# The Naked Scientists Forum

### Author Topic: If you cooled an atomic clock to just above absolute zero would time dilate?  (Read 12328 times)

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #25 on: 04/03/2012 07:31:46 »
Without energy, the entire concept of time has problems, since nothing would change.  If nothing changed, time would be a meaningless concept.

But that's not an issue in reality, since we can never remove all energy from a system.  Even if we're at the zero-point energy (the lowest you can get in any system), there is still energy.

It only becomes meaningless when you removed both the 'arrow' and 'passage' of time.  If the passage of time slows to the point where it is stationary then time has effectively stopped but the arrow of time still remains.  As time is the measure by which things change then you could say that the concept of time under that condition is meaningless.  Never the less, the arrow still remains.

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #26 on: 04/03/2012 07:51:27 »
Without energy, the entire concept of time has problems, since nothing would change.  If nothing changed, time would be a meaningless concept.

But that's not an issue in reality, since we can never remove all energy from a system.  Even if we're at the zero-point energy (the lowest you can get in any system), there is still energy.

As I understand it, I believe you are saying that time would still flow forward albeit very slowly because of zero point energy. But energy (photons) are their own antiparticle and contain no arrow of time other than that imposed upon them by gravity.  So what you say is true.  However, before the creation of the Universe zero point energy would still exist but without time and without causality,.

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #27 on: 04/03/2012 08:24:21 »
If I use the concept of 'virtual particles' any 'energy' is allowed as long, as it's fast enough whatever that means, under or over Plank time. That statement creates an question of what 'energy' really is thought to be, something 'unlimited' but regulated inside Plank time, or??

Ah well, some day my head will stop aching, hopefully :)

This does cause big problems for the standard model.  Now if matter and antimatter are gravitationally repulsive, as yet unproven one way or the other.  No assymetry of baryonic matter would be required to explain the unbelievable unbalance of matter over antimatter.  If, at the big bang both matter and antimatter were created in equal quantities then the arrow of time was double ended and time flowed equally in both directions at the same rate.  The forward and backward flow of time cancelled each other, so effectively no time was involved.  Quantum mechanics allows for this.  The particles that did not mutually annihilate gravitationally sorted into two separate universes, one made of matter the other antimatter.  Both going different directions in time (but each going forward in time from its own reference frame).  If you consider the two as one system then the length of time that they have both existed as a pair is always zero.

I seem to have digressed and I don't want to sidetrack the thread.  I mentioned the above purely to attempt to answer yor_on's point about virtual particles, QM and time.
« Last Edit: 04/03/2012 08:30:22 by MikeS »

#### JP

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #28 on: 04/03/2012 14:58:10 »
Without energy, the entire concept of time has problems, since nothing would change.  If nothing changed, time would be a meaningless concept.

But that's not an issue in reality, since we can never remove all energy from a system.  Even if we're at the zero-point energy (the lowest you can get in any system), there is still energy.

It only becomes meaningless when you removed both the 'arrow' and 'passage' of time.  If the passage of time slows to the point where it is stationary then time has effectively stopped but the arrow of time still remains.  As time is the measure by which things change then you could say that the concept of time under that condition is meaningless.  Never the less, the arrow still remains.

If you remove all energy, then there is no arrow nor passage of time, since nothing ever changes.  In other words, you can't draw an arrow of zero length, since you have no idea which way it points.

#### yor_on

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #29 on: 04/03/2012 18:02:21 »
I agree, 'virtual photons' is a discussion by itself, just as indeterminacy Mike :)

It's hard not to agree with JP there, I too believe that you need 'change' to find an 'arrow', or just 'time'. And any change should involve the concept of transformations of energy, as far as I can see. That's also why I find the universe so well planned, giving us a locally same 'arrow of time', no matter what you do, or go. Because it's that arrow that makes everything 'fit' for us, presenting us with a same environment, be it here on or Mars, timewise. You grow a flower, and it will behave the same (loosely speaking here, ignoring gravity etc) wherever you are.

