[imatfaal (OP)]

Mike - please stop with "light travels instantaneously ... in its own reference frame" - this is not accepted science.  It is an extension of SR (to an impossible inertial light speed frame) that is completely against the postulates of SR itself.  It is quite acceptable in its own thread (and it is fascinating) - but as an answer to another's question in the main forum it is not ok

[MikeS]

imatfaal

We are talking about Time which mainline science does not seem to be happy discussing.
If I have misled anyone I apologise, that was not my intention.

"If light does not travel instantaneously ... in its own reference frame"  What does it do?  What does mainline science have to say about this?

[imatfaal (OP)]

Mike - scientists love discussing almost anything, an insatiable appetite for knowledge and incurable curiosity are pretty much prerequisites.  However, when it comes to making statements, propounding theories, and coming up with hypotheses then the language of mathematics must be used - and it is very hard to encompass the human instinctual knowledge of time within maths, this is why much of the scientific discussion of time seems wanting.

the photon's local frame / what a photon "experiences" is not a valid question under special relativity - observation, experience, and measurement cannot be divorced from matter, which in turn has mass, this means it cannot go the speed of light, which means it cannot be in the photon's frame .  more, it means the photon cannot have a local frame because frames are inertial.  the more in depth explanations of the behaviour of light are in electromagnetics, quantum theory and qed.  you might want to consider how gamma-gamma interaction (which I think is still theoretical - but might have been glimpsed) occurs for timeless particles 

[MikeS]

Clip
"the photon's local frame / what a photon "experiences" is not a valid question under special relativity - observation, experience, and measurement cannot be divorced from matter, which in turn has mass, this means it cannot go the speed of light, which means it cannot be in the photon's frame .  more, it means the photon cannot have a local frame because frames are inertial." 

Would you explain this please?  A photon is not accelerating, why is its frame not inertial?

[MikeS]

Ok, so the question does not make sense under special relativity but maybe that is a shortcoming of SR.

A photon experiences no passage of time (because it travels instantaneous [from its reference point etc].  It's a simple concept that seems to fail when you try to describe it using language or perhaps more precisely the recognised language of physics.
Let me phrase it another way.  If you had a clock riding a photon in a light ray it would not register any passage of time.  (yes, I know it is impossible as the clock has mass but hopefully it is the thought that counts.)  Therefore, in some sense, the photon travels at infinite speed.

What I was trying to get at in this post  above http://www.thenakedscientists.com/forum/index.php?action=post;quote=378151;topic=42810.0;last_msg=378329
was that it seems to me
What we call 'Time'  is the difference in the infinite speed of light and its measured finite speed. That delay represents 'Time'.  The delay is caused by the curvature of space-time, the geodesic of which is longer than the straight line between any two points in space.

[imatfaal (OP)]

Inertial implies mass.  I wouldn't say it was a shortcoming of SR - merely a part of the physical world that isn't covered by SR; let's face it SR is strictly constrained in areas of application. 

You still have not explained why you think the photon travels instantaneously - you cannot use SR!  A clock cannot ride a photon - and the thought is impossible to extrapolate from; a gedanken that starts with an impossible scenario can generate any outcome with no reference to truth, logic or theory.   

The fact that time dilates when observed from a frame in relative motion - and the notion that you have extrapolated that the clock stops at c - is from special relativity.  but SR requires that frames are inertial - those that can involve mass and acceleration; you are attempting to use a theory to show something that is outside the realms of application.  light/light speed is special, it's weird, and we don't really know why - it might be ok to just extend normal inertial frames to mass-less frames but we just do not know.

[MikeS]

Depending on how you look at it a photon either travels at infinite speed from its reference point
Or
A photon does not experience time or distance.

Note
A photon as it does not experience time or distance cannot carry times arrow.  However as it follows the geodesic of curved space-time that gives time an arrow.

quote imatfaal
clip "The fact that time dilates when observed from a frame in relative motion - and the notion that you have extrapolated that the clock stops at c - is from special relativity.  but SR requires that frames are inertial - those that can involve mass and acceleration; you are attempting to use a theory to show something that is outside the realms of application."
What you say is true but maybe this is just a limitation of SR.

The generally accepted view is a photons does not experience time or distance.  The reason this is the accepted view is that a photon does not have an inertial reference frame under SR therefore; it cannot be described as traveling at infinite speed.  SR no matter how good and accurate, does have limitations, so it is may not be complete.

