning at 99.8% 8% of maximum. The black hole is not just a mathematical abstraction. It is a real physical object of extraordinary size and power. The first thing you notice approaching from afar is the visual distortion of the background starfield. Gravitational lensing, the bending of light by the black holes gravity is deflecting starlight from sources behind and around the hole. The stars are not where they appear to be. Their images are distorted, stretched, and multiplied by the specific geometry of the cur spacetime. If you look directly at the black hole, you see not a dark circle against a uniform starfield, but an extraordinary visual pattern. A bright ring of light surrounding a dark shadow with specific asymmetric brightening on one side with multiple images of individual stars appearing at specific positions determined by the complicated lightbending geometry of the kermetric.
This visual effect, the specific appearance of a black hole to an observer with good eyes and perfect physics knowledge is what the event horizon telescope images are capturing from a distance of millions of light years. The photon ring, the specific bright ring produced by light that has orbited the black hole one or more times before escaping to infinity, is a direct observational signature of the strong field geometry of the cur. Solution. As you approach more closely, the visual effect intensifies. The photon ring grows brighter and more prominent. The shadow, the dark region where the black hole absorbs all incoming light, grows larger in your field of view. The star field behind you, the stars in the direction you came from is increasingly compressed into a smaller and smaller patch of sky by the extreme gravitational lensing. And ahead of you in the direction of the hole, the specific multiple imaging geometry of the strongly curved spacetime creates a complex, beautiful, deeply strange visual panorama that has no analog in any experience available without extreme gravity. Now approach the specific orbit where the 1 hour equals 7 years time dilation occurs. the innermost stable circular orbit around a near maximally rotating black hole. This orbit is extremely close to the event horizon for Gargantua. With its specific parameters, the event horizon is at a radius of approximately 100 million km, roughly the Earth's sun distance. The innermost stable orbit for a near maximally spinning black hole is dramatically closer to the horizon than for a nonrotating one for a maximally spinning black hole. It is at essentially the same radius as the horizon. On this orbit, the gravitational field is extreme. But a specific and remarkable property of the KUR geometry, the reason that stable orbits can exist so close to the horizon of a rapidly rotating black hole is that the frame dragging effect of the rotation is providing an additional support against the infall toward the singularity. The rotating spacetime is literally pulling your orbit along, adding centrifugal like support that allows you to remain at a radius that would be impossible to maintain around a nonrotating black hole of the same mass. The tidal forces at this orbit, the specific differential gravity that would stretch a human body depend on the mass of the black hole.
For a sufficiently massive black hole, one of 100 million solar masses, the tidal forces at the innermost stable orbit, are manageable, a human body would not be stretched appreciably. The tidal gradient across a meter scale body at this distance from a 1000 million solar mass black hole is small enough that you would not feel it. This is why for interstellar's purposes a planet can orbit at this location without being tidily disrupted. The black hole is massive enough that the tidal forces at the innermost stable orbit are gentle.
Now let me describe the specific phenomenon of gravitational red shift because this is the specific observable consequence of time dilation that connects the abstract mathematics to real astrophysical observations.
When light is emitted by a source deep in a gravitational well and travels outward to a distant receiver, it loses energy as it climbs against the gravitational potential. The specific mechanism is the same as the time dilation effect. It is in fact the same effect viewed from the perspective of the photon rather than the clock. Think of it this way. The source deep in the gravitational field near the black hole is emitting light at a specific frequency. That frequency is determined by the specific atomic transition producing the light. The quantum mechanics of the atom which is independent of the gravitational field in the local frame of the source. The atom vibrates at its natural frequency determined by the masses and charges of the electrons and nucleus. But from the perspective of a distant observer, the source is in a region where time is flowing more slowly. The atom is vibrating at what appears to the distant observer to be a lower rate because all processes at the source are running at the dilated rate. The light arriving at the distant observer therefore has a lower frequency. It has been redshifted by the gravitational field. The specific amount of red shift depends on the ratio of the gravitational potential at the source to the gravitational potential at the receiver. For a source deep near a black hole and a receiver far from it, the red shift can be enormous. For a source right at the event horizon, the gravitational red shift is infinite light from the event horizon is redshifted to infinite wavelength to zero frequency effectively disappearing.
This is the direct observational connection between time dilation and red shift. They are the same phenomenon. The difference in the rate of time flow between different positions in a gravitational field seen from two different perspectives. The time dilation is the difference in clock rates. The gravitational red shift is the difference in photon frequencies.
Both arise from the same underlying geometric fact that the structure of time in curved spacetime varies with position. The specific gravitational red shift from the innermost stable orbit of gargantua to infinity. The red shift that a distant observer would measure for light emitted from the planet Miller is a factor of approximately 61,320.
