[PmbPhy]

What is the difference between gravity potential, and gravity potential energy?

Do they have different values?

See - https://en.wikipedia.org/wiki/Gravitational_potential

[alancalverd]

So when a physicist observes that my clock is running slower than his clock, and I observe that his clock is running faster than mine, and he tells me that we can deduce that we are in differing gravity potentials - does this mean that we are experiencing differing amounts of gravity potential energy?

You don't experience potential energy.

[timey (OP)]

What is the difference between gravity potential, and gravity potential energy?

Do they have different values?

See - https://en.wikipedia.org/wiki/Gravitational_potential

Thank you for going to the trouble of googling wiki for me Pete.

I have indeed posted that very link here at this site a dozen times or more in last two years.

Where:

It is analogous to electric potential with mass playing the role of charge

...is interesting to me.

I have read literally dozens of physics books, and have no trouble accessing Wiki myself.
The reason the title is posted as a question is because the site demands it.  Otherwise it would be posted as
'Hey, guys and girls... Let's talk about gravity potential energy and explore the time dilation phenomenon in the gravity potential'

[timey (OP)]

So when a physicist observes that my clock is running slower than his clock, and I observe that his clock is running faster than mine, and he tells me that we can deduce that we are in differing gravity potentials - does this mean that we are experiencing differing amounts of gravity potential energy?

You don't experience potential energy.

To quote your own words, the 100kg cannonball started out with more potential energy in the higher gravity potential than the 10kg cannonball.

So let's say that you and I are of the same weight.  If you are in the higher gravity potential, and I am in the lower gravity potential, you will have more potential energy than I will have.

And what makes you so sure that potential energy is not experienced?
If a body can have more or less of this energy, and this energy is what gets converted into kinetic energy, then why would a body not experience it?

It seems pretty clear to me, as shown by the cannonballs on the trampolines, that gravity potential energy has physical consequences in that differing mass value cannonballs bounce to same height.
Or are you telling me that potential energy is just a mathematical convenience that bears no physical reality and is just used as a means to describe observation mathematically?

[alancalverd]

You can experience pleasure, nausea or acceleration. You can have arms, legs or potential energy. Difference between the ongoing action of an external force and an extant static property. 

This is really fundamental to the development of Newtonian and relativistic mechanics.

[timey (OP)]

And...if one is aging in keeping with their clock, it could be said that one is experiencing time in the same way the clock is.

You could of course just say that time runs faster where the clock is and be done with it, apart from the observer dependant issue which fudges things up a tad, or you could look for a physical reason why time is running faster for both the clock and the person, and indeed consider a physical cause for the phenomenon of time itself...  If one wanted to, which I do.

[timey (OP)]

In addition to post above:

In the meantime, a person's body at an h from M and the clock he has with him will both have a value of potential energy.
If we drop them both from that height  onto their separate trampolines, both will land on trampoline, and bounce to same height at same time.
The person will have a greater m, greater p, and greater potential energy throughout than the clock will, but a remains the same for both.
If time dilation at h from M where to be caused by potential energy, then value of m would not affect the rate of this time dilation, just as m value does not affect a in free fall, therefore a rate of time caused by gravity potential energy could be thought to be affected by m in the same way as m affects a.

(It occurs that someone might want to move this thread to New Theories as I am straying from currently held notions now)

[alancalverd]

And...if one is aging in keeping with their clock, it could be said that one is experiencing time in the same way the clock is.

obviously. Just like two people watching the same film from adjacent seats.

You could of course just say that time runs faster where the clock is and be done with it, apart from the observer dependant issue which fudges things up a tad, or you could look for a physical reason why time is running faster for both the clock and the person, and indeed consider a physical cause for the phenomenon of time itself...  If one wanted to, which I do.

Nothing "observer dependent" but everything "observer position dependent"  No fudge - the prediction, based only on Maxwell and other observations, is precisely reflected in the measurement .

The physical reason is because gravity warps spacetime, as shown by increasingly subtle experiments.

[alancalverd]

If time dilation at h from M where to be caused by potential energy, then value of m would not affect the rate of this time dilation,

Nonsense. pe = mgh. It's linearly dependent on m.

a rate of time caused by gravity potential energy could be thought to be affected by m in the same way as m affects a.

It doesn't, as Galileo pointed out.

