Can Standing Still Make Time Pass Faster Than the Speed of Light?

[abbott287]

It seems if one could travel at the speed of light, they would never age. Time stops. So if someone wants to slow down the aging process, say compared to their friends, they need to take a trip as close to the speed of light as possible. Contrary to that, many young children can't wait to get older. Does standing as still as possible make time pass the fastest, or is their a way to make someone age even quicker. Not sure how to state this, but is there something opposite the speed of light that would make one age instantly, or is standing perfectly still the fastest time can pass? Thanks for any help on another dumb question that interests me.

 

[bcrowell]

You can travel to a cosmological void, where the gravitational potential is higher than on Earth's surface. Due to gravitational time dilation you'll age somewhat more quickly, but I don't think the effect will be very large.

If closed timelike curves existed in our universe, you could age yourself as rapidly as you liked. But CTCs probably don't exist in our universe.

There is the question of whether there is some fundamental limit on the speed-up, and the thing about CTCs probably indicates that the answer depends on the cosmological structure of our universe. This may be related to the question of whether it is possible to perform an infinite computation, which is discussed in these references:

Baez, J., 2004, "The End of the Universe.", http://math.ucr.edu/home/baez/end.html

Dyson, Time without end: Physics and biology in an open universe, Reviews of Modern Physics 51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447.

Krauss and Starkman, 1999, Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, http://arxiv.org/abs/astro-ph/9902189

Katherine Freese and William Kinney, 2002, The ultimate fate of life in an accelerating universe, http://www.arxiv.org/abs/astro-ph/0205279

 

[ghwellsjr]

I thought that the higher the gravitational potential, the slower you would age. I thought that if you were "standing still", you were in a gravitational potential. I thought if you got to a place where there was no gravity, ie, you were in free fall and therefore unable to "stand still" you would be aging at the maximum rate, relative to your friend back here on earth. But of course the difference is miniscule.

Did I get this all wrong?

 

[yuiop]

I thought that the higher the gravitational potential, the slower you would age.

No, it the other way around. A person on top of a very tall tower on the Earth's surface ages faster than a person in a deep mine.

I thought that if you were "standing still", you were in a gravitational potential.

Standing still is not the definition of being in a gravitational potential, but if you are standing still on the surface of a gravitational body like the Earth, then you are subject to constant proper acceleration (as measured by your bathroom scales) so you would be ageing slower than someone in freefall or moving inertially in deep space.

I thought if you got to a place where there was no gravity, ie, you were in free fall and therefore unable to "stand still" you would be aging at the maximum rate, relative to your friend back here on earth. But of course the difference is miniscule.

Did I get this all wrong?

This last bit is sort of correct. As long as you are not moving relative to your friend on the surface of the Earth and as long as you are subject to zero proper acceleration then you would be be ageing faster than your friend.

So all else being equal, if you attach accelerometers to two people, the one experiencing the least acceleration ages the most. While you are sitting at a desk reading this you are usually subject to 9.8m/s^2g of acceleration.

 

[Quinzio]

Without considering gravitational fields, the best you can do to age faster is avoiding to accelerate. That seems not difficult to achieve.
This not the same as "standing still" because you could as well be moving at any speed you like, even close to c, but you don't have to accelerate.
But you cannot age faster than that because there is always the speed limit c.

You can even consider gravitational fields, with the knowledge that standing still on the Earth surface is being accelerated at 9,8m/s2, while not accelerating means free falling.
The exact opposite of common experience.

This is always only valid in your RF.
Given you don't accelerate, you are the fastest aging object in your RF.

 

[Matterwave]

Riding on a satellite in freefall orbit should make you age faster than people standing still on Earth. The amount, though...would probably be on the order of a few seconds over the course of a natural life-time (just my gut instinct on the size of the effect for Earth).

 

[pervect]

Jumping up and down will help :-)

Specifically, you want to move to a region of higher potential (away from massive bodies), without moving too quickly (to avoid relativistic time dilation).

The path that accomplishes this will be a geodesic path. This was a question Feynman used to ask graduate students in GR to test their saavy.

However, the effects of being in orbit aren't the optimal path to take - you're better off not orbiting, but getting as far away as you can.