The light from the planet's surface arrives at the distant observer at a frequency 61,320 times lower than it was emitted. This corresponds to a wavelength 61,320 times longer. Visible light from the planet surface emitted in the wavelength range of 400 to 700 nmters arrives at the distant observer in the microwave or radio range. The planet is effectively invisible invisible light to the distant observer not because it is dark but because the gravitational red shift has shifted all its visible light out of the visible band. This is a specific and important observational consequence of extreme time dilation near a real black hole with the parameters that produce 1 hour 27year time dilation. Not only does time pass more slowly, the electromagnetic radiation from that region is also dramatically redshifted, making direct observation extraordinarily difficult.
Let me now take you to the specific astrophysical systems in which gravitational time dilation has been measured. Not in the extreme regime of stellar or super massive black holes where the effects are too large to survive long enough to measure directly but in the specific intermediate regime of binary pulsar systems where general relativity has been tested with extraordinary precision. The discovery of the first binary pulsar PSRB 1,913 + 16 by Russell Hulse and Joseph Taylor in 1974 was one of the most important discoveries in the history of gravitational physics. Holse and Taylor found a pulsar in orbit around another neutron star binary system in which both the timer and the clock are in a gravitational field that varies as the orbit progresses.
A pulsar in a binary orbit experiences periodic changes in its gravitational potential as it moves between the nearest point to its companion, the periastron, and the farthest point, the apastron. At periastron, the pulsar is deeper in the gravitational field of its companion and therefore experiences more gravitational time dilation than at apistron. This periodic variation in the gravitational time dilation produces specific measurable variations in the apparent pulse timing that accumulate over time. Taylor and his colleagues measured the timing of PSRB 1,913 + 16 over decades, accumulating one of the most precise data sets in observational astrophysics, and found perfect agreement with the general relativistic prediction for the gravitational time dilation, the special relativistic time dilation from the varying orbital velocity, and most dramatically the orbital decay produced by the emission of gravitational radiation.
which removed energy from the orbit and caused the orbital period to decrease at a specific predicted rate. For this work, confirming general relativity's predictions in a strong field environment and providing the first evidence for gravitational wave emission, Holen Taylor received the Nobel Prize in physics in 1,993.
The specific magnitude of the gravitational time dilation measured in the Holtz Taylor binary is small compared to the black hole case. The neutron stars are massive but not as massive as stellar black holes and the orbital separations are larger than the innermost stable orbit. But the measurement demonstrates that the specific equations of general relativity for time dilation in strong gravitational fields are correct at the level of precision that precision pulsar timing can achieve which is extraordinary. Let me now tell you about the event horizon telescope. The specific instrument that has directly imaged the photon ring and shadow of real black holes and how its observations connect to the time dilation physics. The event horizon telescope is a specific global network of radio telescopes distributed across multiple continents that are coordinated to function as a single earthsized telescope using a technique called very long baseline interferometry or VBI. By combining observations from telescopes separated by the diameter of Earth, the EHT achieves an angular resolution of approximately 20 microarchse seconds, sufficient to resolve features at the scale of the event horizon of the super massive black holes in M87 and the Milky Way center. In 2019, the EHT published the first direct image of a black hole, the super massive black hole at the center of the galaxy, M87, located approximately 55 million light years from Earth. The image showed the specific predicted morphology of the photon ring and the dark shadow, the visual signature of the strong field cur geometry that Thorne and others had calculated decades earlier. In 2022, the EHT published the first image of Sagittarius A times the super massive black hole at the center of the Milky Way, approximately 26,000 lighty years from Earth. Sagittarius A times has a mass of approximately 4 million solar masses, dramatically smaller than M87, 6.5 billion solar masses. And it flickers on time scales of minutes to hours, reflecting the specific orbital dynamics of hot gas near the innermost stable orbit. The specific features visible in the EHT images, the photon ring, the shadow, the specific asymmetric brightening are all direct manifestations of the strong field cur geometry. The photon ring is produced by light that has orbited the black hole one or more times. Light that has been bent around the hole by the extreme space-time curvature and escaped to reach our telescopes. The shadow is the specific projection of the event horizon on the photon capture cross-section. The specific set of photon trajectories that end inside the hole rather than escaping to infinity. The asymmetric brightening, the specific pattern in which one side of the photon ring is brighter than the other is produced by the Doppler boosting and gravitational beaming of the hot gas orbiting the black hole. The gas on the approaching side moving toward the observer is boosted in brightness by special relativistic Doppler shift. The gas on the receding side is dimmed by the same effect. The specific pattern of brightening in the EHT image encodes the rotation direction and the specific spin of the black hole information that is directly connected to the time dilation physics because it is the spin that determines how extreme the frame dragging is and therefore how close to the horizon the innermost stable orbit can be. The EHT measurements of the spin of M 87 times and Sagittarius A times derived from the specific morphology of the photon ring and the variability pattern of the near horizon gas are direct observational tests of the curr geometry.
