Can time dialation really just be the slowdown of physical processes?

  • #26
PAllen
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Lets consider a simpler constant velocity scenario. Let us say we have observer A on top of a huge tower of height r and observer B is orbiting at near light speed relative to A at radius R. As B passes A they would both agree the other's clock is running slower. When B completes an orbit both will agree less total time has passed on B's clock. Agree?
No. Having done the calculation I recommended, I see there is no such discrepancy. For circular motion, there is asymmetry - at all times, A thinks B's clock is slower, and B thinks A's clock is faster.
Secondly, if something was orbiting at near light speed, the centripetal forces would be enormous and there would be an additional time dilation effect on B similar to gravitational time dilation due to the equivalence principle. Agree?
You can model it this way, but such arguments are tricky. Certainly it justifies the lack of symmetry.
P.S. I might be wrong on that last one. I seem to recall an experiment that demonstrated that the time dilation of a particle in a cyclotron is purely a factor of its relative speed and completely independent of the acceleration. Hmmmm. Was it that you could attribute the time dilation to either speed or equivalent gravity but not both? :confused:

Anyway, any equivalent gravitational time dilation would not be reciprocal.
The time dilation of particle in accelerator can be computed purely based on its speed, but the effect is asymmetric. The lab thinks the particle's time is slow; the particle thinks the lab's time is fast.
 
  • #27
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I don't care much for poorly defining a term and then going off on a logic trip based on it. :wink:
As far as I know, we have yet to determine if time is analogue or made up quanta. Certainly we have never measured anything with sub-Planckian frequencies. As I recall, one of the concerns with Steven Hawking's explanation of the Hawking radiation, is that it requires sub-Planckian frequencies, so that seems to a concern to some in field. Also, Einstein demonstrated that energy comes in packets or quanta and from that it follows that light frequencies and wavelengths occur in discrete steps rather than being a continuous spectrum. I think this is probably a open subject. To me the universe makes a lot more sense in terms of granular discrete units, even it turns out that not all quanta are equal to Planckian units. Almost certainly the quanta of mass if the Planck mass but I think it too early to tell if the Planck unit for time is more physically fundamental that an arbitrary unit.
 
  • #28
As far as I know, we have yet to determine if time is analogue or made up quanta. Certainly we have never measured anything with sub-Planckian frequencies. As I recall, one of the concerns with Steven Hawking's explanation of the Hawking radiation, is that it requires sub-Planckian frequencies, so that seems to a concern to some in field. Also, Einstein demonstrated that energy comes in packets or quanta and from that it follows that light frequencies and wavelengths occur in discrete steps rather than being a continuous spectrum. I think this is probably a open subject. To me the universe makes a lot more sense in terms of granular discrete units, even it turns out that not all quanta are equal to Planckian units. Almost certainly the quanta of mass if the Planck mass but I think it too early to tell if the Planck unit for time is more physically fundamental that an arbitrary unit.
A quantum of time doesn't fit into any theory I'm aware of; what are you talking about? Time is either a measurement, or a dimension; you might as well ask for the quanta of length. These are not things which ask for or require quanta, even if they have a limit to their divisibility.
 
  • #29
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No. Having done the calculation I recommended, I see there is no such discrepancy. For circular motion, there is asymmetry - at all times, A thinks B's clock is slower, and B thinks A's clock is faster.
I disagree on the grounds that for a very large orbital radius, B's path locally is almost a straight line and it approximates simple Special Relativity and A thinks B's clock is slower and B thinks A's clock is slower. Special Relativity includes (as I am sure you know) transverse Doppler time dilation effect and taking everything else into account including the relativity of simultaneity and am pretty sure we have done this calculation in the past and the relationship was symmetrical.

The time dilation of particle in accelerator can be computed purely based on its speed, but the effect is asymmetric. The lab thinks the particle's time is slow; the particle thinks the lab's time is fast.
Is this not essentially the same in principle as the object orbiting the Earth?
 