Ideally you'd jump up and "coast" into interstellar space, then land down right where you started. Depending on how much time you had, you'd want to optimize your jump to avoid the Earth's closeness (for small jumps), the Sun's closeness (for longer jumps), and eventually for really long jumps you'd be worrying about the galaxy's gravity, or the local cluster of galaxy's gravity, or the local supercluster - if you could live that long, which is rather unlikely.

 

[GrayGhost]

No, it the other way around. A person on top of a very tall tower on the Earth's surface ages faster than a person in a deep mine.

In GR, is the rate of time related to the gradient or the potential? I'm assuming the potential. So it's not the force of gravity that matters, but the depth in the well, yes? A lower depth in the well is considered a lower gravitational potential, yes?

GrayGhost

 

[ghwellsjr]

I thought that the higher the gravitational potential, the slower you would age.

No, it the other way around. A person on top of a very tall tower on the Earth's surface ages faster than a person in a deep mine.

Specifically, you want to move to a region of higher potential (away from massive bodies)...

So a higher gravitational potential means less gravity? That seems backwards, what am I missing?

 

[yuiop]

So a higher gravitational potential means less gravity? That seems backwards, what am I missing?

Higher gravitational potential is linked to higher potential energy which has the potential to be converted to kinetic energy. Things generally move from high potential to low potential like a ball rolling down a hill goes from high to low. In Newtonian physics if you have an object at a given height (potential) and drop the object, it accelerates because potential energy is being converted to kinetic energy. Lower down the additional kinetic energy is compensated for the by the reduced potential energy of the object, preserving the conservation of energy principle.

 

[yuiop]

In GR, is the rate of time related to the gradient or the potential? I'm assuming the potential. So it's not the force of gravity that matters, but the depth in the well, yes? A lower depth in the well is considered a lower gravitational potential, yes?

Yes to the last question and yes, time dilation is a function of gravitational potential rather than gradient.

 

[yuiop]

Riding on a satellite in freefall orbit should make you age faster than people standing still on Earth. The amount, though...would probably be on the order of a few seconds over the course of a natural life-time (just my gut instinct on the size of the effect for Earth).

That depends on the radius of the satellite orbit. I will quote bcrowell here from an old thread:

For satellites in low Earth orbit (which includes almost all crewed activity), the kinematic effect dominates. But for satellites in higher orbits (e.g., GPS and geosynchronous satellites), the gravitational effect dominates.

See https://www.physicsforums.com/showthread.php?t=507230

So a person in low Earth orbit ages less than a person on the surface of the Earth and a person in high Earth orbit ages faster than a person on the surface.

 

[GrayGhost]

So a higher gravitational potential means less gravity? That seems backwards, what am I missing?

Imagine a hollow sphere. A gravity well surrounds it which attracts bodies toward it. One can imagine the slope (gradient) of the well increasing as one approaches the surface of the sphere. The higher the slope, the higher the G force. Inside the hollow sphere, the gravitational gradient becomes flat, and so there is no attraction at all. The gravitational potential is the lowest here, and is the same everywhere. You'd float freely w/o accelerating.

Inside a solid sphere such as the earth, the slope of the well begins decreasing once inside the outer surface of the sphere (so less G force), and at the center of gravity the slope is zero (0-G). The gravitational potential is at its lowest at the center of gravity. No G-force there, but the potential is (I think) at its lowest point there ... which (I think) means time is the slowest.

We'll see what the experts say.

GrayGhost

 

[yuiop]

Imagine a hollow sphere. A gravity well surrounds it which attracts bodies toward it. One can imagine the slope (gradient) of the well increasing as one approaches the surface of the sphere. The higher the slope, the higher the G force. Inside the hollow sphere, the gravitational potential is flat, and so there is no attraction at all. You'd float freely w/o accelerating. Inside a solid sphere such as the earth, the slope of the well decreases once inside the outer surface of the sphere (so less G force), and at the center the slope is zero (0-G). The gravitational potential is flat at the center of gravity, if using flat spacetime locally as the reference. No G-force there, but the potential is (I think) at its lowest point there ... which (I think) means time is the slowest. We'll see the experts say.