If the cur solution is correct, if real black holes are described by the mathematics of Einstein's general relativity, then the specific relationship between spin and photon ring morphology should match the EHT observations.
Within current measurement uncertainties, they do. Let me now tell you about something that I think is the most important frontier in observational tests of strong field time dilation. the specific program of pulsar timing near the galactic center that is beginning to probe the gravitational field of Sagittarius A times with unprecedented precision. Sagittarius A times the 4 million solar mass black hole at the Milky Way center is surrounded by a specific stellar population called the stars. young massive stars in highly eccentric orbits around the black hole with orbital periods of years to decades. The monitoring of these stars by the infrared telescopes of the KEK Observatory and the European Southern Observatory's VLT has produced the most precise measurement of Sagittarius A's mass and the specific orbital dynamics of the stars closest to the black hole particularly S2 which passes within approximately 120 AU of Sagittarius A times at its closest approach have provided tests of general relativistic orbital procession and gravitational red shift.
The S2 star with an orbital period of approximately 16 years has been monitored through multiple complete orbits since 2002. At its 2018 closest approach, the S2 star was moving at approximately 2.7% of the speed of light relative to the black hole. And its light was gravitationally redshifted by the specific amount predicted by general relativity for its position in the gravitational field of Sagittarius A.
The measured gravitational red shift at closest approach, a frequency shift of approximately 200 km/s or roughly one part in 1,500 agreed with the general relativistic prediction to within the measurement uncertainties.
This is a specific direct measurement of gravitational time dilation near the galactic center black hole. Not as dramatic as the 1 2 60 1,320 ratio of the interstellar scenario. The S2 stars closest approach is far enough from Sagittarius A times that the time dilation effect is subtle, but it is the closest thing to a direct measurement of gravitational time dilation near a real super massive black hole that current technology has achieved. The future frontier involves finding pulsars near Sagittarius A. A pulsar, a rotating neutron star emitting regular radio pulses in a tight orbit around Sagittarius A times, would provide a precision clock in an extreme gravitational field that would allow the gravitational time dilation to be measured with a precision that the S2 star timing cannot approach. Pulsar timing provides timing precision of micros secondsonds to nanconds, orders of magnitude more precise than the optical velocity measurements used for S2. No pulsar has yet been discovered in a tight orbit around Sagittarius A. The galactic center region is radio at low frequencies because of the interstellar scattering and the specific sensitivity and frequency coverage of current radio telescopes limits the discovery of pulsars there. But the square kilometer array with its dramatically enhanced sensitivity at the high frequencies needed to see through the galactic center scattering screen is specifically identified as the instrument that could find such a pulsar. If a pulsar were found in an orbit comparable to S2s or in a tighter orbit with a period of a year or less, it would be the most extraordinary natural laboratory for strong field general relativity ever found. The specific timing of the pulsar through its orbit around Sagittarius eight times would provide measurements of gravitational time dilation, orbital procession, frame dragging from the black hole spin, and gravitational wave emission. All at signal to noise ratios that would far exceed any existing test of strong field gravity. The hunt is underway. The SKA is being built specifically with the Galactic Center pulsar search as one of its highest priority science goals. Let me now address something that is important for a complete understanding of black hole time dilation. The specific question of what happens to information near the event horizon and how time dilation connects to the most profound unsolved problem in theoretical physics. The information paradox first clearly articulated by Stephven Hawking in the 1970s involves a specific and fundamental tension between general relativity and quantum mechanics at the event horizon of a black hole. General relativity says that the event horizon is a point of no return. Once something crosses it, it can never escape.
Specifically, the time dilation at the horizon is infinite from the outside perspective. An object falling into the black hole takes an infinite coordinate time to reach the horizon even though it reaches it in a finite proper time.
Quantum mechanics says that the vacuum near the event horizon is not empty. The Hawking radiation mechanism. Hawking specific calculation of the quantum processes near the event horizon predicts that the black hole emits thermal radiation with a specific temperature proportional to the surface gravity of the hole. The black hole slowly loses mass through this Hawking radiation and eventually over astronomically long time scales for astrophysical black holes evaporates completely. The paradox is this.
Hawkings original calculation predicted that the Hawking radiation is perfectly thermal. It contains no information about what fell into the black hole.