On the one hand we have ‘a photon travels at infinite speed’
And on the other we have
‘a photon does not experience time or distance’.
Are these two aspects in conflict?  No, a photon does not experience time because at the speed of light (in a vacuum) the clock has stopped and distance has shrunk to zero and this is equivalent to infinite speed.  A photon does not experience time as it is traveling at infinite speed (from its reference point)  [With apologies to SR but I need a way to describe it.]  These two things aren’t actually in conflict, unless viewed strictly from the confines of SR.

In an earlier post I said this

“What we call 'Time'  is the difference in the infinite speed of light and its measured finite speed. That delay represents 'Time'.  The delay is caused by the curvature of space-time, the geodesic of which is longer than the straight line between any two points in space.”

Another way of stating the above (in trying to overcome the limitations of SR) would be

What we call ‘Time’ is the difference between zero travel time of a photon and its measured finite speed. That delay represents 'Time'.  The delay is caused by the curvature of space-time, the geodesic of which is longer than the straight line between any two points in space.”

The passage of time is therefore (I believe) represented by the relationship of energy (photons) and gravity.

[imatfaal (OP)]

Mike - I have split this topic off from the OP - it was a distraction. You are making unfounded and unreferenced claims that belong in new theories.

I would love to see any work on this topic as you do say that it is a generally accepted view

[Bill S]

In various places I think I have tried the patience of a number of scientific posters with this sort of discussion.  The fact is I have still not managed to get my head round it.

Mike asks a question to which I would really like to see an answer:  "If light does not travel instantaneously ... in its own reference frame"  What does it do?  What does mainline science have to say about this?

a gedanken that starts with an impossible scenario can generate any outcome with no reference to truth, logic or theory. 

Didn’t Einstein start a gedanken by imagining himself keeping pace with light?

The delay is caused by the curvature of space-time, the geodesic of which is longer than the straight line between any two points in space.

I thought the definition of a geodesic was that it represents the shortest distance between two points in curved spacetime.

[imatfaal (OP)]

In various places I think I have tried the patience of a number of scientific posters with this sort of discussion.  The fact is I have still not managed to get my head round it.

Mike asks a question to which I would really like to see an answer:  "If light does not travel instantaneously ... in its own reference frame"  What does it do?  What does mainline science have to say about this?

It is a very difficult question.  What we cannot do is extend SR - which is the commonest reason to assume that the photon does not experience time.   Most physics educators would answer the initial question by starting "the photon does not have a valid inertial local frame..." ie assuming that the old chestnut had reared its head.  Assuming you had persuaded them you weren't on these lines you would get some headscratching.   It's a very hard question to ask let alone answer - it tends to get into areas of philosophy and ontology that cannot really be hard science because of the lack of testability and falsifiability.   Way beyond my paygrade there is theoretical talk and hopeful experimental proof of gamma/gamma interaction - ie two-photon physics; does this imply a photon interacting whilst travelling at c and thus timeless?  I don't know 

a gedanken that starts with an impossible scenario can generate any outcome with no reference to truth, logic or theory. 

Didn’t Einstein start a gedanken by imagining himself keeping pace with light?

  Dunno - possibly (would love to see it), he was slightly more subtle than the average forum poster and could probably get away with it; they didn't call him Einstein for nothing you know.

The delay is caused by the curvature of space-time, the geodesic of which is longer than the straight line between any two points in space.

I thought the definition of a geodesic was that it represents the shortest distance between two points in curved spacetime.

Agree completely.

[MikeS]

In various places I think I have tried the patience of a number of scientific posters with this sort of discussion.  The fact is I have still not managed to get my head round it.

Mike asks a question to which I would really like to see an answer:  "If light does not travel instantaneously ... in its own reference frame"  What does it do?  What does mainline science have to say about this?

a gedanken that starts with an impossible scenario can generate any outcome with no reference to truth, logic or theory. 

Didn’t Einstein start a gedanken by imagining himself keeping pace with light?

The delay is caused by the curvature of space-time, the geodesic of which is longer than the straight line between any two points in space.

I thought the definition of a geodesic was that it represents the shortest distance between two points in curved spacetime.

Bill, yes you are quite right but a curved line between two points is longer than a straight line between the same two points.  It is still the shortest distance between two points in curved space-time.  That's the point I was trying to make.