Imagine the opposite. That time indeed would 'tick' differently for you, slower at some places, faster at others. Time is a very localized concept, and of 'one even measure' as I think of it. The most interesting thing about it is how far you can scale it down. Myself I expect the arrow to break down around Planck scale, indeterminism taking its place. And the really fascinating thing is that you can only define something like 'indeterminacy' when using a arrow to study it from. Only then will the concept be visible, and meaningful.

Without the arrow we would all be in a 'superposition'.

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #30 on: 04/03/2012 21:17:53 »
Without energy, the entire concept of time has problems, since nothing would change.  If nothing changed, time would be a meaningless concept.

But that's not an issue in reality, since we can never remove all energy from a system.  Even if we're at the zero-point energy (the lowest you can get in any system), there is still energy.

It only becomes meaningless when you removed both the 'arrow' and 'passage' of time.  If the passage of time slows to the point where it is stationary then time has effectively stopped but the arrow of time still remains.  As time is the measure by which things change then you could say that the concept of time under that condition is meaningless.  Never the less, the arrow still remains.

If you remove all energy, then there is no arrow nor passage of time, since nothing ever changes. In other words, you can't draw an arrow of zero length, since you have no idea which way it points.

Gravity demonstrates the arrow of time.  If you drop a tea cup it falls to the ground and shatters.  This demonstrates the arrow of time.  Place another tea cup on the ground and it still demonstrates the arrow of time by remaining firmly in place despite nothing ever changing.  It is not necessary to have change to demonstrate the arrow of time, only the passage of time.

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #31 on: 04/03/2012 21:25:35 »
I agree, 'virtual photons' is a discussion by itself, just as indeterminacy Mike :)

It's hard not to agree with JP there, I too believe that you need 'change' to find an 'arrow', or just 'time'. And any change should involve the concept of transformations of energy, as far as I can see. That's also why I find the universe so well planned, giving us a locally same 'arrow of time', no matter what you do, or go. Because it's that arrow that makes everything 'fit' for us, presenting us with a same environment, be it here on or Mars, timewise. You grow a flower, and it will behave the same (loosely speaking here, ignoring gravity etc) wherever you are.

Imagine the opposite. That time indeed would 'tick' differently for you, slower at some places, faster at others. Time is a very localized concept, and of 'one even measure' as I think of it. The most interesting thing about it is how far you can scale it down. Myself I expect the arrow to break down around Planck scale, indeterminism taking its place. And the really fascinating thing is that you can only define something like 'indeterminacy' when using a arrow to study it from. Only then will the concept be visible, and meaningful.

Without the arrow we would all be in a 'superposition'.

I don't see why.  Placnk time is the shortest quantum of time that is possible.  It only refers to the rate at which time passes, it says nothing about the arrow of time.  Please see my previous post in answer to JP for my explanation.

#### JP

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #32 on: 04/03/2012 21:28:33 »
It is not necessary to have change to demonstrate the arrow of time, only the passage of time.

Ok, as soon as you come up with a theory in which nothing changes, but we can measure time, let me know.

#### yor_on

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #33 on: 05/03/2012 01:48:09 »
Planck scales is a definition relating to what is possible for us to measure. "One Planck time is the time required for light to travel, in a vacuum, a distance of 1 Planck length."

"In physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify particular algebraic expressions appearing in physical law.

Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of natural units among other systems, but are considered unique in that these units are not based on properties of any prototype object, or particle (that would be arbitrarily chosen) but are based only on properties of free space. The universal constants that Planck units, by definition, normalize to 1 are the:

Gravitational constant, G;
Reduced Planck constant, ħ;
Speed of light in a vacuum, c;
Coulomb constant,
Boltzmann constant, kB (sometimes k).