When the black hole evaporates, all the specific information about the infalling matter, the specific quantum states of every particle that ever crossed the horizon is lost. This violates a fundamental principle of quantum mechanics, the principle of unitarity, which says that quantum evolution is reversible and information is never destroyed. The resolution of this paradox, the specific mechanism by which information escapes from an evaporating black hole is the most important unsolved problem at the intersection of general relativity and quantum mechanics. It is directly connected to the time dilation physics because the event horizon the specific surface where time dilation becomes infinite is the specific location where the paradox is most acute. Recent work particularly the developments in the understanding of quantum gravity through the ADIs CFT correspondence and the specific calculations of the page curve and the quantum extreal surfaces has suggested that information is indeed preserved in the Hawking radiation and that the semiclassical calculation that Hawking originally performed misses specific quantum gravitational effects that become important over the evaporation time scale.
The specific mechanism involves a specific quantum gravity effect called the island formula. A specific prescription for computing the entropy of the Hawking radiation that accounts for specific quantum gravitational corrections near the horizon. The island formula gives an entropy that initially increases as the black hole radiates following the thermal behavior and then turns around and decreases following the page curve that unitarity requires. This is extraordinarily technical. The specific calculations involve quantum field theory and curved spacetime, the mathematics of holography and the ads CFT duality and specific tools from quantum information theory. But the conceptual point is profound. The resolution of the information paradox, the specific mechanism by which quantum mechanics and general relativity are reconciled at the event horizon is directly connected to the specific geometry of the horizon that produces the extreme time dilation. The infinite time dilation at the horizon is the geometric signature of the same physical reality that produces the information paradox. the specific structure of the event horizon as a one-way membrane in spaceime. Let me now tell you about something that connects the black hole time dilation story to the broader narrative of this series. The specific way that the physics of extreme gravity near black holes is connected to the questions about life, consciousness, and the future of civilization that we've been exploring. We've established throughout this series that the universe operates according to specific physical laws. Laws that produce extraordinary phenomena including the formation of black holes, the curvature of spaceime, and the specific geometric structure that gives rise to extreme time dilation. These laws are not negotiable.
They are not optional. They apply to everything, including to the specific organized matter that constitutes living beings and civilizations.
The specific fact that time dilation near a black hole is real. That it is the same physics that makes GPS work that has been confirmed in binary pulsar timing that is directly visible in the EHT images of real black holes means that the universe we live in is genuinely deeply different from the intuitive picture that everyday experience provides. In everyday experience, time is universal. Everyone ages at the same rate. The universe has a single shared. Now, these intuitions are wrong. They are the specific limit of general relativity in weak gravitational fields, which is correct to high precision in the environments we normally encounter, but which breaks down dramatically near black holes. Near black hole, time is not universal. Two observers at different positions in the gravitational field are genuinely physically aging at different rates. Not apparently genuinely. The biological, chemical, physical processes in each observer's body are proceeding at different rates determined by the local space-time geometry at each observer's position. This has a specific and extraordinary implication for the long-term future of civilization. One that is usually not discussed in the context of existential risk or long-term planning. If a future technological civilization wanted to extend its subjective lifespan to experience more time than the cosmological time scales of the universe would normally allow, it could do so by exploiting gravitational time dilation. Not by the modest factors available near ordinary stellar mass black holes, the tidal forces near a stellar mass black hole at the innermost stable orbit would be lethal. But near a sufficiently massive super massive black hole, one with enough mass that the tidal forces at the innermost stable orbit are manageable, the time dilation could be extreme enough to allow a civilization to experience subjective eons while only cosmological years pass in the outside universe. This is not fantasy. It is the specific physics of the cur metric applied to the specific parameters of real astrophysical objects. Sufficiently massive rotating black holes exist. We have imaged them with the EHT.
The innermost stable orbits of near maximally spinning super massive black holes have manageable tidal forces for sufficiently massive holes. The time dilation at those orbits is extreme. A civilization with the technology to survive in the extreme environment near a super massive black hole to manage the radiation, the tidal forces, the accretion disc environment could in principle experience billions of years of subjective time while only millions of years pass in the universe outside.
The eventual heat death of the universe would be pushed billions of subjective years into the future from the perspective of the time dilated civilization. This is not a proposal. It is a thought experiment that emerges naturally from the specific physics of the curric. And it illustrates a profound point. The universe's physical laws, while they don't spare any civilization from ultimate cosmic death, do provide specific loopholes in the experience timeline that are genuinely consequential for thinking about the long-term future of intelligence in the cosmos. Let me close this second part with something that I think is the most important and most underappreciated insight about time dilation near black holes. a specific point about what the physics is telling us not just about black holes but about the nature of time itself. The specific ratio 1 hour equals seven years is not just a number. It is a specific quantitative measure of the difference in the structure of time at two different positions in the universe.
It is saying that the geometry of spacetime, the specific four-dimensional fabric within which all physical processes occur, has a profoundly different structure at different positions. That the relationship between events, the ordering of causes and effects, the specific metric that defines what we call time. All of these are local properties of the space-time geometry, not global, universal facts.