[MikeS]

imatfaal

Please correct me if I am wrong (didn't really need to ask did I) but I understand you to be saying that mainline science, including SR and GR has no views on what a photon experiences on the subjects of either, time or distance?

[imatfaal (OP)]

The delay is caused by the curvature of space-time, the geodesic of which is longer than the straight line between any two points in space.

I thought the definition of a geodesic was that it represents the shortest distance between two points in curved spacetime.

Bill, yes you are quite right but a curved line between two points is longer than a straight line between the same two points.  It is still the shortest distance between two points in curved space-time.  That's the point I was trying to make.

No - this is a fundamental misunderstanding of manifolds.  In a curved spacetime there is no "straight line"; there is the goedesic.  The best way to understand the difference is back to our old friend the distance between London and New York - the quickest way is the great circle route - but the shortest distance is the tunnel through the earth.  Now we switch to maths if we consider the surface of the earth as a mathematical sphere and not as a ball then there is NO tunnel (there are no aircraft either)  the shortest distance imaginable/calculable/do-able is the geodesic great circle.  To make a tunnel you need to move into a 3rd spatial dimension and the sphere has only two.

The 2d surface (that we can understand might be embedded in 3d space, but does not need to be!) is all there is in this example - the difficult bit is understanding that our 3d space behaves the same way.  Space is a 3d setup with x,y,z axes ie up/down right/left in/out etc.  Spacetime is a 4d setup with time as a fourth dimension.  There is no tunnel between two points in either space or spacetime without stepping to an additional space dimension.   

Mike you are not alone by not being able to visualise this - practically no one can, I cannot.  But I can visualise the 2d sphere - and the constraints you would be under in you were on that sphere a la Flatland.  BTW I cannot recommend Flatland too highly.  And from this I can almost get my head around curved 3d space.  It is not that spacetime is a thingie which curves within something else (which would allow the straightline tunnel) but that the shortest distance between two points IS the curved geodesic - that is crucial.

imatfaal
Please correct me if I am wrong (didn't really need to ask did I) but I understand you to be saying that mainline science, including SR and GR has no views on what a photon experiences on the subjects of either, time or distance?

"...photon experiences..."  that's the nub of the question.  How does a massless, fundamental, stable boson experience anything?  We know how the environment will affect the photon, how fast it goes, its energy and momentum - perhaps deep in qed there are concepts of what a photon actually is.  As I have said previously there is lots of research on gammagamma interaction - which tries to probe a similar question.  You seem to be asking what happens to a photon when it is not interacting with anything - how could we possibly tell, we can only observe, measure, theorize when there is an interaction.

[MikeS]

imatfaal
I understand what you are saying about geodesics, I agree and that's what I said.  The point I was trying to make, obviously not very successfully is that gravity has curved space-time (or vice versa) and introduced the concept of time.  The curvature seems to represent both gravity and time.  Without gravity and hence time there would be no curvature of space and the distance between the two points would be shorter.  The difference in distance in space time from the length of the geodesic and a straight line distance between the same two points in flat space represents what we call time.  That's how I see it.

[Bill S]

Without gravity and hence time there would be no curvature of space and the distance between the two points would be shorter.

This would be true only if spacetime is stretched when it is curved; otherwise, when the distorting mass is removed the two points move apart so that the straight line between them remained the same.  Try it with a flexible ruler.   

[MikeS]

Bill it is certainly possible to do what you said but that is not what I am talking about, see below.

We can't visualise the four dimensions of space-time so let's forget time for the moment.  We can, however, visualise three dimensional space. 

Let us visualise the universe, without gravity, as a sphere where its diameter represents the shortest distance between two points. 

If we now visualise it with gravity, one half of the circumference equals the geodesic between the same two points. 

The geodesic in the universe with gravity is longer than the straight line distance in the universe with no gravity.
To make the geodesic of the universe with gravity the same length as the straight line distance in the universe with no gravity, the diameter of the sphere has to be decreased.  The universe with gravity is smaller (less diameter and less volume) than the universe with no gravity.  This is exactly what we would expect.  The difference in length (or longer path of light) is caused by gravity and represents what we call 'Time'

Energy, in the form of photons creates pressure to cause the universe to expand (the same principle that keeps stars inflated).  Gravity limits that expansion and is trying to make the universe contract.  The relationship between energy and gravity decides the time dilation factor.  The passage of time is proportional to energy and inversely  proportional to gravity.