  • #30
PAllen
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As far as I know, we have yet to determine if time is analogue or made up quanta. Certainly we have never measured anything with sub-Planckian frequencies. As I recall, one of the concerns with Steven Hawking's explanation of the Hawking radiation, is that it requires sub-Planckian frequencies, so that seems to a concern to some in field. Also, Einstein demonstrated that energy comes in packets or quanta and from that it follows that light frequencies and wavelengths occur in discrete steps rather than being a continuous spectrum. I think this is probably a open subject. To me the universe makes a lot more sense in terms of granular discrete units, even it turns out that not all quanta are equal to Planckian units. Almost certainly the quanta of mass if the Planck mass but I think it too early to tell if the Planck unit for time is more physically fundamental that an arbitrary unit.
Einstein explained that light of a given frequency comes in discrete chunks of energy. He did not find, and there is zero evidence, that freqency and period are not condinuos quantities. One consequence of assuming they must be, is that you accept that velocity is quantized - since changing your velocity relative to a source continuosly changes its frequency (as you measure it).

So, whether your hypothesis is true or not, it is outside of GR + QFT as currently understood.
 
  • #31
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I don't care much for poorly defining a term and then going off on a logic trip based on it. :wink:
That first sentence was just my "right brain" talking. You could have easily dispensed it and considered only the parts that come after.

Frequency is simply cycles per unit of "time", so what we call "time" is simply just an arbitrary number that represents a cycle.

In fact, the second is now defined as:

"The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."

In other words, it means that there is 1/9,192,631,770th of a second per cycle of the "radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom".

It would seem that as one adds more energy to a particle, whereby it attains more mass and inertia as well, the rate of time in an object goes down to a proportional extent. Realize that objects in an inertial, non-accelerating, accelerated frame will experience a clock slowdown proportional to the amount of energy had by it. A meson decays slower when moving relativistically, even if it is a straight line, and even when it is not accelerating!

If you have two mesons moving in opposite directions relativistically, you can consider a frame of reference where one meson is stationary, and another frame of reference where the other meson is stationary. If you have a third observer at the center of momentum frame of both mesons whereat both mesons collide it at the same time and decay at the same time (post-deceleration relative to the center of momentum), then it would follow that, in the two aforementioned frames, the meson in one frame decays at the same rate as the other. Therefore, the delay in the decay of a meson has nothing to do with relative motion to an arbitrary observer. It is determined inversely to the amount of energy that the meson has, which is based upon its invariant mass, which is independent of the observer chosen.
Had I instead wrote just that, then you couldn't claim that I based all of it on my not-to-be-taken-too-literally assertion that "time is simply inverse frequency".
 
  • #32
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Lets consider a simpler constant velocity scenario. Let us say we have observer A on top of a huge tower of height r and observer B is orbiting at near light speed relative to A at radius R. As B passes A they would both agree the other's clock is running slower. When B completes an orbit both will agree less total time has passed on B's clock. Agree?
I agree if the first observation is performed with a momentarily co-moving inertial frame, or based on a momentary calibration in order to establish a nearly inertial frame (in principle that may just be possible).
[...] I seem to recall an experiment that demonstrated that the time dilation of a particle in a cyclotron is purely a factor of its relative speed and completely independent of the acceleration. Hmmmm. Was it that you could attribute the time dilation to either speed or equivalent gravity but not both? :confused:

Anyway, any equivalent gravitational time dilation would not be reciprocal.
Exactly! If you count with both, you count the same effect double. :smile:
 
  • #33
PAllen
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I disagree on the grounds that for a very large orbital radius, B's path locally is almost a straight line and it approximates simple Special Relativity and A thinks B's clock is slower and B thinks A's clock is slower. Special Relativity includes (as I am sure you know) transverse Doppler time dilation effect and taking everything else into account including the relativity of simultaneity and am pretty sure we have done this calculation in the past and the relationship was symmetrical.
This 'limiting' argument is the one I made a few posts back to samshorn. He suggested I follow my advice and calculate and would find I was wrong. He was correct in this.

Transverse doppler correctly explains lab's perception of circular moving emitter. For the reverse, you cannot use a formula based on inertial frames without care. Instead, imagine an emitter in the lab in the center of a the particle's motion. It is emitting spherical wave fronts. In the lab inertial frame, you compute that the time between each front intersecting the particle differs by less proper time for the particle than lab time between fronts. Thus the particle experiences higher frequency. Expanding the radius doesn't change this. Circular motion just cannot be modeled inertially.

Further showing the traps here, if you compare the circular moving body to an adjacent inertial body (rather than one at its center of motion), you *can* approximate them as inertial frames in relative motion.
Is this not essentially the same in principle as the object orbiting the Earth?
Yes, which is why I wanted to correct my original post after samshorn pointed out my error.
 