What does this mean for how we should think about time? It means that time is not a backdrop. Time is not the container in which events occur. Time is a relationship, a specific local geometrically defined relationship between events that is determined by the curvature of the spaceime in which those events are embedded. Two events that are simultaneous for one observer, two clocks that read the same time in one frame are not necessarily simultaneous for another. Two observers in different gravitational fields who synchronize their clocks at the same moment will find that their clocks differ after a period of time with no error on either clock's part purely because of the difference in the geometry of the time dimension at their respective positions.
Time is not one thing. It is many things, as many things as there are positions in the gravitational field of the universe. Each with its own specific local rate, each related to the others by the specific equations of general relativity that describe the curved space-time geometry. 1 hour equals 7 years. That sentence is not a paradox.
It is not a contradiction. It is the specific quantitative expression of a profound truth about the universe that the structure of time is local geometric and determined by the distribution of mass and energy in the spaceime that we inhabit. Einstein's gift to physics was not just a set of equations. It was a new way of understanding what space and time are not fixed universal absolute quantities but dynamic local geometric relationships that are shaped by the content of the universe they describe.
And near a black hole near a region where mass is concentrated into such extreme density that the curvature of spaceime becomes extreme. This dynamical local nature of time expresses itself in the most dramatic most viscerally comprehensible way available in the physical universe. In part three, I want to bring everything together into the complete picture of what time dilation near black holes means for the future of black hole science, for the specific program of observations that will test the strong field predictions of general relativity in the coming decade and for what I think is the most profound and most personally significant implication of the entire story. what it means that the universe contains regions where time passes at radically different rates. And what this tells us about the specific nature of time, of experience, and of what it means to exist in a universe where the geometry of spaceime is not fixed but dynamic. 1 hour equals 7 years. The physics is confirmed. The implications are extraordinary and the story is not finished. So we had arrived at this place where gravitational time dilation near a black hole is not a theoretical curiosity but a confirmed measured daily exploited physical reality confirmed in binary pulsar timing built into GPS correction algorithms directly visible in the asymmetric photon ring brightness of the EHT images of M87 times and Sagittarius A and approaching direct measurement through the timing of stars in tight orbits around the galactic center black hole where the specific ratio 1 hour equals 7 years emerges from the correct application of the curt metric to a near maximally rotating super mass of black hole physics that is not approximation but precise quantitative calculation.
And where the deepest implication of gravitational time dilation is a profound revision of what time itself is not a universal background against which events occur, but a local geometric dynamical property of curved spacetime that varies with position in a gravitational field. Now I want to bring it all the way home to ask what the next decade of black hole science will reveal about strong field time dilation and the specific geometry of real rotating black holes. to address the specific philosophical implications of living in a universe where time is not universal.
What it means for how we think about experience, consciousness, and the long-term trajectory of intelligent life. And to close with what I think is the most profound and most personally significant thing that the one hour equals 7 years story tells us not about black holes specifically but about the specific nature of the universe we inhabit and our relationship to it. Let me start with the future of the science.
The event horizon telescope's first images of M87 times and Sagittarius A times were extraordinary achievements, but they were in an important sense the beginning of a program rather than its culmination. The specific angular resolution of the current EHT approximately 20 microarchse seconds achieved by combining observations from eight telescope stations across the globe is sufficient to resolve the photon ring and shadow of the two nearest super massive black holes accessible from Earth. But it is not sufficient to resolve the internal structure of the photon ring. the specific multiple ring components produced by light that has orbited the black hole different numbers of times whose detailed morphology would provide the most precise tests of the current metric available from imaging. The next generation EHT NGHT is currently in the design and planning phase. It will add new telescope stations to the global network increasing the baseline coverage and the effective aperture. More critically, it will add new observing frequencies, higher frequency observations that provide higher angular resolution and better characterize the specific plasma physics of the accretion disc, separating the geometric effects of the curved spaceime from the astrophysical effects of the emitting material. The specific scientific goal of the NGHT that is most directly relevant to the time dilation physics is the resolution of the photon ring substructure. The photon ring consists of a specific series of exponentially narrowing rings each produced by light that has completed one more half orbit around the black hole before escaping.
The outermost ring is the n equals one ring light that has gone halfway around the hole. The next is n equals 2 light that has gone all the way around and so on with each successive ring exponentially narrower and exponentially brighter than the next. The specific radi widths and brightness ratios of these photon sub rings are determined entirely by the mass and spin of the black hole. They are pure signatures of the curr geometry with no dependence on the specific astrophysical properties of the emitting plasma. Resolving and characterizing these sub rings would provide the most precise test of the curmetric and therefore of the specific time dilation geometry near the event horizon ever achieved. The NGHT is projected to have sufficient resolution to detect the N equals 1 photon ring of M87 times directly and potentially to characterize the N=2 ring. If the curric is correct, if real super massive black holes are described by the mathematics of general relativity, the photon subring structure will match the prediction precisely. Any deviation would be a specific signal of physics beyond general relativity of modified gravity theories of exotic compact objects or of new physics at the event horizon scale. Let me tell you about the specific program of space-based gravitational wave detection LISA and how its observations will test strong field time dilation in the most extreme environments accessible. We've discussed LISA in previous conversations. The laser interferometer space antenna scheduled for launch in the mid 2030s.