We live in an energy dominated era of the universe hence the expansion.   http://en.wikipedia.org/wiki/Matter-dominated_era (Stars are converting and have converted much of their nuclear fuel into energy.  Ultimately there will be a time when the fuel runs out and there will be no more input of energy.)

Energy (photons) without the intervention of gravity travel infinitely fast or do not experience time [or distance] (take your pick).  They are emitted and they arrive instantaneously.  Therefore, causality does not exist.  Times arrow does not exist.  This would seem to be possibly the state of things before the start of the universe.  Energy existed in the void but before the creation of time.

Without time quantum mechanics allows for an unlimited amount of energy to exist anywhere in the void.  Its existence is not limited to any time duration as time does not yet exist.  ('Anywhere' becomes meaningless as 'distance' is also meaningless without time.)

With the existence of energy and the creation of matter came gravity, time and the Universe.

[MikeS]

You cannot talk about ‘Time’ without considering ‘Gravity’ as the two are intertwined in space-time.

Einstein showed us that gravity is the same as acceleration but to the best of my knowledge he did not elaborate upon that.

Acceleration is the rate of change of velocity with time.  We normally think of this as a progressive change in distance covered, with time but it is equally valid to think of it as a change in the ‘going rate or dilation of time’ with distance.

Time gravitationally dilates near to a large mass.  Therefore time passes slower near to the Earths surface than it does further away.  This difference is progressive.  A way of visualizing this is to consider ‘the going rate of time’ or time dilation to be in shells around the Earth like layers of an onion.  Each shell represents a particular time dilation factor with the greatest time dilation being closest to the Earth getting progressively less in each subsequent layer as you travel further from the Earth.  The Earth, like all objects is continually passing through space-time.  If we think of these shells of time as continually collapsing on the Earth, each shell of time dilates as it approaches the Earths surface.  It is perhaps easiest to visualize it by considering space to be filled by something, say  aether.   This aether is continually being sucked into the Earth like a waterfall but all over the Earths surface .  The aether may or may not exist, the important point is it carries shells of time with it and these shells of time dilate more as they approach the Earth.  As shells of time dilate approaching the Earth so the Earth accelerates through these shells of time.  This is where the acceleration comes from; it is an acceleration in time.  All massive bodies produce a gravitational ‘field’ as they accelerate through time.  The aforementioned also explains why bodies fall within a gravitational field.  As the aether or shells of time fall upon the Earth so do other bodies that are within that sphere of influence.  They are swept along with the changing rate of time dilation.  As any object (mass) approaches the Earth (or any massive body), it enters shells of more and more dilated time.  This reduces all of the useful energy of the object as entropy increases.  The increased entropy represents a state of increased stability within the system.  (When any two objects combine, time for them dilates, entropy increases and they reach a state of greater stability.  For example a book on a table has more usable energy than the same book on the floor.  The book on the floor is more stable as it can't fall off the table)

Gravity then is the Universes way of returning to its ground state, which ideally would be zero useable energy, near zero temperature,  near zero passing time and near zero size (added 01-02-2012.  zero entropy). These conditions represent the Universes most stable configuration and these conditions are best met within a black hole.

[imatfaal (OP)]

You cannot talk about ‘Time’ without considering ‘Gravity’ as the two are intertwined in space-time.

  of course you can.  Gravity is an artefact of warped spacetime - but space time does not require gravity.  Many theories rely on flat space - SR for one.

Einstein showed us that gravity is the same as acceleration but to the best of my knowledge he did not elaborate upon that.

  Quite a lot of his work was based on the fact that in a local and small enough frame that acceleration and gravity were equivalent.

Acceleration is the rate of change of velocity with time.  We normally think of this as a progressive change in distance covered, with time but it is equally valid to think of it as a change in the ‘going rate or dilation of time’ with distance.

Acceleration is the second time derivative of position - your first sentence had it spot on. Your second definition is dubious

Time gravitationally dilates near to a large mass.

  Technically it is the gravitational potential 

   Therefore time passes slower near to the Earths surface than it does further away.  This difference is progressive.  A way of visualizing this is to consider ‘the going rate of time’ or time dilation to be in shells around the Earth like layers of an onion.  Each shell represents a particular time dilation factor with the greatest time dilation being closest to the Earth getting progressively less in each subsequent layer as you travel further from the Earth.

