[Farsight]

Er, well the second is defined as the interval for a certain number of the atomic events. The number was chosen to line up with more traditional definitions for the second. As you point out, the fundamental "tick" is an electromagnetic event with the atom.

And if the space is different, the underlying motion associated with this event is slower. It's a spin-flip, the electron is turning over. You can get a feel for this by stretching an eleastic band over your finger and thumb. Stick a pencil in, and turn the pencil over 180 degrees tensioning the elastic, then let go. It vibrates back and forth.   

The light output could be delayed in a very variable fashion, but it would have no effect on the frequency of the microwave resonator. The light output is only sampled periodically to make very infrequent and very minute adjustments to the frequency of the microwave resonator. I believe the detector only responds to the number of photons that reach it. I'm not sure how they know to adjust up or down because I would assume that the light output will diminish if the resonator is slow or fast relative to the caesium events.

It makes no odds, electromagnetic phenomena propagate at a slower rate in a region of lower gravitational potential.

Being pedantic, you can't really say that the events are happening at a "slower rate", because that seems to suggest that time itself is invariant.

Things move slower, that's all. When the motion is cyclic like the spin-flip, we call the result an event.

[Farsight]

Both spaces are flat Minkowski space and I think we are assuming that the physical laws are the same, as measured locally, at each location and that it would be expected that the gravitational potential is purely relative and has no meaning in absolute terms. Are these correct assumptions to work with?

Yes, both spaces are flat and local physical laws are the same. But whilst that  gravitational potential is relative, it does have an absolute meaning. It's saying something pretty fundamental about the nature of space at that location, and relative measurements tell you that the difference between locations is very real.   

If, then, the only difference is that space is "stretched" more in one region than the other then this "scaling" must apply to (x,y,x,-ct) equally mustn't it? If not what coordinate transformation would apply?

I wouldn't say space is "stretched". Instead it's "squashed" in the radial direction, and we're trying to set that aside to make it clear that the -ct term has changed. The best colloquial term I can find is that space is "stronger" in a region of lower gravitational potential.

In SR the basis for the Lorentz transformation is the constancy of c to all observers. Is the only effect of gravitational potential (Φ) that c is a function of Φ and that this would be the basis of any coordinate transformation?

Not quite, because of the radial length contraction that equates to the SR length contraction. The effect of gravitational potential on c is the one to home in on. 

This seems reasonable but is it all consistent with observation or gedanken experiments?

Yes, absolutely. Clocks run slower, even light clocks, along with all physical processes. We have the GPS clock adjustment, and it's the Shapiro Delay. The time component of this is the most important, more important than any path change. 

Edit: Amrit is correct when he says this is not a new theory. The concept that "time is change" goes back to Aristotle, it resurfaced as Presentism in 1908, and was only fully appreciated by Godel and Einstein in 1949. And I'm afraid clocks don't measure time. What they actually measure is motion. This might be cyclical motion such as the turning of a cog or the vibration of a crystal or an electron bond, and we might label these cyclical motions as events. But the important thing to grasp is if that motion goes slower, the clock goes slower. It's not time going slower, it's motion. And that motion is through space. When you "stop the clock" or "freeze the frame" what you're actually stopping is motion. I've written an essay called "Time Explained" to flesh out the details of all this, but people consider this sort of thing to be "New Theories". That's because it's not in line with the common current concept of time as something that flows and that we travel through. It isn't, and we don't. There is absolutely no scientific evidence to back up this common concept of time, none whatsoever.

[graham.d]

"Yes, both spaces are flat and local physical laws are the same. But whilst that  gravitational potential is relative, it does have an absolute meaning. It's saying something pretty fundamental about the nature of space at that location, and relative measurements tell you that the difference between locations is very real." - Farsight

This is what I was getting at but I have not really thought it through yet. Unfortunately I have to work too :-) If Gravitational Potential has an absolute range, then there must come a point where the this should be detectable within the spacetime region itself - like a BH singularity for example. It is unusual in nature to find brickwall phenomena where there is no effect of a parameter but when it reaches a certain value there is a dramatic change. Though, come to think of it, it may be that the assumption of flatness may start to be invalid, covering a smaller and smaller region, as the potential gets lower. Then this would be noticeable. Though this would depend on whether this changed faster than the the space compression.