GrayGhost

I am by no means an expert, but that I believe is essentially correct. It does however demonstrate that what I said earlier about the person experiencing the least proper acceleration ages the most is not always true, if we are talking about the interior of solid or hollow gravitational masses.

 

[GrayGhost]

I am by no means an expert, but that I believe is essentially correct. It does however demonstrate that what I said earlier about the person experiencing the least proper acceleration ages the most is not always true, if we are talking about the interior of solid or hollow gravitational masses.

OK, thanx. I did screw up the wording a little bit though. I've reworded the post since you saw it.

GrayGhost

 

[ghwellsjr]

Higher gravitational potential is linked to higher potential energy which has the potential to be converted to kinetic energy. Things generally move from high potential to low potential like a ball rolling down a hill goes from high to low. In Newtonian physics if you have an object at a given height (potential) and drop the object, it accelerates because potential energy is being converted to kinetic energy. Lower down the additional kinetic energy is compensated for the by the reduced potential energy of the object, preserving the conservation of energy principle.

But when we are talking about potentials, aren't we always talking about potential difference between two points? So doesn't this mean that in the absence of gravity or as pervect said, "away from massive bodies", there really is no number we can associate with this condition. Can't we call this gravitational potential zero if we want and as we move toward any massive body the gravitational potential is more negative?

Or to put it another way, if we start on the survace of Earth and move far away from massive bodies we will get one value for the gravitational potential but if we started on the surface of Jupiter and moved to the same place away from massive bodies we would get a larger value for the gravitational potential?

 

[Mike_Fontenot]

[...]
Does standing as still as possible make time pass the fastest, or is their a way to make someone age even quicker. Not sure how to state this, but is there something opposite the speed of light that would make one age instantly, or is standing perfectly still the fastest time can pass?
[...]

First of all, think about what EXACTLY you mean by someone's "rate of ageing". You will probably be able to see that the phrase, without further qualification, actually has NO meaning at all.

There's no way that any particular person can perceive his own rate of ageing as anything other than what it IS. It's somewhat analogous to a computer "perceiving" the passage of time only as how many cpu cycles have occurred since some previous "incident" ... if the computer's clock is slowed down, there's no way for the computer to "perceive" that occurred. Or, another analogy is that, to a surgical patient on an operating table, there is NO perceived time between when he loses consciousness from the anesthesia and when he wakes up.

The ONLY way the phrase "the rate of someone's ageing" has any meaning is when his ageing is compared with someone else's ageing. There IS meaning to the question, "Is person A ageing faster than person B, at some given instant in person A's life?". But, in special relativity, there is NOT just one answer to that question ... person A will generally come to a different conclusion about the answer to that question than person B will. And they are BOTH correct.

Once you have asked the question properly, the answer is that, according to person A, it is possible for person B to be ageing at an arbitrarily greater rate, or at an arbitrarily lesser rate, then person A. It is even possible for person A to conclude that person B is getting YOUNGER at an arbitrarily large rate, as person A is getting older.

If you want to pursue these issues further, I recommend that you start with these links:

https://www.physicsforums.com/showpost.php?p=2934906&postcount=7

https://www.physicsforums.com/showpost.php?p=2923277&postcount=1

Mike Fontenot

 

[bcrowell]

I am by no means an expert, but that I believe is essentially correct. It does however demonstrate that what I said earlier about the person experiencing the least proper acceleration ages the most is not always true, if we are talking about the interior of solid or hollow gravitational masses.

A free-falling world-line has extremal aging compared to world-lines that differ from it infinitesimally and that start and end at the same events P and Q. Extremal doesn't necessarily mean maximal. It could be a minimum or a saddle point. Even if it is a maximum, it's not necessarily a global maximum. I think the world-line of someone floating weightless at the center of the Earth has locally maximal aging, but not globally maximal aging.

But when we are talking about potentials, aren't we always talking about potential difference between two points? So doesn't this mean that in the absence of gravity or as pervect said, "away from massive bodies", there really is no number we can associate with this condition. Can't we call this gravitational potential zero if we want and as we move toward any massive body the gravitational potential is more negative?

Or to put it another way, if we start on the survace of Earth and move far away from massive bodies we will get one value for the gravitational potential but if we started on the surface of Jupiter and moved to the same place away from massive bodies we would get a larger value for the gravitational potential?