 

The Earth, like all objects is continually passing through space-time.  If we think of these shells of time as continually collapsing on the Earth, each shell of time dilates as it approaches the Earths surface.

Nope - gonna have to explain that more.

  It is perhaps easiest to visualize it by considering space to be filled by something, say  aether.   This aether is continually being sucked into the Earth like a waterfall but all over the Earths surface .  The aether may or may not exist, the important point is it carries shells of time with it and these shells of time dilate more as they approach the Earth.  As shells of time dilate approaching the Earth so the Earth accelerates through these shells of time.  This is where the acceleration comes from; it is an acceleration in time.  All massive bodies produce a gravitational ‘field’ as they accelerate through time.  The aforementioned also explains why bodies fall within a gravitational field.  As the aether or shells of time fall upon the Earth so do other bodies that are within that sphere of influence.  They are swept along with the changing rate of time dilation.  As any object (mass) approaches the Earth (or any massive body), it enters shells of more and more dilated time.  This reduces all of the useful energy of the object as entropy increases.  The increased entropy represents a state of increased stability within the system.  (When any two objects combine, time for them dilates, entropy increases and they reach a state of greater stability.  For example a book on a table has more usable energy than the same book on the floor.  The book on the floor is more stable as it can't fall off the table)

  You might want to give some more concrete examples, be more specific and do some maths to back that up

Gravity then is the Universes way of returning to its ground state, which ideally would be zero useable energy, near zero temperature,  near zero passing time and near zero size. These conditions represent the Universes most stable configuration and these conditions are best met within a black hole.

  Your conditions are not complementary; in a situation of zero gravitational potential where is the time dilation coming from? Near zero size would mean that any radiation is constrained to short wavelength, high frequency ...

[MikeS]

You cannot talk about ‘Time’ without considering ‘Gravity’ as the two are intertwined in space-time.

  of course you can.  Gravity is an artefact of warped spacetime - but space time does not require gravity. Many theories rely on flat space - SR for one.

Einstein showed us that gravity is the same as acceleration but to the best of my knowledge he did not elaborate upon that.

  Quite a lot of his work was based on the fact that in a local and small enough frame that acceleration and gravity were equivalent.[/color]

Acceleration is the rate of change of velocity with time.  We normally think of this as a progressive change in distance covered, with time but it is equally valid to think of it as a change in the ‘going rate or dilation of time’ with distance.

Acceleration is the second time derivative of position - your first sentence had it spot on. Your second definition is dubious

Time gravitationally dilates near to a large mass.

  Technically it is the gravitational potential

   Therefore time passes slower near to the Earths surface than it does further away.  This difference is progressive.  A way of visualizing this is to consider ‘the going rate of time’ or time dilation to be in shells around the Earth like layers of an onion.  Each shell represents a particular time dilation factor with the greatest time dilation being closest to the Earth getting progressively less in each subsequent layer as you travel further from the Earth.

 

The Earth, like all objects is continually passing through space-time.  If we think of these shells of time as continually collapsing on the Earth, each shell of time dilates as it approaches the Earths surface.

Nope - gonna have to explain that more.

  It is perhaps easiest to visualize it by considering space to be filled by something, say  aether.   This aether is continually being sucked into the Earth like a waterfall but all over the Earths surface .  The aether may or may not exist, the important point is it carries shells of time with it and these shells of time dilate more as they approach the Earth.  As shells of time dilate approaching the Earth so the Earth accelerates through these shells of time.  This is where the acceleration comes from; it is an acceleration in time.  All massive bodies produce a gravitational ‘field’ as they accelerate through time.  The aforementioned also explains why bodies fall within a gravitational field.  As the aether or shells of time fall upon the Earth so do other bodies that are within that sphere of influence.  They are swept along with the changing rate of time dilation.  As any object (mass) approaches the Earth (or any massive body), it enters shells of more and more dilated time.  This reduces all of the useful energy of the object as entropy increases.  The increased entropy represents a state of increased stability within the system.  (When any two objects combine, time for them dilates, entropy increases and they reach a state of greater stability.  For example a book on a table has more usable energy than the same book on the floor.  The book on the floor is more stable as it can't fall off the table)

  You might want to give some more concrete examples, be more specific and do some maths to back that up

Gravity then is the Universes way of returning to its ground state, which ideally would be zero useable energy, near zero temperature,  near zero passing time and near zero size. These conditions represent the Universes most stable configuration and these conditions are best met within a black hole.