The radial direction for the sqashing of space would presumably not be important if we could assume that the spacetime region was sufficiently flat (a small enough volume for example). I'm trying to stick with a Minkowski metric rather than a Schwartzchild metric - but maybe this cannot be done. Going back to the mirror spacing, this would mean the mirror spacing would be smaller as viwed by a distant observer at a higher potential. This would then mean that that c would have to change (be slower) with a higher order than the space compression to produce the gravitational time dilation. Have you a web reference that gives the coordinate tranformation that should be applied for a change in Gravitational Potential? It should take these effects into account.

[Farsight]

There is a "brick wall" phenomenum, graham - at the event horizon of a black hole. The coordinate speed of light at the event horozon is zero according to all observers in the universe at large, and the radial length contraction is total. This is the Schwartzchild metric, where the singularity is at the event horizon "surface", rather than at a point in the centre.

No, I'm afraid I don't have a web reference for a coordinate tranformation that should be applied for a change in gravitational potential. This: http://casa.colorado.edu/~ajsh/schwp.html isn't bad, but the problem is that if light has stopped you don't actually have a coordinate system any more. All measurements take a finite time in your proper time, but forever as far as the rest of the universe is concerned, so those measurements are never actually made.

This is quite a good article too: http://www.mathpages.com/rr/s7-02/7-02.htm. The author doesn't agree with me, but he does mention the Weinberg field interpretation, which is what I'm talking about here.

[graham.d]

Thanks, I'll take a look when time permits. I was referring to a coordinate transformation before the limit of a singularity although if it doesn't include that, it is incomplete. In any case, my point was to see whether the approach of the singularity was detectable (before the singularity was reached) from inside the spacetime region that was being "compressed". Having thought about it, I think not. I mentioned before that it may be increasingly difficult to have a region of approximately flat space approaching such a condition, and this would be detectable. This is analogous to increasing tidal forces when approaching a BH however, a sufficiently huge BH would allow crossing of such a horizon without noticeable tidal forces (i.e. local space is reasonably flat). To take this analogy further, does this mean the gravitational potential has gone negative? I appreciate this would have no meaning to the outside observer any more than the state of anything crossing a BH event horizon.

Mathpages are generally excellent - I don't know why I didn't look there anyway. I will take a look. Thanks.

[Geezer]

Er, well the second is defined as the interval for a certain number of the atomic events. The number was chosen to line up with more traditional definitions for the second. As you point out, the fundamental "tick" is an electromagnetic event with the atom.

And if the space is different, the underlying motion associated with this event is slower. It's a spin-flip, the electron is turning over. You can get a feel for this by stretching an eleastic band over your finger and thumb. Stick a pencil in, and turn the pencil over 180 degrees tensioning the elastic, then let go. It vibrates back and forth.   

The light output could be delayed in a very variable fashion, but it would have no effect on the frequency of the microwave resonator. The light output is only sampled periodically to make very infrequent and very minute adjustments to the frequency of the microwave resonator. I believe the detector only responds to the number of photons that reach it. I'm not sure how they know to adjust up or down because I would assume that the light output will diminish if the resonator is slow or fast relative to the caesium events.

It makes no odds, electromagnetic phenomena propagate at a slower rate in a region of lower gravitational potential.

Being pedantic, you can't really say that the events are happening at a "slower rate", because that seems to suggest that time itself is invariant.

Things move slower, that's all. When the motion is cyclic like the spin-flip, we call the result an event.

LOL - it's not really "slower". If we are measuring time by counting atomic events, we always observe the same number of atomic events for a particular amount of time. My point is that we have to be very careful when we use measures that are a function of time.

[Geezer]

I guess a good question is whether or not a "good" clock (meaning one that measures local time accurately) is in practice any different than measuring time itself.  I don't know the answer, but I've been assuming that it isn't.

JP - I think that any clock is actually measuring the passage of time in its locality. And clocks can include anything from atomic activity, chemical processes, large pendulums and rotating orbs. I think our intution suggests there is some sort of absolute time, even though science tells us it's not so.