Each of these constants can be associated with at least one fundamental physical theory: c with special relativity, G with general relativity and Newtonian gravity, ħ with quantum mechanics, ε0 with electrostatics, and kB with statistical mechanics and thermodynamics. Planck units have profound significance for theoretical physics since they simplify several recurring algebraic expressions of physical law by nondimensionalization. They are particularly relevant in research on unified theories such as quantum gravity.

Physicists sometimes semi-humorously refer to Planck units as "God's units". Planck units are free of anthropocentric arbitrariness. Some physicists argue that communication with extraterrestrial intelligence would have to employ such a system of units in order to be understood. Unlike the meter and second, which exist as fundamental units in the SI system for (human) historical reasons, the Planck length and Planck time are conceptually linked at a fundamental physical level."

It may not be the 'smallest' scale possible, but it also has to do with how you define 'reality'. Under Plank scale all classical definitions breaks down, and SpaceTime as we know it 'disappear'. And as we live in SpaceTime I would call that pretty special.

And that's also where our arrow should start to behave weirdly as I think of it.

#### yor_on

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #34 on: 05/03/2012 03:18:05 »
At that scale QM needs to quantify gravity, which hasn't been done yet, as far as I know?

But it has to do with that arrow and indeterminacy. At what scale becomes 'indeterminacy'? What happens to a 'field' as you scale it down to Plank size? Is it still a 'field', or does it become 'discrete bits', etc? A lot of physics ignore scales, as they find it improbable that the laws would differ by scaling something up or down. "Clearly, it cannot be a fundamental law of physics that processes involving N particles or fewer are reversible, while those with greater than N particles are irreversible. What is N? 100? 10,000? 3,486,756,493?"

But the way I look at it :) it do seems plausible. And doing like that 'fractals/repeating patterns' becomes interesting indeed, as well as 'emergences', changing the properties we measure. And as I define the arrow to be a very local process, springing out from that same scale in every point of SpaceTime, with indeterminacy and probability at its origin, I think of the Planck scale as a very special place, although I can't be sure of course.

And 'constants' becomes one of the most important things to search for, as they should define the patterns we see.
=

And 'fields' of course, not 'bits'. You can have excitations in a field, and those can be quantifiable but myself I prefer a 'field concept'. This is my own view but I expect fields to be what it is, and then we have relative motion creating excitations as well as .. etc etc :) But it also depends on how you define those 'fields'. And that's what the arrow defines for us, not anything static but something having a direction and a order, and doing it all 'locally'.

ah well, it's my view :)
« Last Edit: 05/03/2012 03:50:58 by yor_on »

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #35 on: 05/03/2012 08:50:13 »
yor_on

When I wrote
"Placnk time is the shortest quantum of time that is possible. "

I meant just that.
"In physics, a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction".
http://en.wikipedia.org/wiki/Quantum

I was not talking about quantum mechanics.

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #36 on: 05/03/2012 09:07:42 »
It is not necessary to have change to demonstrate the arrow of time, only the passage of time.

Ok, as soon as you come up with a theory in which nothing changes, but we can measure time, let me know.

That is not what I said.  What I said was "It is not necessary to have change to demonstrate the arrow of time, only the passage of time."

A plumb-bob (weight on a string) demonstrates the arrow of time by pointing towards the center of the Earth's gravity.  It does this without motion (change).  Release it and it will accelerate in the same direction.  This is proof of the arrow of time, both when static and in motion.  In motion of course it also demonstrates the 'passage' of time.

I don't think this is proposing a new theory, it's just common sense.

#### yor_on

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #37 on: 05/03/2012 11:29:27 »
Mike it sounds like we're thinking of different things here?

Imagine something frozen, no 'motion' anywhere to be measured in it. Is there a 'time' for it? For you measuring it still exist a arrow to measure in, but for whatever you froze? To measure must always involve 'change' for the observer, but not necessary for what you measure, if we use 'change' as a description of what a arrow do. It's trying for finding the simplest definition of what a arrow is.