LISA will detect gravitational waves at millhertz frequencies. The specific range produced by super massive black hole mergers and extreme mass ratio in spirals. The extreme mass ratio inspiral emery is a specific class of gravitational wave source that provides the most precise test of the cur metric accessible to LISA. An emery occurs when a compact object, a stellar mass black hole, a neutron star, or a white dwarf, spirals into a super massive black hole through the gradual emission of gravitational radiation. The inspiral is extraordinarily slow. The compact object completes hundreds of thousands to millions of orbits around the super massive black hole before finally crossing the horizon. Each orbit traces a specific path through the curved cur space spacetime and the specific pattern of the resulting gravitational wave signal encodes the precise geometry of that spacetime. The specific reason EMRI are such powerful probes of the cur geometry is the accumulation of phase over hundreds of thousands of orbits.
The specific gravitational wave phase accumulated by the inspiral is extraordinarily sensitive to the precise details of the spaceime through which the orbit is tracing. A small deviation from the cur metric. Any modification to the geometry of the strong field region would accumulate over those hundreds of thousands of orbits into a phase shift that is detectable by LISA's extraordinary sensitivity. The time dilation physics is directly embedded in the emery signal. The specific rate at which the inspiral accumulates gravitational wave phase depends on the specific orbital dynamics in the cur space spacetime including the specific frame dragging, the specific radial and azimuthal orbital frequencies and the specific energy and angular momentum loss rates from gravitational wave emission. All of these are determined by the cur metric and all of them reflect the specific time dilation geometry at each point along the orbit. LISA will detect hundreds to thousands of Emery events over its nominal mission lifetime. Each one is a specific probe of the KUR geometry in the strongfield regime. The accumulated data set will provide tests of general relativity near black holes at a precision that no other observational technique can approach and will either confirm the curmetric as the correct description of astrophysical black holes or reveal specific deviations that would indicate new physics at the event horizon scale. Let me now address the philosophical implications of time dilation and specifically the question of what the relativity of time means for how we should think about the nature of experience and consciousness in the universe. The standard picture of consciousness, the picture implicit in most philosophical discussions of mind and experience assumes that experience occurs in time. That consciousness is a process, a sequence of mental states connected by causal and temporal relationships.
That the richness and completeness of a conscious life is measured at some level by the duration of experience by how much time the conscious being has to think, perceive, feel, and understand.
Gravitational time dilation disrupts this picture in a specific and profound way. If time is not universal, if the rate at which time passes is a local geometric property of the spaceime in which a conscious being is embedded, then the duration of conscious experience is not a property of a being's physical situation in the cosmos. It is a property of their position in the gravitational field. Two beings born at the same cosmic moment in the same galaxy in the same epic of the universe's history can experience radically different amounts of subjective time before death simply by occupying different positions in the gravitational structure of the cosmos.
The being orbiting near the event horizon of a massive rotating black hole experiences in one hour of local time the subjective richness of one hour of experience, one hour of thought, of sensation, of conscious engagement with the world. But in that same hour, seven years pass for beings far from the black hole. Who has experienced more? The question seems simple. The being far from the black hole has lived seven years of conscious experience to the first beings. 1 hour. But from the perspective of the being near the black hole, their one hour is complete. They have thought all their thoughts for that hour. Experienced all their sensations engage with their environment for 60 minutes. The seven years and the 1 hour are both genuine complete intervals of conscious experience just in geometrically different regions of spaceime. This is not a paradox. in the logical sense but it is a profound challenge to the intuitive picture of experience as something that occurs in a single universal time. The universe does not have a universal time. It has a collection of local times each determined by the local geometry of spaceime each equally valid each representing genuine experience for the conscious beings embedded in that local geometry. What this means for the value and significance of conscious experience is deeply challenging to articulate. If experience is local, if it occurs in local time, not universal time, then the comparison between the experiences of beings in different gravitational environments is in some deep sense incommensurable.
Not because we lack the right measuring rod, because there is no single measuring rod. The geometry of time is not global. It is local. And local time is all there is. Let me now tell you about something that connects the time dilation story to the specific question of intelligence and civilization in the long-term future of the cosmos. We've established in previous conversations the existential risk discussion, the rare earth discussion, that the long-term future of intelligence in the universe is genuinely uncertain. The specific risks to civilizational continuity are real and not negligible.