We sense the the passage of time is smooth, but if it was in fact quite jittery I think it would be impossible to detect that it actually was jittery without some sort of absolute timing device which was independent of local time (which I think is impossible!)

I'm going to have to lie down for a bit now  []

[amrit (OP)]

Time does not run on its own. There is no passage of time.
Time dilatations means exactly that clock run slower.
Not because of time run slower.
There is no physical time behind run of a clock.
Clock run in a timeless space.

[Farsight]

..In any case, my point was to see whether the approach of the singularity was detectable (before the singularity was reached) from inside the spacetime region that was being "compressed". Having thought about it, I think not.

You certainly won't observe the time dilation or the  length contraction locally, but there actually be a way to find out that things are changing by measuring the fine structure constant. Search the internet for "tests of Lorentz invariance" to read about other ideas for this. I'm all for relativity, but I wouldn't rule out some subtle breach here.

I mentioned before that it may be increasingly difficult to have a region of approximately flat space approaching such a condition, and this would be detectable. This is analogous to increasing tidal forces when approaching a BH however, a sufficiently huge BH would allow crossing of such a horizon without noticeable tidal forces (i.e. local space is reasonably flat). To take this analogy further, does this mean the gravitational potential has gone negative? I appreciate this would have no meaning to the outside observer any more than the state of anything crossing a BH event horizon.

I don't see how a gravitational potential can go negative. The gradient in gravitational potential is "why things fall down". If there's no gradient at all, things don't fall down. If the gradient is uniform you still fall down, but there's no tidal force. There's only a tidal force when the gradient changes say between your head and your feet. There's a gradient in the gradient, as it were.

[Farsight]

LOL - it's not really "slower". If we are measuring time by counting atomic events, we always observe the same number of atomic events for a particular amount of time. My point is that we have to be very careful when we use measures that are a function of time.

It really is slower, Geezer. If you could actually film those atomic events at the different locations then put them up on a split screen, you'd see it. And the definition of the second is the other way round. The number of atomic events defines the second. It increases with reducing gravitational potential because the motion underlying the events is slower. Amrit is right. Time doesn't "run" and it doesn't "pass". When a clock goes slower it's because things move slower. Godel and Einstein really did work this out in 1949.

[Geezer]

LOL - it's not really "slower". If we are measuring time by counting atomic events, we always observe the same number of atomic events for a particular amount of time. My point is that we have to be very careful when we use measures that are a function of time.

It really is slower, Geezer. If you could actually film those atomic events at the different locations then put them up on a split screen, you'd see it. And the definition of the second is the other way round. The number of atomic events defines the second. It increases with reducing gravitational potential because the motion underlying the events is slower. Amrit is right. Time doesn't "run" and it doesn't "pass". When a clock goes slower it's because things move slower. Godel and Einstein really did work this out in 1949.

OK - I'll admit I'm being pedantic, but I think it's important to precise when we talk about time.

I don't think we can really use the terms "slower" or "faster" because speed is a function of time, so there is no difference in speed. There is no "absolute" time, so when you say "slower", I think you really mean that the count of observed events at different locations can differ (assuming we have some method to observe or record those events.)

[graham.d]

"I don't see how a gravitational potential can go negative. The gradient in gravitational potential is "why things fall down". If there's no gradient at all, things don't fall down. If the gradient is uniform you still fall down, but there's no tidal force. " - Farsight

I do understand this Farsight but linearity in potential, in itself, does not preclude a negative value. You can have linearity in Potential from + to - infinity with respect to an arbtrary spacial measure (say r) and its differential with respect to r would be a constant. It is also obvious that it would be the second derivative that would result in tidal forces.

My point was simply that someone can pass through a BH event horizon and there would be no specific local measurement to mark that event providing the BH were large enough to minimise destructive tidal forces. But what would be their Gravitational Potential? There is no doubt that it would continue to fall as they moved toward the BH centre. From a distant observer's perspective they would have zero GP as they reach the EH but that time dilation would infinitely delay the event. In this sense negative GP values are "cosmically censored". From the perspective of the person crossing a BH EH, I guess it would not be the first thing on his mind. I'm never sure what he would see though there are some interesting simulations and animations on the web. Perhaps he should see the distant observer having infinite GP.