  • #34
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Lets consider a simpler constant velocity scenario. Let us say we have observer A on top of a huge tower of height r and observer B is orbiting at near light speed relative to A at radius R. As B passes A they would both agree the other's clock is running slower. When B completes an orbit both will agree less total time has passed on B's clock. Agree?
No. Having done the calculation I recommended, I see there is no such discrepancy. For circular motion, there is asymmetry - at all times, A thinks B's clock is slower, and B thinks A's clock is faster.
Lets consider a simpler constant velocity scenario. Let us say we have observer A on top of a huge tower of height r and observer B is orbiting at near light speed relative to A at radius R. As B passes A they would both agree the other's clock is running slower. When B completes an orbit both will agree less total time has passed on B's clock. Agree?
I agree if the first observation is performed with a momentarily co-moving inertial frame, or based on a momentary calibration in order to establish a nearly inertial frame (in principle that may just be possible).
PAllen and harrylin obviously disagree with each other. Okay folks, so what is the consensus?
 
  • #35
PAllen
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PAllen and harrylin obviously disagree with each other. Okay folks, so what is the consensus?
Actually, I don't know that Harrylin and I disagree. See the 3d paragraph of my post #33. I think this is what Harrylin is referring to.
 
  • #36
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A quantum of time doesn't fit into any theory I'm aware of; what are you talking about? Time is either a measurement, or a dimension; you might as well ask for the quanta of length. These are not things which ask for or require quanta, even if they have a limit to their divisibility.
To me a limit to divisibility is a definition of quanta. Plank came up with his units when he solving the black body problem and the "ultraviolet catastrophe". The only reason the ultraviolet catastrophe does not occur in reality is because wavelengths and frequencies occur in discrete units and the maximum possible frequency is 1/(Planck time unit). Einstein demonstrated that energy also comes in discrete quanta. Planck units occur in the equations for:

Thermal Energy per particle per degree of freedom.
Boltzmann's entropy formula.
Plack's relation for energy and angular frequency.
Planck's law for black body temperature.
Bekenstein-Boltzmann constant.
Bekenstein-hawking black hole entropy.
Schrodinger's equation.
Coulomb's law.
Maxwell's equations.

Ref: http://en.wikipedia.org/wiki/Planck_units#Planck_units_simplify_key_equations

The quanta of length (for wavelengths anyway) comes about naturally as a result of the constant speed of light and the quanta of time. A quanta of time means light has frequencies that are discrete quanta and because frequency*wavelength=speed of light, wavelengths naturally occur as discrete quanta. You only need time to be in discrete units and everything else related to time such as frequency, wavelength, energy etc. becomes discrete.
 
  • #37
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Actually, I don't know that Harrylin and I disagree. See the 3d paragraph of my post #33. I think this is what Harrylin is referring to.
Earlier you seemed to disagree.

Nvm.

Lets consider a simpler constant velocity scenario. Let us say we have observer A on top of a huge tower of height r and observer B is orbiting at near light speed relative to A at radius R. As B passes A they would both agree the other's clock is running slower. When B completes an orbit both will agree less total time has passed on B's clock. Agree?
The funny thing is that this is not actually describing a constant velocity scenario. The directions of the motions are changing. SR cannot model this. This is exactly like an orbiting version of the twin paradox. It should be obvious to anyone who understands the twin paradox that there is a discrepancy that will cause clock B to lag behind clock A, just as what you would expect for the relativistic twin in the twin paradox. The circular motion does not reduce this effect. Either the time of B lags behind A, or you must somehow refute the resolution to the twin paradox.
 
  • #38
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PAllen and harrylin obviously disagree with each other. Okay folks, so what is the consensus?
Not necessarily:
- We agree with yuiop about the measurement based on a co-moving inertial frame.
- For a measurement based on the rotating system itself, If I correctly understood him then PAllen was thinking of a for circular motion uncorrected Doppler measurement, an analysis that I did not make. I had in mind a comparison of light signals from the Earth's clock with two temporarily Einstein-synchronised clocks.
 
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  • #39
PAllen
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Earlier you seemed to disagree.

Nvm.
Well, looking back I did not always distinguish a comparison between rate of an adjacent inertial clock with one at the center of motion (for a circularly moving body). So I don't know there is disagreement, just incomplete descriptions in some cases.