The eventual thermodynamic evolution of the universe toward heat death is an astronomical time scale reality. The question of how intelligent life can persist and flourish in the face of these challenges is one of the deepest questions in the philosophy of the cosmos. Time dilation near black holes offers a specific and extraordinary perspective on this question. The universe's thermodynamic evolution, the gradual increase of entropy toward the heat death, unfolds on a specific cosmological time scale. The last stars will burn out in approximately 104 years. The last black holes will evaporate through Hawking radiation in approximately 10 67 to 10 100 years. On these time scales, the universe becomes progressively more hostile to the specific organized structures that support complex chemistry and biology.
But these time scales are measured in coordinate time. The time far from any massive object in the low density nearly flat spacetime of the intergalactic medium. Near a massive rotating black hole, the relationship between local time and coordinate time is precisely what gravitational time dilation quantifies. A civilization orbiting close to the event horizon of a near maximally rotating black hole would experience dramatically more local time for each unit of coordinate time than a civilization in the intergalactic medium. For a time dilation factor of 61,320, the specific interstellar ratio, the 1014 coordinate years before the last stars burn out, corresponds to 61,320 * 1014 years of local time, approximately 6 * 10, 18 years of subjective time. The heat death that would occur in 10 14 coordinate years would from the perspective of the time dilated civilization be six quintilion years in the subjective future. This is not a solution to the eventual heat death of the universe. It merely postpones the local experience of it dramatically and it requires solving the specific engineering challenges of living near a black hole. The radiation environment, the accretion disc hazards, the specific gravitational and tidal dynamics. These challenges are formidable beyond any current technological capability. But the specific physics of time dilation means that the universe's thermodynamic horizon, the specific coordinate time before the cosmos becomes inhospitable is not the universal horizon for the experience of intelligent life. For being sufficiently advanced to exploit the time dilation near black holes, the subjective future available to them is vastly longer than the coordinate future suggests.
The universe's geometry is in this specific sense more hospitable to the long-term persistence of conscious experience than the simple cosmological time scales imply. Not because the laws of thermodynamics are violated. They are not. But because the relationship between coordinate time and local time is determined by the local geometry of spaceime. And the specific regions of spacetime near massive rotating black holes have a geometry that provides an extraordinary leverage of subjective time over coordinate time. Let me now address the specific question that I think is most important for understanding the personal significance of time dilation. The question of what it means for individual human experience that time is not universal. In everyday life, we never notice time dilation. The difference in clock rates between the floor and the ceiling of a room is phento seconds per day. The difference between sea level and the top of Mount Everest is approximately 30 microsconds per day. The difference between Earth's surface and GPS satellite orbit is 45 micros per day. These differences are real. They are measured. They are exploited. They matter for precision technology, but they are completely imperceptible to human experience. We live in a world where for all practical experiential purposes, time is universal. Everyone we know ages at the same rate. Everyone shares the same. Now the relativity of simultaneity and the differential flow of time that general relativity describes are in the human scale world irrelevant to experience.
But knowing that they are true, knowing that the specific intuition of universal time is wrong, that time is genuinely physically local changes something about how we understand ourselves and our universe. It means that the universe is stranger than we think. Not metaphorically stranger, specifically physically stranger. The fabric of reality, the specific geometric structure that underlies all of our experience is not what our intuition suggest. It is curved, dynamic, locally variable, and profoundly different in its structure near massive objects from what it is in the empty space of our everyday experience. We are fortunate in a specific sense to live in a region of the universe where time is nearly uniform, where the gravitational potential varies little enough over the scales of human experience that the differential flow of time is imperceptible. We exist in the specific regime of weak field slow motion gravity where Newtonian mechanics and the intuition of universal time are excellent approximations to the underlying general relativistic reality.
But we also live in a universe where that approximation breaks down spectacularly, dramatically, and beautifully near the most extreme objects the laws of physics allow. Near a black hole spinning at 99.8% of maximum with a mass of 100 million solar masses, 1 hour truly does equal 7 years.
The approximation of universal time doesn't just break down. it fails by a factor of 61,320.
Knowing this, understanding the specific physics that produces this ratio, the specific geometry of the cur metric, the specific equivalence principle argument that connects gravity and time, the specific experimental confirmations from GPS and pulsars, and the EHT is one of the most profound intellectual experiences available to a human being.
It is the specific experience of learning that the universe is genuinely different from what common sense would predict. That the intuitions shaped by evolution for survival in the weak field slow motion world of everyday experience are specifically dramatically quantifiably wrong in the strong field regime. This is what great physics does.
It reveals the specific strangeness of reality that is hidden behind the veil of ordinary experience. And it does so not through vague mysticism or poetic metaphor, but through specific quantitative experimentally confirmed mathematics.