  Your conditions are not complementary; in a situation of zero gravitational potential where is the time dilation coming from? Near zero size would mean that any radiation is constrained to short wavelength, high frequency ...

Imatfaal

Thanks for your feedback, I do appreciate it.  I will try to address all of your queries.

We know that time is affected by gravity or gravitational potential, if you like, so gravity has to be considered when talking about time.  You say “gravity is an artifact of warped space-time” but I think this is like the chicken and the egg, which came first.  In the normal universe, not a black hole, you can’t have gravity without time and you can’t have time without gravity.  You say that “space-time does not require gravity”   It does, without gravity time has no arrow.  There is no space-time without gravity.  No mass equals no gravity which is essentially the condition probably prevailing prior to the birth of the universe.  Whether or not time existed prior to the birth of the Universe may be debatable but it probably did not.

I did say “to the best of my knowledge”.  Did Einstein actually explain in what way a massive object is accelerating?

Average acceleration is the change in velocity (Δv) divided by the change in time (Δt).  There are two factors that affect acceleration, the change in velocity and time.  Changing either will affect the acceleration. Normally we think of acceleration as being the change in velocity.  That is, an increase in the distance covered in a given time.  However by keeping the distance constant but contracting time (speeding up) we still have acceleration.  Have I made that clear?

I agree the but the result is “Time gravitationally dilates near to a large mass.”

It is not easy to either visualize or explain but here goes.
The Earth is continually passing through space time.  The easiest way for me to visualize this is to consider time as being concentric shells surrounding the Earth.  The closest shell being the most time dilated (due to gravity), becoming progressively less dilated further away.  The Earth is passing through time or you could think of it as time flowing over the Earth.  Each shell has a different time dilation factor.  The Earth passes through them, (it is easier to think of the shells as collapsing upon the Earth)  As the shells collapse upon the Earth, you can picture this as time passing more slowly as it approaches the Earth.  From the Earths reference frame time passes faster as it passes from its existing time shell (reference frame) into the next. In other words, the Earth is accelerating. I hope that made it clear?


I have elaborated on much of the above elsewhere in this reply and hope that has clarified matters.  I would be happy to explain in more detail anything still unclear.  I do not think there is much that is new in all of this. It is more like assembling known pieces of a jigsaw puzzle.  Unfortunately, I am not a mathematician, I wish I was.


I should have added and near zero entropy.
I believe the conditions are indeed complementary and consistent with a black hole.  The time dilation is an artifact of the intense gravitational field of the black hole.
Whilst radiation still exists, the universe reflects this in its size.  It is only with the absorption of all radiation could the universe deflate to zero size.

As a side issue, I believe the ground state of the Universe is as described above.  If, as believed by many the Universe is doomed to expand forever and ultimately die through lack of fuel.  It will never reach its ground state despite the ground state being more stable.  This is one reason that makes me believe it is not doomed to expand forever.

[imatfaal (OP)]

MikeS and his amazing technicolour dreampost

You cannot talk about ‘Time’ without considering ‘Gravity’ as the two are intertwined in space-time.

  of course you can.  Gravity is an artefact of warped spacetime - but space time does not require gravity. Many theories rely on flat space - SR for one.

We know that time is affected by gravity or gravitational potential, if you like, so gravity has to be considered when talking about time.  You say “gravity is an artifact of warped space-time” but I think this is like the chicken and the egg, which came first.  In the normal universe, not a black hole, you can’t have gravity without time and you can’t have time without gravity.  You say that “space-time does not require gravity”   It does, without gravity time has no arrow.  There is no space-time without gravity.  No mass equals no gravity which is essentially the condition probably prevailing prior to the birth of the universe.  Whether or not time existed prior to the birth of the Universe may be debatable but it probably did not.

you can have an instantaneous force - although not a perceived action or consequence.  gravity, to be seen or observed needs the passing of time, but does not have time as a component in the classical newtonian formulation F=GMmr^-2.   that time is dilated by differing gravitational potentials is different in a subtle way - the difference needs alternate positions of observation to be obvious - ie you cannot look at your watch and say Oh Time is dilated here.  time has a clear direction without gravity and there is spacetime without gravity - the whole of Special relativity is based on flat space time with non-accelerating frame of reference - ie there is no gravity there.