As for a 'rate' of time, that's when I think of clocks. We use clocks to chop up the arrow into humanly adapted bits of 'time', adapted to the planet we live on. But I think I agree on the idea of 'time' being something more than the 'arrow' we see. There must be something deeper from where that arrow can come. The arrow may break down, but that doesn't answer what 'time' is, as I see it.

#### JP

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #38 on: 05/03/2012 13:57:11 »
It is not necessary to have change to demonstrate the arrow of time, only the passage of time.

Ok, as soon as you come up with a theory in which nothing changes, but we can measure time, let me know.

That is not what I said.  What I said was "It is not necessary to have change to demonstrate the arrow of time, only the passage of time."

A plumb-bob (weight on a string) demonstrates the arrow of time by pointing towards the center of the Earth's gravity.  It does this without motion (change).  Release it and it will accelerate in the same direction.  This is proof of the arrow of time, both when static and in motion.  In motion of course it also demonstrates the 'passage' of time.

I don't think this is proposing a new theory, it's just common sense.

Sorry, that doesn't work.  If you have no change a plumb bob hanging there tells you nothing.  You have no way of knowing if it's floating in space or pulled by gravity until you try to move it (which requires motion and the expenditure of energy) or until you drop it (which requires motion).

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #39 on: 05/03/2012 17:57:15 »
It is not necessary to have change to demonstrate the arrow of time, only the passage of time.

Ok, as soon as you come up with a theory in which nothing changes, but we can measure time, let me know.

That is not what I said.  What I said was "It is not necessary to have change to demonstrate the arrow of time, only the passage of time."

A plumb-bob (weight on a string) demonstrates the arrow of time by pointing towards the center of the Earth's gravity.  It does this without motion (change).  Release it and it will accelerate in the same direction.  This is proof of the arrow of time, both when static and in motion.  In motion of course it also demonstrates the 'passage' of time.

I don't think this is proposing a new theory, it's just common sense.

Sorry, that doesn't work.  If you have no change a plumb bob hanging there tells you nothing.  You have no way of knowing if it's floating in space or pulled by gravity until you try to move it (which requires motion and the expenditure of energy) or until you drop it (which requires motion).

I don't agree. The plumb-bob points downward and we know that is the direction that it will travel through space-time if released.   The arrow exists even without motion.  I agree entirely that with motion the arrow is much more obvious.

If you could lower a clock on a long piece of rope into the event horizon of a black hole it would gradually slow down until it stopped.  If the clock were to be pulled back out from the event horizon the clock would register the passage of time increasing.  The arrow of time for the clock pointed forward as it approached the EH and pointed forward as it left the EH.  Surely the arrow did not cease to exist when it was at the EH despite there being no 'passage' to time.

Imagine a hypothetical sealed box with a divider.  There are different gasses in the two compartments.  The box is chilled to absolute zero and the divider 'magically' removed.  The gases do not mix but the arrow of time is still there as we know that when the temperature rises the gases will mix.  At absolute zero, entropy is at a maximum and time has stood still.  An input of energy is necessary for the gases to mix.  Or to put it another way without an input of energy there can be no further increase in entropy.  Entropy being the main arrow of time.

We may not be able to demonstrate the arrow of time without motion but we are certainly aware of it.

#### yor_on

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #40 on: 05/03/2012 22:29:42 »
The arrow is local Mike, very local. It express itself through changes as I see it. you can make up a hypothetical situation in where for example someone set in stasis can 'think' but that is no proof. Take a vacuum, there you have indeterminacy, or ''virtual photons' aka 'zero point energy' according to main stream physics. Is that a arrow?

to me you always need a outcome for an arrow to show, something changing creating a past, a present with a future to assume. You could assume that a arrow should exist for all vacuum, but I don't think so myself, not unless that vacuum delivers 'outcomes' and 'changes', as virtual particles becoming real for example, then you have a outcome and a change, even if only momentarily, reverting. But for matter it's different, matter (mass) always interact and change.

But that is just a arrow, then you have 'time' itself. Whatever creates arrows.