Let me close with the most important and most personally significant thing that the one hour equals 7 years story tells us. Not about black holes specifically, but about the universe and our relationship to it. Throughout this series, we've been building a picture of a universe that is more complex, more surprising, and more deeply structured than everyday experience suggests. The gravitational wave background pervading all of space. The pre- Big bang information encoded in the CMBB anomalies. The hidden planet sculpting the outer solar system. The local bubble creating the stars being born around us.
The Mars subsurface anomalies pointing towards something unexplained. The magnetic field weakening in a pattern that resembles reversal onset. At every scale, in every domain, the same discovery reality extends further, is more surprising, and is more fundamentally different from the simplified models than the previous generation of understanding anticipated.
The black hole time dilation story is the most dramatic version of this discovery. At the most fundamental level, the level of what space and time themselves are. The universe contains regions where time passes at radically different rates. Not because of exotic, untestable, speculative physics, but because of the specific confirmed GPS calibrated, pulsar timed EHTimaged physics of curved spaceime that has been tested to exquisite precision across a century of experimental and observational verification. The universe we live in is not the universe of common sense. It is the universe of general relativity, a fourdimensional curved spaceime whose geometry is determined by the distribution of mass and energy whose temporal structure varies with position and whose most extreme regions near black holes produce effects that are not just quantitatively different from everyday experience but qualitatively fundamentally different in the structure of time itself. 1 hour equals 7 years. This sentence is not just about the specific physics of a specific curved black hole at a specific spin parameter with a specific mass. It is about the specific nature of time in the universe we inhabit. About the fact that time is local, geometric, and dynamic. And that the specific geometry of space-time near extreme objects produces ratios between local times that are not just large but spectacularly dramatically existentially large. Seven years of one person's life, seven years of experience, of aging, of relationships, of history, compressed into one hour of another person's experience. Not through magic, not through science fiction, through the specific curvature of the four-dimensional geometry of spacetime as described by the field equations of general relativity confirmed by a century of experimental verification directly imaged by the event horizon telescope. The universe made this possible. The specific laws of physics, not chosen by any designer, not selected for any purpose, permit the existence of rotating black holes whose near horizon geometry produces extreme time dilation.
And the specific universe we inhabit has produced these objects in every massive galaxy in the centers of galaxy clusters in the remnants of the most massive stars. Super massive rotating black holes are not exotic theoretical possibilities.
They are the specific observed imaged gravitational wave detected X-ray luminous centers of the most massive galaxies in the observable universe. The time dilation is happening right now in M8755 million lighty years away. gas orbiting the photon ring of the 65 billion solar mass spinning black hole is experiencing time at a dramatically different rate from the distant stars of the host galaxy in Sagittarius a * 26,000 lighty years away at the center of our own galaxy the hot flares of gas orbiting the four million solar mass black hole are experiencing time at rates that differ dramatically from the rate experienced by the stars of the Milky Ways disc. And here we are on the surface of a rocky planet orbiting a middle-aged star in the outer arm of a spiral galaxy in the specific region of spaceime where the gravitational potential is low enough and the curvature gentle enough that our intuition of universal time is an excellent approximation.
able to look out at a universe where that intuition fails spectacularly and able to understand through the specific mathematics of general relativity through the specific measurements of atomic clocks and binary pulsars and the event horizon telescope exactly how and why it fails. This understanding, this specific, quantitative, physically precise understanding of the structure of time in the universe is one of the most extraordinary things our species has achieved. Not because it has practical consequences for everyday life. It doesn't. Not directly because it is true. Because the universe is genuinely, specifically, quantifiably this strange. Because the intuitions that evolution shape for survival in the Newtonian world of ordinary gravity are wrong. Precisely wrong, quantifiably wrong. Wrong by a factor of 61,320 in the most extreme accessible case. And because human mathematics and human observation and human experimental precision have been sufficient to discover how wrong they are and to calculate the specific correct answer. 1 hour equals 7 years. That sentence is a specific quantitative measure of how different the universe is from common sense. How much richer, how much stranger, how much more deeply structured the reality we inhabit is than the reality our intuitions construct. The universe made time local, made it geometric, made it extreme, near massive rotating objects, made it so different from our everyday experience that the difference can be expressed as a ratio of 61,320 to1 and made it so that this extraordinary fact is not speculative, not theoretical, not a feature of models that might be wrong, but a direct consequence of the most precise precisely tested physical theory in the history of science confirmed in every regime accessible to current technology. That is what 1 hour equals 7 years means. Not Hollywood, not metaphor, not approximation. The universe telling us what it is through the specific language of curved spaceime and rotating black holes and the geometry of time. And we for the first time in the history of our species are listening carefully enough to hear what it's saying. The story is real. The physics is confirmed. And the universe is exactly as strange as the mathematics says.
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