It's the same as in Newtonian mechanics. Yes, gravitational potentials are only defined up to an additive constant. The gravitational time-dilation ratio relates to the difference in gravitational potential.

The ONLY way the phrase "the rate of someone's ageing" has any meaning is when his ageing is compared with someone else's ageing. There IS meaning to the question, "Is person A ageing faster than person B, at some given instant in person A's life?". But, in special relativity, there is NOT just one answer to that question ... person A will generally come to a different conclusion about the answer to that question than person B will. And they are BOTH correct.

This is partly right and partly wrong. You're right that the question is meaningless unless you pose it correctly. I would distinguish three cases:

(1) In a general, non-static spacetime, the only well-defined comparison is to compare the proper time along two world-lines A and B, each of which starts at the same event P and each of which ends at the same event Q. If you pose the question in this way, then there is always a well-defined answer; A and B will not come to different conclusions.

(2) In a static spacetime with no additional symmetries beyond staticity (i.e., no additional Killing vectors besides the timelike one), there is a preferred rest frame at any given point. For example, in a Schwarzschild spacetime, the preferred rest frame is the one at rest relative to the source of the field. In this case, the gravitational potential is well defined, and there is a sensible way of defining a gravitational time dilation factor, without worrying about the technicalities referred to in #1. For example, the Pound-Rebka experiment http://en.wikipedia.org/wiki/Pound–Rebka_experiment measured the gravitational time dilation between the top and bottom of a tower in this way.

(3) In SR, which you were referring to, the spacetime is static, but there are additional symmetries beyond staticity, and therefore there is no preferred rest frame. The only meaningful comparison is the kind described in #1. You get maximal aging by not accelerating, and there is no meaningful way of making comparisons except when observers A and B are reunited at event Q.

It is even possible for person A to conclude that person B is getting YOUNGER at an arbitrarily large rate, as person A is getting older.

In SR, it's only meaningful to compare proper times for world-lines that intersect at P and Q. With that restriction, you don't get results like this.

 

[PAllen]

A further comment on orbiting versus sitting on the ground. As noted in an earlier post, there is kinematic effect of orbital speed versus the gravitational potential difference. However (even ignoring comparison to sitting on the ground), the reason that an orbit is not necessarily the 'fastest aging between two given spacetime points' is because there is a family of geodesics between these points. The global maximum aging rate is for the most extremal of this family of geodesics. That one (assuming only one massive body in the universe) is always the free fall path going radially outword and falling back.

Thus, if your chosen events are one orbit apart in time, then radial free fall path that meets after one orbit will be the globally maximum aging between those events. If you consider events two orbits apart in time, then there is a longer radial path that will be at its furthest position after one orbit, meeting up after two orbits, etc.

In general, in GR, in physically plausible situations, you have to specify two specific events, and then state there exists a most extremal geodesic between them that constitutes the global maximum age between them. Further, for any other geodesic, there are non-inertial paths that age faster than one of the other geodesics that are only locally extremal (meaning faster than small perturbations of the path).

 

[yuiop]

But when we are talking about potentials, aren't we always talking about potential difference between two points? So doesn't this mean that in the absence of gravity or as pervect said, "away from massive bodies", there really is no number we can associate with this condition. Can't we call this gravitational potential zero if we want and as we move toward any massive body the gravitational potential is more negative?

Yes, you can do that and people often do, but the higher point still has the greatest potential and least gravitational time dilation.

 

[ZealScience]

I think on contrary to twin paradox, you could accelerate Earth away from you and accelerate it back. What I am thinking is that taking the Earth as the non inertial reference frame, then the proper time of the Earth increases, so it comes back with people younger than you are.

 

[ZealScience]

Probably move the Earth close to the black hole, where using metric with coefficient of (1-2MG/c^2R) on time term, so that it would be dialated as R gets smaller.

 

[PAllen]

I think on contrary to twin paradox, you could accelerate Earth away from you and accelerate it back. What I am thinking is that taking the Earth as the non inertial reference frame, then the proper time of the Earth increases, so it comes back with people younger than you are.

Probably move the Earth close to the black hole, where using metric with coefficient of (1-2MG/c^2R) on time term, so that it would be dialated as R gets smaller.