[jeffreyH]

In addition to post above:

In the meantime, a person's body at an h from M and the clock he has with him will both have a value of potential energy.
If we drop them both from that height  onto their separate trampolines, both will land on trampoline, and bounce to same height at same time.
The person will have a greater m, greater p, and greater potential energy throughout than the clock will, but a remains the same for both.
If time dilation at h from M where to be caused by potential energy, then value of m would not affect the rate of this time dilation, just as m value does not affect a in free fall, therefore a rate of time caused by gravity potential energy could be thought to be affected by m in the same way as m affects a.

(It occurs that someone might want to move this thread to New Theories as I am straying from currently held notions now)

For a simple harmonic oscillator a force constant can be defined for any invariant quantity of mass. This breaks down for the gravitational field.

[timey (OP)]

And...if one is aging in keeping with their clock, it could be said that one is experiencing time in the same way the clock is.

obviously. Just like two people watching the same film from adjacent seats.

Ah yes Alan - exactly!  Let's take that analogy further...but first to say so, You state that a body will 'experience' acceleration.  ...And differing rates of time can be considered accelerations or decelerations of the rate of time.
My point being that a body experiencing gravity potential energy related time dilation in the g-field would be akin to a body experiencing acceleration in the g-field, where all m experiences acceleration equally, and therefore all m would also experience an equal rate of time in the gravity potential.

Nonsense. pe = mgh. It's linearly dependent on m.

...And F=ma where m at h experiences the same acceleration, and potential energy is converted into kinetic energy that will bounce differing value of m off a trampoline to same height.
If more potential energy does not cause differing values of m to accelerate at differing rates in the g-field, then why would potential energy cause time dilation to be affected at differing rates for differing values of m in the g-field?

But back to your analogy:
When sitting next to each other the 2 observers are watching a film that is 1 hour long held relative to the rate of time where they are sitting.  We move  1 observer to a higher gravity potential and he observes from the remit of his clock at that higher potential, that 1 hour goes by slower for the clock and the observer on the ground, than it does for himself.
Ok.  Let's say he had a super duper pair of binoculars, because at that h from M where he would physically notice any difference in the clock on the grounds time, he would indeed be a very long distance away, and would need super duper binoculars in order to watch the movie...
This being an impossible scenario, let's just make life easy for ourselves and reduce our distance, but increase the time shift.
We could indeed regard ourselves as being in a time shift as severe as the black hole scenario minus the extended distance remit, where space dimensions are considered flat and constant, and time shift is severe between these flat co-ordinates at h from event horizon.
At an h from event horizon using flat coordinates with gravitational shift, our observer is watching the hour long movie playing on the screen at a lower h from event horizon, where he observes that the clock in that lower potential is running slower than his clock by the value of half an hour.  For every second that passes for him, only 30 of his seconds are passing for the clock below where the movie is playing...
What will the observer in the higher potential observe of the movie?

Will the observer observe just the first half of the movie?
Will the observer observe the whole of the movie as if it were being played in fast forward?
Or will the observer observe that he observes the entire movie in real time motion, but that every other frame of the movie is missing?

[alancalverd]

You don't experience gravitational time dilatation. Your clock is always correct. You can however observe it.

The movie that takes an hour to run on earth will take a few nanoseconds longer when viewed from the moon, or the blnk of an eye when seen from a nearly-black hole..

[timey (OP)]

Well that is not what the NIST report said, nor the news articles which stated that time really does go faster at altitude, and that if you live at top of a tower block, over a period of some 80 or so years, one would have experience a few nano-second faster time and have aged that much faster than his mate on ground floor.
This is also synonymous to concepts held by NASA, where the astronaut experiences via SR time dilation a slowing of their time which is said to cause them to age slower.

You yourself have pointed out in the past that at a certain radius from Earth, that travelling at the velocity required to maintain that orbit, the SR time dilation cancels out the GR time dilation and the clock at that radius traveling at that speed will be ticking equally to a clock on the ground.

So how do you reconcile these concepts with your statement below:

You don't experience gravitational time dilatation. Your clock is always correct. You can however observe it.

...unless by ditching this idea of time being 'correct' anywhere, and then considering that the person in a differing gravity potential with their clock is measuring the universe as per held relative to the rate of time their own clock appears to be ticking at, which really is ticking at a differing rate to one's own.

*

And if the time shift of the observer in a higher potential was exactly 1 half of the observed rate of time where the movie was playing, what would the movie look like then?