I think the following may resolve some confusion:

1) Body in circular motion (A) sees clock at center of motion as moving fast always.

2) (A) sees an adjacent stationary clock (B) as moving slow at the moment of passage; but after an orbit, sees that that the stationary clock (B) is ahead. During large parts of the the orbit, (A) would see (B) going fast, thus explaining the result after a complete orbit.
 
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  • #40
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The funny thing is that this is not actually describing a constant velocity scenario. The directions of the motions are changing. SR cannot model this. This is exactly like an orbiting version of the twin paradox. [..]
SR has no problem to model the effects of non-inertial motion such as accelerating electrons and clocks going in circles - and this has been done right from the start. It's no different from Newton's mechanics which also has no problem with such motions.
 
  • #41
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SR has no problem to model the effects of non-inertial motion such as accelerating electrons and clocks going in circles - and this has been done right from the start. It's no different from Newton's mechanics which also has no problem with such motions.
That is a bit of a half-truth. SR seems to work in only some versions of the twin paradox.

http://www.desy.de/user/projects/Physics/Relativity/SR/TwinParadox/twin_intro.html

Some people claim that the twin paradox can or even must be resolved only by invoking General Relativity (which is built on the Equivalence Principle). This is not true, but the Equivalence Principle Analysis of the twin paradox does provide some additional analysis of the subject. The EP viewpoint is nearly mandatory for understanding some of the twin paradox variations.
http://physics.stackexchange.com/questions/2554/how-is-the-classical-twin-paradox-resolved

Great question and the answer depends on the point of view. Framework of SR will suffice to explain the paradox but you need to account for the acceleration of one of the twins and because of equivalence of acceleration and gravitation (in the elevator sense) this is best understood in the framework of GR. Will try to post an answer later if someone doesn't beat me to it. – Marek Jan 6 at 13:07
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Just one general point, not related specifically to the twin paradox: anyone who tells you that you need general relativity to treat acceleration is confused. General relativity is a theory of gravity. In special relativity, just as in Newtonian mechanics (with Galilean relativity), certain non-accelerating reference frames are preferred, but you can still perfectly well compute things involving accelerating objects! – Matt Reece Jan 6 at 14:51

@Matt: again, yes and no. General relativity is not only the theory of gravity, it is also a theory of general covariance and this topic is often lost in the standard expositions to SR because there SR is treated as a completely linear theory. That's why it's at least morally correct to say that GR (or its tools) is needed to understand acceleration in SR. – Marek Jan 6 at 16:03

[....]

To understand this paradox it's best to forget about everything you know (even from SR) because all of that just causes confusion and start with just a few simple concepts.

[....]

You can see that there was no paradox because we treated the problem as what is really was: computation of proper-time of the general trajectories. Note that this is the only way to approach this kind of problems in GR. In SR that are other approaches because of its homogeneity and flatness and if done carefully, lead to the same results. It's just that people often aren't careful enough and that is what leads to paradoxes. So in my opinion, it's useful to take the lesson from GR here and forget about all those ad-hoc SR calculations.

Just to give you a taste what a SR calculation might look like: because of globally nice coordinates, people are tempted to describe also distant phenomena (which doesn't really make sense, physics is always only local). So the blue twin might decide to compute the age of the green twin. This will work nicely because it is in the inertial frame of reference, so it'll arrive at the same result we did.

But the green twin will come to strange conclusions. Both straight lines of its trajectory will work just fine and if it weren't for the turn, the blue twin would need to be younger from the green twin's viewpoint too. So the green twin has to conclude that the fact that blue twin was in a strong gravitational field (which is equivalent to the acceleration that makes green twin turn) makes it older. This gives a mathematically correct result (if computed carefully), but of course, physically it's a complete nonsense. You just can't expect that your local acceleration has any effect on a distant observer. The point that has to be taken here (and that GR makes clear only too well) is that you should never try to talk about distant objects.
Granted, there is another side to this.