I think the first option would be kinder. Of course, if you want to age faster than everything in the universe, you have more of a challenge (assuming moving the Earth is trivial )

 

[GrayGhost]

It is even possible for person A to conclude that person B is getting YOUNGER at an arbitrarily large rate, as person A is getting older.

B is getting YOUNGER at an arbitrarily large rate, equates to ... B living his life in reverse. Of course, none of this happens from B's own POV who always ages normally with time passing by at normal proper rate.

EDIT: Not that I disagree with what you say here :)

GrayGhost

 

[abbott287]

First of all, think about what EXACTLY you mean by someone's "rate of ageing". You will probably be able to see that the phrase, without further qualification, actually has NO meaning at all.

There's no way that any particular person can perceive his own rate of ageing as anything other than what it IS. It's somewhat analogous to a computer "perceiving" the passage of time only as how many cpu cycles have occurred since some previous "incident" ... if the computer's clock is slowed down, there's no way for the computer to "perceive" that occurred. Or, another analogy is that, to a surgical patient on an operating table, there is NO perceived time between when he loses consciousness from the anesthesia and when he wakes up.

The ONLY way the phrase "the rate of someone's ageing" has any meaning is when his ageing is compared with someone else's ageing. There IS meaning to the question, "Is person A ageing faster than person B, at some given instant in person A's life?". But, in special relativity, there is NOT just one answer to that question ... person A will generally come to a different conclusion about the answer to that question than person B will. And they are BOTH correct.

Once you have asked the question properly, the answer is that, according to person A, it is possible for person B to be ageing at an arbitrarily greater rate, or at an arbitrarily lesser rate, then person A. It is even possible for person A to conclude that person B is getting YOUNGER at an arbitrarily large rate, as person A is getting older.

If you want to pursue these issues further, I recommend that you start with these links:

https://www.physicsforums.com/showpost.php?p=2934906&postcount=7

https://www.physicsforums.com/showpost.php?p=2923277&postcount=1

Mike Fontenot

Sorry I was not more specific, and I see your point! Thanks for putting it into perspective. I think others understood what I was trying to say, as I am getting the answers I was seeking from so many great posts. I guess I should have stated it "aging in respect to a twin here on earth".

On a side note, and not to derail the thread, but around 15 years ago I saw a show (60 minutes maybe?) discussing a medical breakthrough on aging, which came about by studying people who are born with that horrible disease that makes them age far faster than normal. Supposedly they were close to a cure, and were going to be able to slow down the rate of ageing on everyone by 50% or so. Anyone know what ever happened?? I could go for a few of those tablets myself. :)

 

[Mike_Fontenot]

[...]
I guess I should have stated it "aging in respect to a twin here on earth".
[...]

To make the question more precise, you could ask "What is the quotient of the increase in the (inertial) home twin's age, divided by a tiny increase in the traveler's age, at some specified instant of the traveler's life?".

But you STILL have to qualify the question further, in order to get one and only one answer. Different observers will generally get different answers to the above question.

IF you further state that you want the answer to the above question, to be the answer that the HOME TWIN would get, then the answer is that the ratio will always be greater than or equal to one (and it can be arbitrarily large). The ratio would be given by the factor "gamma" that occurs in the time-dilation result.

BUT, if INSTEAD you state that you want the answer to the above question, to be the answer that the TRAVELER would get, then the answer is that the ratio can be arbitrarily greater than one, or equal to one, or arbitrarily smaller than one (including the case where the ratio can be NEGATIVE ... i.e, the home twin can be getting YOUNGER as the traveler gets older). Which of all these possibilities you get, is determined by the magnitude and direction of the traveler's acceleration, and also by the amount of their separation.

Mike Fontenot

 

[abbott287]

To make the question more precise, you could ask "What is the quotient of the increase in the (inertial) home twin's age, divided by a tiny increase in the traveler's age, at some specified instant of the traveler's life?".

But you STILL have to qualify the question further, in order to get one and only one answer. Different observers will generally get different answers to the above question.

IF you further state that you want the answer to the above question, to be the answer that the HOME TWIN would get, then the answer is that the ratio will always be greater than or equal to one (and it can be arbitrarily large). The ratio would be given by the factor "gamma" that occurs in the time-dilation result.

