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

[yuiop]

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.

 

[kmarinas86]

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.

 

[harrylin]

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.

 

[PAllen]

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.

 

[harrylin]

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.

 

[kmarinas86]

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
8

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.

 

[DaveC426913]

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.

 

[PAllen]

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.

 

[kmarinas86]

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.

 

[pervect]

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.

 

[yuiop]

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).

 

[PAllen]

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.

 

[kmarinas86]

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.

 

[DaveC426913]

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.

 

[PAllen]

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 Earth's 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?

 

[Dale]

That is a bit of a half-truth. SR seems to work in only some versions of the twin paradox.

What versions of the twin paradox are you referring to here where SR doesn't work?

 

[yuiop]

Acceleration, when it is uniform, is not "felt" at all by the body (See http://www.gozerog.com/).

The example you linked to is "free fall" which is when a body is moving along a geodesic. Being in free fall is the same as being at rest in special relativity. The body feels no acceleration, but that is not the same as "uniform acceleration". I assumed you meant constant acceleration over time for "uniform acceleration" but I see now that you mean uniform acceleration spatially over a spatially extended body, but that does not really change anything.

It is not possible to maintain spatially uniform acceleration over extended periods at relativistic speeds due to length contraction, so the back of extended object has to accelerate faster than the front of the object. The closest thing to uniform acceleration in relativity is Born rigid motion. Totally uniform acceleration is never (rarely?) found in nature as most gravitational fields are radially non uniform.

Anyway, constant (proper) acceleration over time (due to rocket for example) is measurable by an accelerometer and is non-inertial. When you measure yourself on some bathroom scales it is in fact measuring the force due a constant acceleration of about 9.8g. Acceleration in free-fall is not proper acceleration and so cannot be measured by an accelerometer.

You said "uniform acceleration is not inertial" and we all agreed, but I now realize, you mean free-fall for "uniform acceleration" and I am going to have to disagree. Free fall IS inertial motion. Being at rest in a gravitational field, (such as sitting on your chair) is non-inertial motion. Inertial motion can be defined as motion when no acceleration is measured by an accelerometer and free fall fits into that category.

 

[kmarinas86]

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.

So you think that the acceleration would be felt by the whole water simultaneously? We are talking about a rocket here. Water is not a rigid body. How does having different forces on each of the little H20 molecules, as peaks and valleys of sound waves pass through it, violate the equivalence principle?

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 way yourself in the morning you are measuring the fact the the Earth's surface is uniformly acclerating frame in GR.

What some, like you, call "uniform acceleration", I would call "constant acceleration".

I am not talking about acceleration constant with respect to time. I am talking of acceleration uniform with respect to mass particles of the body.

The way a force is "felt", as far as I know, is by allowing different particles in a body to change their relative motions to one another. If I jump, the particles in my body do not move in lock-step with each other (i.e. they are moving out of phase).

The acceleration of the atoms and molecules rocketship will have a delay tied to the speed of the exhaust (the "DC" component) and another delay tied to the sound through the rocketship's structure (the "AC" component). A gravitational field would seem to have no delay other the speed of light. If the gravitational field is for all intended purposes uniform (e.g. "earth's surface"), then this would be acceleration that is distributed uniformly throughout the body at any given time.

Accelerometers, as far I knew just a few minutes ago, relied on mass dampening effects. However, I will contend that perhaps doppler-based accelerometers can pick up on the type of accelerations which I am talking about, but such is not directly related to accelerations which can be "felt". However, I also suspect that doppler-based accelerometers only pick up on differences of accelerations, but not absolute accelerations.

 

[harrylin]

That is a bit of a half-truth. SR seems to work in only some versions of the twin paradox.[..]

The twin paradox ignores effects of gravitation on clock rate, as does SR.

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.

SR uses the same reference systems as Newton's mechanics, which are operationally defined as non-accelerating wrt the distant stars. I think that that definition even works for your rather extreme case. And yes energy use, if well specified, can also be utilised to determine a change of state of motion.

 

[harrylin]

[..] I am not talking about acceleration constant with respect to time. I am talking of acceleration uniform with respect to mass particles of the body.

The way a force is "felt", as far as I know, is by allowing different particles in a body to change their relative motions to one another. If I jump, the particles in my body do not move in lock-step with each other (i.e. they are moving out of phase).
[..]
Accelerometers, as far I knew just a few minutes ago, relied on mass dampening effects. [..]

No. Accelerometers typically consist of a beam that bends under gravitation as well as under acceleration; its deflection is a measure for the acceleration. Consequently, gravitation (g=constant) has the same effect as constant acceleration (a=constant): it results in a constant output signal such as "9.8 m/s²".

Harald

 

[kmarinas86]

The twin paradox ignores effects of gravitation on clock rate, as does SR.

I've seen so many descriptions of the twin paradox that mention the equivalence principle (and thus GR), but I never was told, until you stated the above, that the legit twin paradox totally ignores it.