[alancalverd]

I'm being very pedantic, but for a very good reason. You don't experience time, you observe the clock. And your clock always tells the correct time. It just happens that time is different at different altitudes, except that in deep space where there is no gravitational field, time is the same everywhere.

[timey (OP)]

Well to be pedantic:

I don't want to be drawn into a philosophical discussion regarding time, but purely as a physics aspect -time and action are related.

So if time is not experienced in relation to an action (of the clock ticking for instance), then in the impossible scenario of two very different times where the observer is watching a movie being played from a place where he observes that the clock where the movie is being played is only ticking 30 seconds for every minute that passes on his clock, what action of the movie will he see?

If action does not experience the time of the clock, then the observer watching the movie playing, where he also observes the clock with the movie as running slower than his own, would notice no difference in the movie and the movie would be 1 hour long for all who watched it, no matter what time anyone's clock is running at.

If we are going to state the observation of the action of the movie as differing when observed from a differing rate of time, then all action must be affected by a differing rate of time.*
Which would very much suggest that we do experience time, describes a person ageing with their clock, and also why it is a person with a clock see's their clock as being the 'correct' time.

*Hence my former questions concerning what an observer who's clock is running at a rate of 1 minute to where the clock where the movie is playing's 30 seconds as seen by the observer, will observe of the 1 hour long movie...

[alancalverd]

T h e  m o v i e  w i l l   s e e m  t o   b e  r u n n i n g  v e r y   s l o w l y    a n d  t h e   c o l o r s   w i l  l   b e  r e d   s h i f t e d . I t w i l l   t a k e  2  "s p a c e h o u r s"  t o   f i n i s h.

It will of course look entirely normal to the guy sitting in the cinema because all his clocks, including the molecules in his eyes and ears are at the same gravitational potential.

This is exactly what Pound-Rebka and GPS satellites have found.

[timey (OP)]

Ah - Good!

Ok - So recognising that when we say that the movie is 1 hour long we are using the guy sitting in the cinema's clock to measure the length of the movie, and also recognising the fact that the movie was produced/filmed in a location where a clock will agree that the movie is 1 hour long...
When we say that the movie would take 2 space hours 'to reach(?)', or is that for the observer in the higher potential 'to view(?), we must recognise that we are also making this assessment based on the timing of the clock in the cinema.

Now we are going to examine:
a) how far away the observer is from the cinema.
And:
b) what watching a 1 hour movie spread out over 2 hours is going to look like.

So for the sake of my not having to get a calculator out - for the purpose of this thought experiment we will state the speed of light as being 60 metres per hour as measured by the cinema's clock.
The observer now in the higher potential had left the cinema at 30 metres per hour, as measured by the cinema's clock, and travelled for 2 hours as observed by the guy in the cinema.
As far as the guy in the cinema is concerned the observer dude above is 60 metres away and it should take light from the movie screen 1 hour to arrive at observer dude's elevated position.
However, the observer dude above has reported that the guy in the cinema's clock is only ticking 30 seconds for every minute that passes on the clock he took with him, and cinema guy can observe that for every 30 seconds that passes by on his clock, observer dude's clock is ticking 60 seconds, therefore cinema guy works out that it will take the light from the cinema 2 hours to reach observer dude...
But this cannot be so because the speed of light is constant, and if the light were to travel 60 metres it would only take 1 hour to do so.  In order to travel for 2 hours at a constant speed of 60 metres per hour, the distance will be 120 metres.
It is not possible to travel a reduced distance while keeping the speed constant so according to SR we can assume that there is a spatial dilation and that the fabric of space is curved between the observer in the higher potential and the cinema.  Anything travelling from cinema to the observer above will have to travel this curve, inclusive of the observer himself's journey to that location.

However it would be equally as possible to say under these circumstances, that both the observer and the light have had to travel through a temporally dilated space, rather than a spatially dilated space.

By remit of the cinema's clock the observer dude's journey took 2 hours at 30 metres per hour and observer dude is now at a location 60 metres in distance above the cinema...
But by the cinema guy's observation of observer dude's clock the journey took observer dude 3 hours. This being because according to cinema guy, observer dude's clock has been steadily running faster for every metre he has travelled.
According to the guy in the cinema, by the remit of observer dude's clock, the guy in the cinema will think the observer dude has travelled a greater distance than 60 metres, this being 90 metres.
So given that the cinema guy has already worked out that the light from the movie screen takes 2 hours to reach observer dude, and light travels 120 metres in 2 hours, he then notes that though observer dude's clock will appear to himself (cinama guy) from the potential of the cinema to be running fast at that higher gravity potential, that observer dude's clock happens to appear to cinama guy as running slow when travelling at that half light speed velocity, and cinema guy might put these extra metres down to a spatial dilation of space, or attribute his own perception of observer dude's time as having been slowed due to his velocity as a factor, or a combination of both...