http://www.scientificamerican.com/article.cfm?id=how-does-relativity-theor Because of these types of incomplete explanations, to many partially informed people, the accelerations appear to be the issue. Therefore, it is believed that the general theory of relativity is required to explain the paradox. Of course, this conclusion is based on yet another mistake, since we don't need general relativity to handle accelerations. The paradox can be unraveled by special relativity alone, and the accelerations incurred by the traveler are incidental.
The wikipedia article on the twin paradox states:

http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

Special relativity does not claim that all observers are equivalent, only that all observers at rest in inertial reference frames are equivalent.
The problem I have with the SR approach is, "What if we simply do not know if something is an inertial frame?" For instance, the acceleration of our galaxy relative to another is not something can be picked up by an accelerometer, because the galactic gravitational forces on the accelerometer would be essentially uniform. It therefore is impossible to define an absolute inertial frame. On the other hand, if we do some accounting for the energy required to accelerate the spaceship, and the subsequent time dilation factor that results from it, then it would be clear that the second twin has a higher time dilation factor than earth twin. Then we wouldn't have to figure out which frame is actually inertial.
 
  • #42
DaveC426913
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That first sentence was just my "right brain" talking. You could have easily dispensed it and considered only the parts that come after.

Had I instead wrote just that, then you couldn't claim that I based all of it on my not-to-be-taken-too-literally assertion that "time is simply inverse frequency".
Agreed. I had no issue with the second part, and only commented on the first part, not being sure if you intended that the second part followed from the first part.
 
  • #43
PAllen
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The problem I have with the SR approach is, "What if we simply do not know if something is an inertial frame?" For instance, the acceleration of our galaxy relative to another is not something can be picked up by an accelerometer, because the galactic gravitational forces on the accelerometer would be essentially uniform. It therefore is impossible to define an absolute inertial frame. On the other hand, if we do some accounting for the energy required to accelerate the spaceship, and the subsequent time dilation factor that results from it, then it would be clear that the second twin has a higher time dilation factor than earth twin. Then we wouldn't have to figure out which frame is actually inertial.
If you are talking about cosmology and gravity, you do, indeed, need GR. For acceleration in contexts where cosmology and gravity are inconsequential, you only need SR, and the simplest way to do it is compute observables (for any observer) in any inertial frame of your choosing. No need to get bogged down in non-inertial frames in SR.

Using either SR where valid, or GR, there is no ambiguity as to what is inertial: if an accelerometer measures no force, you are inertial.
 
  • #44
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if an accelerometer measures no force, you are inertial.
Uniform acceleration isn't inertial. Is it actually possible for an accelerometer to measure uniform acceleration? As far I know, it can't be done.
 
  • #45
pervect
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In special relativity physicists talk about time dilation, saying that as an object moves faster relative to another that its "clock" moves slower and therefore time slows down. Could it be fair to say that time doesn't actually slow down, but all matter and energy reactions slow down and therefore "time" itself moves unchanged, but these physical processes slow down making it appear time is slower?

Follow up question, if so, could the reason all these physical processes are forced to slow down as velocity increases is because as energy goes into momentum it is taken away from these physical processes and these processes must therefore slow down relative to a reference frame at a lower velocity?

I have a problem calling the time dilation effect "time dilation" if it is not actually time, but the fundamental processes of physics that simply slow down as velocity increases relative to a slower reference frame. Meaning the CLOCK slows down as its velocity increases because its physical processes are simply moving slower, but time itself doesn't actually slow down.

Is this idea right, wrong, or an unprovable theory, and why?
It's hard to be positive, but experience leads me to believe (at the 90% plus level) that you are still thinking of time that's universal, something that's the same for all observers.

You can represent the set of points that occur "at the same time" in several ways, one of the most useful is a space-time diagram. If you draw the set of points that occur "at the same time" on such a diagram, it's a line.

The point of relativity is that different observers draw different lines to represent the notion of simultaneity. The lines they draw are different sets of points or events, they aren't the same line in any sense at all.

This leads to ambiguity when comparing clocks, except when the clocks are at precisely the same place. One of the effects of this ambiguity as that observer A can think observer B's clocks are slow, and observer B can think that A's clocks are slow. Both are right, using their own notion of "simultaneity". The issue is that in relativity, simultaneity is relative.

Here's an example of a space-time diagram of two observer's comparing each other's clocks. One observer uses the green lines as their notion of "simultaneity". The other observer uses the red lines. The drawing is to scale and illustrates how A can find B's clocks tick at 4/5 the usual rate, while B also finds A's clocks tick at 4/5 the usual rate.
 