Anyway, this is not so profound as I first thought and is not leading to any great insight. It does suggest that GP would depend on from whose perspective it is being measured and that the scale can slide so as to define the zero value at (say) an EH.

[amrit (OP)]

LOL - it's not really "slower". If we are measuring time by counting atomic events, we always observe the same number of atomic events for a particular amount of time. My point is that we have to be very careful when we use measures that are a function of time.

It really is slower, Geezer. If you could actually film those atomic events at the different locations then put them up on a split screen, you'd see it. And the definition of the second is the other way round. The number of atomic events defines the second. It increases with reducing gravitational potential because the motion underlying the events is slower. Amrit is right. Time doesn't "run" and it doesn't "pass". When a clock goes slower it's because things move slower. Godel and Einstein really did work this out in 1949.

OK - I'll admit I'm being pedantic, but I think it's important to precise when we talk about time.

I don't think we can really use the terms "slower" or "faster" because speed is a function of time, so there is no difference in speed. There is no "absolute" time, so when you say "slower", I think you really mean that the count of observed events at different locations can differ (assuming we have some method to observe or record those events.)

speed is not function of time, speed is a function of motion that run in space (and not in time)
ve measure speed with clocks

v = d/tn  where tn is a last "tick" of clock.

[JP]

speed is not function of time, speed is a function of motion that run in space (and not in time)
ve measure speed with clocks

v = d/tn  where tn is a last "tick" of clock.

I disagree.  Everything I've ever learned in mainstream physics on the subject says that speed a ratio of change in position to change in time.  Classically speaking, speed=dx/dt (dx distance moved in a short time, dt).  Do you have a source for your claim?

[amrit (OP)]

speed is not function of time, speed is a function of motion that run in space (and not in time)
ve measure speed with clocks

v = d/tn  where tn is a last "tick" of clock.

I disagree.  Everything I've ever learned in mainstream physics on the subject says that speed a ratio of change in position to change in time.  Classically speaking, speed=dx/dt (dx distance moved in a short time, dt).  Do you have a source for your claim?

Yes now we will change this idea as there is no experimental data for it. Nothing happens in time as time is a mind frame through which we experience motion in space.

[Farsight]

I disagree. Everything I've ever learned in mainstream physics on the subject says that speed [is] a ratio of change in position to change in time.

There no easy way to say this, JP, but it has to be said: everything you've ever learned on the subject is wrong. It sounds awful I know, but look to the evidence. What we actually see is space and motion through it. We don't see time flowing or any travel through time. The motion is through space. So motion gains precedence over time. Time is reduced to a cumulative measure of local motion, such as the motion of light or caesium spin-flips. For a reference, see A World Without Time: The Forgotten Legacy of Godel and Einstein. Godel and Einstein worked it out in 1949: you don't need time to have motion, you need motion to have time.

Amrit is right. Shame he's wrong about that photon clock, but hey-ho. Hi amrit!

[Geezer]

speed is not function of time, speed is a function of motion that run in space (and not in time)
ve measure speed with clocks

v = d/tn  where tn is a last "tick" of clock.

I disagree.  Everything I've ever learned in mainstream physics on the subject says that speed a ratio of change in position to change in time.  Classically speaking, speed=dx/dt (dx distance moved in a short time, dt).  Do you have a source for your claim?

Yes now we will change this idea as there is no experimental data for it. Nothing happens in time as time is a mind frame through which we experience motion in space.

JP is providing the accepted definition for speed. If you remove time from the definition, I think you are referring to something other than speed. To avoid confusion you should probably use a different name for whatever it is you are referring to.

Mind you, it would be good if you are correct, because, if you are, it means I'm not really getting older. I just think I'm getting older as I move around in space  []

[JP]

I disagree. Everything I've ever learned in mainstream physics on the subject says that speed [is] a ratio of change in position to change in time.

There no easy way to say this, JP, but it has to be said: everything you've ever learned on the subject is wrong. It sounds awful I know, but look to the evidence. What we actually see is space and motion through it. We don't see time flowing or any travel through time. The motion is through space. So motion gains precedence over time. Time is reduced to a cumulative measure of local motion, such as the motion of light or caesium spin-flips. For a reference, see A World Without Time: The Forgotten Legacy of Godel and Einstein. Godel and Einstein worked it out in 1949: you don't need time to have motion, you need motion to have time.