Or cinema guy could consider that observer dude had been moving through open space where time is running slower...
If time were running slower in the space observer dude was moving through as an exact negative to observer dude's onboard clock's increased time as observed by cinema guy, then observer dude would travel exactly 60 metres.
If the light from the movie screen then takes 2 hours as held relative to cinema guy's clock to reach observer dude's location at 60 metres above the cinema, the light will have been travelling through temporally dilated space where at each open space coordinate of the 60 metres distance time is running slower, but at each coordinate the speed of light still travels 60 metres per hour held relative to the negative length of second of that coordinate.
An observer at that coordinate would then also observe the speed of light to be travelling at 60 metres per hour by the remit of his clock's increased tick rate at that coordinate...
I realise that this is extremely hard to visualise so I will explain:

If we take the speed of 60 metres per hour held relative to a second that is 50% shorter, then the distance travelled is halved.
If we take the speed of 60 metres per hour held relative to a second that is 50% longer, then the distance is doubled.
And this all looks pretty confusing until you remember that the speed travelled at is being held relative to a second as observed of the cinema's clock and the percentages of +50% and -50% are also being held relative to a second as observed of the cinema's clock...
A speed of light as measured by the cinema clock that takes 50% longer time to travel a metre, and a speed of light as measured by the cinema clock that takes a 50% quicker time to travel a metre both result in the same distance travelled.
(This is an alternative remit to the spatial dilation of SR, but hasn't yet added the velocity related time dilation of SR to the picture)

b) watching a 1 hour movie spread out over 2 hours, or as from the higher potential, a 1 hour movie crammed into half an hour.

Remembering that it is 2 of cinema guy's hours that we are holding this measurement relative to, and that by the remit of observer dude's clock the 1 hour movie as observer dude observes of cinema guy's clock, is over in half an hour by the remit of his own clock, we then run into simultaneity problems.
What does observer dude observe of the light arriving from the movie screen where the movie is playing in the cinema below?
Well firstly you say that the light will be redshifted having taken 2 hours of cinema guy's hours to arrive at observer dude's location, but observer dude will only be able to view 1 of his hours worth of the light arriving at his location, which is equal to half an hour of cinema guy's time.
So in order to retain simultaneity can we say that the observer dude will only observe every other frame of the movie playing below?
And observer dude can, by understanding that his observation is time frame dependent, calculate via probability what the action is between the frames that he cannot view?
(This remit actually uses the SR length contraction/time dilation maths to say that an observation is proportional to the difference in rate of time between observer and observed as an 'observational time frame dependency' concept, rather than as an extension of spatial distance concept)

[alancalverd]

Ok - So recognising that when we say that the movie is 1 hour long we are using the guy sitting in the cinema's clock to measure the length of the movie,

yes

and also recognising the fact that the movie was produced/filmed in a location where a clock will agree that the movie is 1 hour long...

no. Have you never seen timelapse or high speed films? It can take years or milliseconds to make a 1 hour film!

When we say that the movie would take 2 space hours 'to reach(?)',

if the observer is 2 light-hours away - around Jupiter at a guess

or is that for the observer in the higher potential 'to view(?),

yes

we must recognise that we are also making this assessment based on the timing of the clock in the cinema.

no, 2 space hours is 2 hours measured on the space clock. It was 1 hour on the cinema clock.This is a simple gravitational redshift problem. Well, not so simple because to get a 50% redshift you'd need the cinema to be on a neutron star or hurtling away at a sizeable fraction of c.

[jeffreyH]

Coming to a cinema no longer near you.

[timey (OP)]

But the movie is playing at a rate of frames that render its length as 1 hour long.  Unless you take the movie to the higher potential and play it there, where it will also be 1 hour long.
*
The speed of light as per the thought experiment is 60 metres per hour.
*
The space clock's time is going twice as fast as the cinema time.  1 hour of the cinema clock's time will be half an hour space clock time as measured by the space clock, not 2 hours.
But 1 hour of the space clock's time will be 2 hours cinema time as measured by the cinema clock.