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  • #46
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The funny thing is that this is not actually describing a constant velocity scenario. The directions of the motions are changing.
You are right. I was sloppy. I should of said constant speed.
SR cannot model this.
Yes it can. In my scenario both observers are at the same altitude so we can ignore gravity.
This is exactly like an orbiting version of the twin paradox.
Agree.
It should be obvious to anyone who understands the twin paradox that there is a discrepancy that will cause clock B to lag behind clock A, just as what you would expect for the relativistic twin in the twin paradox. The circular motion does not reduce this effect. Either the time of B lags behind A, or you must somehow refute the resolution to the twin paradox.
Agree. I said the total elapsed time for B will be less than that of A after one orbit and both A and B will agree on this. What I also said is that as A passes nearby B (at the same altitude) they will both think the other's clock is ticking at a slower rate (just as in the regualar twins paradox)


Uniform acceleration isn't inertial.
Agree.
Is it actually possible for an accelerometer to measure uniform acceleration?
Yes it can.
As far I know, it can't be done.
Yes it can (if you mean measuring uniform acceleration or using Special Relativity to analyse situations that involve constant acceleration - or non uniform acceleration if the acceleration is not due to gravity).
 
  • #47
PAllen
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Uniform acceleration isn't inertial. Is it actually possible for an accelerometer to measure uniform acceleration? As far I know, it can't be done.
Sure it is. In a uniformly accelerating rocket, put a rock on a scale and it measures your acceleration.
 
  • #48
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if an accelerometer measures no force, you are inertial.
Uniform acceleration isn't inertial. Is it actually possible for an accelerometer to measure uniform acceleration? As far I know, it can't be done.
Sure it is. In a uniformly accelerating rocket, put a rock on a scale and it measures your acceleration.
Acceleration, when it is uniform, is not "felt" at all by the body (See http://www.gozerog.com/).

If you have a column water with a few holes and place it inside a larger water-tight container strapped onto a rocket chair, accelerating, is the pressure of the water uniform throughout? No it is not.

Also, do you think the acceleration would be felt by the whole water simultaneously? It would not. The speed of sound (i.e. the speed limit to the "AC" component of mechanical energy), among other things, will cause a delay. In stark contrast to this, acceleration relative to a distant gravitational source is nearly 100% uniform through the whole body, and so no effect directly proportional to acceleration would be picked up. Such acceleration is invisible to the observer, as is the acceleration of a person is to that person when taking the trip down in one of Zero G Corporation's parabolic flight maneuvers.
 
  • #49
DaveC426913
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Also, do you think the acceleration would be felt by the whole water simultaneously? It would not. The speed of sound (i.e. the speed limit to the "AC" component of mechanical energy), among other things, will cause a delay. In stark contrast to this, acceleration relative to a distant gravitational source is nearly 100% uniform through the whole body,
That violates the Principle of Equivalance.
 
  • #50
PAllen
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Acceleration, when it is uniform, is not "felt" at all by the body (See http://www.gozerog.com/).

If you have a column water with a few holes and place it inside a larger water-tight container strapped onto a rocket chair, accelerating, is the pressure of the water uniform throughout? No it is not.

Also, do you think the acceleration would be felt by the whole water simultaneously? It would not. The speed of sound (i.e. the speed limit to the "AC" component of mechanical energy), among other things, will cause a delay. In stark contrast to this, acceleration relative to a distant gravitational source is nearly 100% uniform through the whole body, and so no effect directly proportional to acceleration would be picked up. Such acceleration is invisible to the observer, as is the acceleration of a person is to that person when taking the trip down in one of Zero G Corporation's parabolic flight maneuvers.
Total nonsense. Gravity is not felt by a free falling frame. Gravity = NOT SR. The acceleration of uniformly accelerating rocket is trivially measured inside it.

In GR, free fall is *not* uniform acceleration, it s *no* accleration. (Technically, proper acceleration). In GR, uniform acceleration is trivial to detect. When you weigh yourself in the morning you are measuring the fact the the earths surface is uniformly acclerating frame in GR.

The correct comparison in your silly water example is a cylinder of water on the earth's surface versus *stabilized* in a uniformly acceleration rocket. The result would be the same: higher pressure on the bottom. What you seem to be missing is that, to a very good approximation, the surface of the earth is uniformly accelerating frame. Don't you feel the acceration?
 
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