BUT, if INSTEAD you state that you want the answer to the above question, to be the answer that the TRAVELER would get, then the answer is that the ratio can be arbitrarily greater than one, or equal to one, or arbitrarily smaller than one (including the case where the ratio can be NEGATIVE ... i.e, the home twin can be getting YOUNGER as the traveler gets older). Which of all these possibilities you get, is determined by the magnitude and direction of the traveler's acceleration, and also by the amount of their separation.

Mike Fontenot

Let me try again then! Two twins are standing on earth. They are very young, and one really wants to grow older faster than his brother, so he can be "bigger and beat him up". In a years time, (or you can pick any time frame if it helps) what can he do to age as fast as possible so that upon his return to earth, (if in fact he has to leave for maximum ageing rate) he has aged as much as possible in the allowed time span compared to his brother. So at the end, it would be in BOTH of their reference frames, just as a person taking a trip at light speed and coming back is younger than his twin who stayed on earth. Maybe there is a way he could age at an infinite rate compared to the twin on earth? (In which case he would be dust upon his return!)

 

[Mike_Fontenot]

If the twins are initially co-located, and the home twin always remains inertial, and the traveler eventually returns so that the twins are again co-located, then the twin who accelerated will ALWAYS (in special relativity) be younger than his twin when they are finally reunited. The traveler MAY WELL legitimately conclude that the home twin is much younger than he is, during certain portions of the trip while they are separated, but once they are reunited again, the total amount of ageing by the home twin will always be greater.

Mike Fontenot

 

[pervect]

There is very little the little brother can do to age faster with standard physics. He might be able to age a few tenths of a second over a years time by choosing the right orbit around the sun.

From the point of view of an observer looking down at the solar system, the maximal aging orbit would look something like the diagram below.

The brother "spirals out" away from the Earth to escape, going as quickly as possible into a trajectory where he coasts getting as far away from the sun as he can while still being able to rejoin his brother. I"m not sure how far away he'd get, I'd guess less than 1 additional au though.

While he wants to get away from the Earth as well, escaping the gravitational time dilation of the sun's gravity will be his main concern on this time scale (1 year), as it has a bigger effect.The gravitationally induced time dilation is somewhere on the order of 10^-8, which would give .3 seconds over the course of a year if one could completely escape the sun's gravity. But a year isn't enough time to come even close to doing this. SO I'm guessing maybe a third of that, probably less.

If you recall my earlier post (I'm not sure you saw it), trying to move far away too fast will be conunterproductive because of velocity induced time dilation overwhelming the small effect (but the only effect that makes you age faster of being further away from the sun.

There's a few oddball things that could in theory allow him to age more, the one that comes to mind is a gravitationally significant amount of exotic matter.

The above is a rather coordinate-dependent description of what goes on,but it's probably the easiest to understand...

 

[PAllen]

Let me try again then! Two twins are standing on earth. They are very young, and one really wants to grow older faster than his brother, so he can be "bigger and beat him up". In a years time, (or you can pick any time frame if it helps) what can he do to age as fast as possible so that upon his return to earth, (if in fact he has to leave for maximum ageing rate) he has aged as much as possible in the allowed time span compared to his brother. So at the end, it would be in BOTH of their reference frames, just as a person taking a trip at light speed and coming back is younger than his twin who stayed on earth. Maybe there is a way he could age at an infinite rate compared to the twin on earth? (In which case he would be dust upon his return!)

Zealscience earlier proposed the only way to accomplish this, lunatic as it is. You would need to accelerate (objective, not relative) the Earth to near lightspeed and back, while you hung in orbit around the sun waiting for them, for many years. I commented that if you want to age fast compared to the universe, your task is a bit larger.

 

[Mike_Fontenot]

Yeah, if you want to be able to beat up your twin (by eventually being much older than him), then you've got to send HIM on the trip, and YOU stay put.

 

[abbott287]

Yeah, if you want to be able to beat up your twin (by eventually being much older than him), then you've got to send HIM on the trip, and YOU stay put.

Lol! Great thinking! Thanks to all for the interesting info. So much to learn, and so little time. I need that trip worse than either twin!