Amrit is right. Shame he's wrong about that photon clock, but hey-ho. Hi amrit!

I did a bit of poking around to find out what Godel actually did, scientifically.  What Godel did, it seems, was to work out solutions to Einstein's field equations that show that an object moving normally through the universe (i.e. on time-like paths) could go back in time. 

Does this cause problems with physics in our universe?  Almost certainly not, since Godel's universes are not our universe.  It might have philosophical implications about time being a "special" dimension. 

At any rate, back to your post.  I disagree with the conclusions you're drawing.  We certainly don't see "space and motion through it."  What we "see" (and how GR describes the universe) is paths in space-time.  What we locally define as velocity is a measurement of the slope between the space and time components of that path at any point.  Since these paths are geometrical objects, what you can physically measure are distances.  From these distances you can derive slopes.  Therefore, time is a fundamental quantity (it's a measure of "distance") and speed is a derived quantity (it's a measure of slope, or a ratio of "distances.")

Can you provide any scientific evidence to the contrary?

[amrit (OP)]

I disagree. Everything I've ever learned in mainstream physics on the subject says that speed [is] a ratio of change in position to change in time.

There no easy way to say this, JP, but it has to be said: everything you've ever learned on the subject is wrong. It sounds awful I know, but look to the evidence. What we actually see is space and motion through it. We don't see time flowing or any travel through time. The motion is through space. So motion gains precedence over time. Time is reduced to a cumulative measure of local motion, such as the motion of light or caesium spin-flips. For a reference, see A World Without Time: The Forgotten Legacy of Godel and Einstein. Godel and Einstein worked it out in 1949: you don't need time to have motion, you need motion to have time.

Amrit is right. Shame he's wrong about that photon clock, but hey-ho. Hi amrit!

Yes this picture here on the first page how mirrors are moving and so photon has longer way and photon clock ticks slower is ridiculous.
Mora than that: when you move mirrors that atom run between them along the direction of the fast aircraft motion that photon clock should shrink and so “tick” faster what is contrary to SR

[amrit (OP)]

I disagree. Everything I've ever learned in mainstream physics on the subject says that speed [is] a ratio of change in position to change in time.

There no easy way to say this, JP, but it has to be said: everything you've ever learned on the subject is wrong. It sounds awful I know, but look to the evidence. What we actually see is space and motion through it. We don't see time flowing or any travel through time. The motion is through space. So motion gains precedence over time. Time is reduced to a cumulative measure of local motion, such as the motion of light or caesium spin-flips. For a reference, see A World Without Time: The Forgotten Legacy of Godel and Einstein. Godel and Einstein worked it out in 1949: you don't need time to have motion, you need motion to have time.

Amrit is right. Shame he's wrong about that photon clock, but hey-ho. Hi amrit!

I did a bit of poking around to find out what Godel actually did, scientifically.  What Godel did, it seems, was to work out solutions to Einstein's field equations that show that an object moving normally through the universe (i.e. on time-like paths) could go back in time. 

Does this cause problems with physics in our universe?  Almost certainly not, since Godel's universes are not our universe.  It might have philosophical implications about time being a "special" dimension. 

At any rate, back to your post.  I disagree with the conclusions you're drawing.  We certainly don't see "space and motion through it."  What we "see" (and how GR describes the universe) is paths in space-time.  What we locally define as velocity is a measurement of the slope between the space and time components of that path at any point.  Since these paths are geometrical objects, what you can physically measure are distances.  From these distances you can derive slopes.  Therefore, time is a fundamental quantity (it's a measure of "distance") and speed is a derived quantity (it's a measure of slope, or a ratio of "distances.")

Can you provide any scientific evidence to the contrary?

There is no time in the universe. Photon (and all other motions) moves in space only. With clocks we measure numerical order of motion.
Never until know time was measured or observed as motion is observed and experienced. We measure with clocks motion and not time. Time is in the mind, we experience motion in time "past-present-future" that is a mind creation. Universe is without time as predicted by Einstein and Godel. See my post "Block Universe" in new theories.