#### yor_on

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #41 on: 05/03/2012 22:50:59 »
To see where we differ. If the arrow is around Planck scale then it exist everywhere, although with a vacuum as a special property. As long as we're talking mass that arrow will express itself. That you can use relative motion to create a new relation relative something, or a different speed, won't change the origin of that arrow. It's local, always of a same measure locally. Although you, when comparing 'frames of reference', find other 'clocks' to differ relative your local 'time' it doesn't change the fact that when you position yourself at that position, where that clock you once found to 'tick' out of sync was,  you will find that clock and yours to agree, and be in sync. And your lifespan never change relative your wrist watch, no matter where you go, or how fast.

You have one arrow, not many. The twin experiment isn't about you slowing or speeding up your 'time'. If it was your wristwatch would give you more or less time relative some biological clock you measure 'time' against, but it doesn't.

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #42 on: 06/03/2012 08:04:10 »
The arrow is local Mike, very local. It express itself through changes as I see it. you can make up a hypothetical situation in where for example someone set in stasis can 'think' but that is no proof. Take a vacuum, there you have indeterminacy, or ''virtual photons' aka 'zero point energy' according to main stream physics. Is that a arrow?

to me you always need a outcome for an arrow to show, something changing creating a past, a present with a future to assume. You could assume that a arrow should exist for all vacuum, but I don't think so myself, not unless that vacuum delivers 'outcomes' and 'changes', as virtual particles becoming real for example, then you have a outcome and a change, even if only momentarily, reverting. But for matter it's different, matter (mass) always interact and change.

But that is just a arrow, then you have 'time' itself. Whatever creates arrows.

No it isn't.  Entropy is the main arrow of time.  Gravity is 'probably' the main example of entropy and there is nowhere in the Universe that is not subject to gravity or entropy.  The arrow is not local but universal.  Time in the Universe 'essentially' only flows forward not backward. Only the passage of time is local to position and therefore variable.  Yes, there are many local arrows of time but they all point in the same direction as do 'essentially' all arrows of time within the Universe.

Time has two aspects, direction what we call the arrow of time and rate of passage.  It is possible to be aware of the direction of the arrow as I have pointed out in various examples above even without the passage of time.  I agree that being 'aware' of the direction is not the same as observing the direction which does require change (the passage of time).

To see where we differ. If the arrow is around Planck scale then it exist everywhere, although with a vacuum as a special property. As long as we're talking mass that arrow will express itself. That you can use relative motion to create a new relation relative something, or a different speed, won't change the origin of that arrow. It's local, always of a same measure locally. Although you, when comparing 'frames of reference', find other 'clocks' to differ relative your local 'time' it doesn't change the fact that when you position yourself at that position, where that clock you once found to 'tick' out of sync was,  you will find that clock and yours to agree, and be in sync. And your lifespan never change relative your wrist watch, no matter where you go, or how fast.

You have one arrow, not many. The twin experiment isn't about you slowing or speeding up your 'time'. If it was your wristwatch would give you more or less time relative some biological clock you measure 'time' against, but it doesn't.

What does that mean?  Planck scale is a measure of the passage of time not direction.  Direction is merely implied as the passage of time is only forward.

Essentially there is but one arrow of time in the Universe and that arrow points forward.  However there are many processes etc. that individually confirm the direction of that arrow.  The arrow of time associated with any process (change) is entropic in nature.  (entropic - to do with entropy)

#### JP

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #43 on: 06/03/2012 17:15:58 »
MikeS, as it's clear you're using this theory to expound your own theory on gravity, I've moved it to new theories.

#### yor_on

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #44 on: 06/03/2012 17:48:14 »
Good move JP. My views isn't exactly mainstream either I guess, although natural logic following what I expect to be true before. I've just recently started to wonder about where the logic implications of a very local arrow would take me. And it's actually Mikes idea, forcing me to think about temperature and 'the arrow' and the rest of you guys discussing it, that made me consider it. It's exactly as when SoulSurfer gave me his idea about radiation, and made me see its implications for my thinking.

So keep on thinking Mike :)
We all benefit from discussing.

« Last Edit: 06/03/2012 17:50:16 by yor_on »

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #45 on: 07/03/2012 08:48:08 »
Thanks yor_on, a few words of appreciation mean a lot to me.

I am just interested in knowledge but not knowledge for knowledge sake.  We would never discover anything new if we never pushed the boundaries a little.  Debate is good.

Mike

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #46 on: 07/03/2012 08:59:18 »
MikeS, as it's clear you're using this theory to expound your own theory on gravity, I've moved it to new theories.

JP
Fair enough but what have I actually said that mainstream would not agree with or is it simply that mainstream has no consensus of opinion in certain areas?  I don't really think that I am proposing anything new.  I am merely trying to clarify much of the 'fog' on gravity, entropy and time.

#### JP

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #47 on: 09/03/2012 13:13:09 »
MikeS,
Sorry for the delay in responding.  I've been busy this week.

The idea that time exists and has an arrow isn't controversial.  Your claim that gravity is the primary driver of that arrow is non-mainstream as is your idea that if you removed all energy from a system, gravitational energy would still provide a strong direction for time.  Obviously gravity has energy and it has a role to play in the energy/entropy flow that does define the arrow of time, but your arguments seem to be going in a different direction.

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #48 on: 09/03/2012 14:47:01 »
MikeS,
Sorry for the delay in responding. I've been busy this week.

The idea that time exists and has an arrow isn't controversial.  Your claim that gravity is the primary driver of that arrow is non-mainstream as is your idea that if you removed all energy from a system, gravitational energy would still provide a strong direction for time.  Obviously gravity has energy and it has a role to play in the energy/entropy flow that does define the arrow of time, but your arguments seem to be going in a different direction.
No prob.
Its not the primary arrow, that's entropy and gravity is perhaps the main example of that.
I think that is true, well gravity.
Does it?  Probably not, but I have to think that one through when I haven't had a beer.
True.
I don't think so.  In what way?
« Last Edit: 09/03/2012 18:25:43 by MikeS »

#### MikeS

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #49 on: 10/03/2012 13:57:13 »
MikeS,
Sorry for the delay in responding. I've been busy this week.

The idea that time exists and has an arrow isn't controversial.  Your claim that gravity is the primary driver of that arrow is non-mainstream as is your idea that if you removed all energy from a system, gravitational energy would still provide a strong direction for time.  Obviously gravity has energy and it has a role to play in the energy/entropy flow that does define the arrow of time, but your arguments seem to be going in a different direction.
No prob.
Its not the primary arrow, that's entropy and gravity is perhaps the main example of that.
I think that is true, well gravity.
Does it?  Probably not, but I have to think that one through when I haven't had a beer.
True.
I don't think so.  In what way?

Ok so I got it wrong.

Yes gravity does (in a sense) have energy.

Question, so how does gravity cause objects to move?

Example 1
For an object to have Gravitational Potential Energy above the Earth's surface, it first has to be lifted there.  The energy expended in lifting it equals its gravitational potential when stationary (at a fixed distance) above the Earth's surface.  This also equals its kinetic energy when released and in free fall.
This example does not require the an input of energy.  The energy has already been expended.

Example 2
Two massive objects are gravitationally attracted to each other.  Where does the energy come from that is required to make them travel towards each other?

When they combine, time (dilates) passes slower for them as a pair than it did for them individually.  This represents a reduction in usable energy.  In other words it's an example of entropy.  It represents the most stable state which is obtained by reaching the lowest possible energy level.
In this example, the energy came from time dilation.

The first part of example (1)  'lifting the object', is example (2) run backwards in time.
« Last Edit: 10/03/2012 14:05:59 by MikeS »

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##### Re: If you cooled an atomic clock to just above absolute zero would time dilate?
« Reply #49 on: 10/03/2012 13:57:13 »