 

[kmarinas86]

No. Accelerometers typically consist of a beam that bends under gravitation as well as under acceleration; its deflection is a measure for the acceleration. Consequently, gravitation (g=constant) has the same effect as constant acceleration (a=constant): it results in a constant output signal such as "9.8 m/s²".

Harald

Wouldn't there be a difference in the deflection seen from the accelerometer's frame when the accelerometer is in free fall versus when the accelerometer is just sitting on the ground? It seems that this could only pick up proper acceleration (per what yuiop said).

 

[Dale]

Accelerometers, as far I knew just a few minutes ago, relied on mass dampening effects. However, I will contend that perhaps doppler-based accelerometers can pick up on the type of accelerations which I am talking about, but such is not directly related to accelerations which can be "felt".

Accelerometers measure "proper acceleration", by definition. The kind of acceleration which cannot be "felt" is called "coordinate acceleration". Whether or not the acceleration is uniform is not relevant, you can have proper acceleration which is uniform in space and time, and you can have coordinate acceleration which is not uniform. In all cases, the coordinate acceleration is not "felt" and the proper acceleration is.

 

[kmarinas86]

Accelerometers measure "proper acceleration", by definition. The kind of acceleration which cannot be "felt" is called "coordinate acceleration". Whether or not the acceleration is uniform is not relevant, you can have proper acceleration which is uniform in space and time, and you can have coordinate acceleration which is not uniform. In all cases, the coordinate acceleration is not "felt" and the proper acceleration is.

Thank you. That is what I needed.

 

[yuiop]

The problem I have with the SR approach is, "What if we simply do not know if something is an inertial frame?"

If we had an accelerometer we would know. If the accelerometer reads zero, then we are in an inertial frame, whether we are rest far away from any gravitational field, or moving relative to something else or free falling in a gravitational field.

Zero reading on accelerometer = zero proper acceleration = inertial motion.

Correspondingly:

Non-zero reading on accelerometer = proper acceleration = non-inertial motion.

Also as Dalespam has already pointed out we can have coordinate acceleration which is inertial, such as free-fall.

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.

Does not matter what galaxy we are in. If the accelerometers read zero they all have inertial motion, but that does not mean they are all subject to the same time dilation. In addition to the velocity time dilation of SR they are subject to the gravitational time dilation of GR which is a function of the altitude from the the gravitational body and the mass of the gravitational body.

It therefore is impossible to define an absolute inertial frame.

Yep, that has always been true in SR. If we could define an absolute inertial frame we would call it the ether and give Lorentz a post-humus Nobel prize.

 

[kmarinas86]

If we an accelerometer we would know. If the accelerometer reads zero, then we are in an inertial frame, whether we are rest far away from any gravitational field, or moving relative to something else or free falling in a gravitational field.
Zero reading on accelerometer = zero proper acceleration = inertial motion.

This would mean that an object in free fall doesn't gain any additional energy, right? Is it also true that, during coordinate acceleration (with no proper acceleration simultaneous to it), what may simply be happening is that the paths of internal momenta in that object converge toward the world line of the path of the overall object? Would that reduce the rate of events involving perpendicular motions with respect to that world line and thereby explain gravitational time dilation? Or is that not looked upon? If that is a different concept than what is used to explain gravitational time dilation in General Relativity, wouldn't it be a redundant explanation for gravitational time dilation?

 

[PAllen]

This would mean that an object in free fall doesn't gain any additional energy, right? Is it also true that, during coordinate acceleration (with no proper acceleration simultaneous to it), what may simply be happening is that the paths of internal momenta in that object converge toward the world line of the path of the overall object? Would that reduce the rate of events involving perpendicular motions with respect to that world line and thereby explain gravitational time dilation? Or is that not looked upon? If that is a different concept than what is used to explain gravitational time dilation in General Relativity, wouldn't it be a redundant explanation for gravitational time dilation?

This thread was all about pure SR effects (including non-inertial motion, but *not* including gravity effects). If you want to discuss energy change during free fall in a gravitational field, that deserves a separate thread. It is complex and unrelated to this thread.

 

[cosmik debris]

There are three types of acceleration in GR.

1). Co-ordinate acceleration - your usual 3 acceleration i.e. the second derivative of position.

2). 4-acceleration - a vector quantity which is invariant.

3). proper acceleration - 4-acceleration projected on to co-moving co-ordinates.

In free fall there is co-ordinate acceleration but 4-acceleration is zero.

 

[PAllen]

There are three types of acceleration in GR.

1). Co-ordinate acceleration - your usual 3 acceleration i.e. the second derivative of position.

2). 4-acceleration - a vector quantity which is invariant.

3). proper acceleration - 4-acceleration projected on to co-moving co-ordinates.

In free fall there is co-ordinate acceleration but 4-acceleration is zero.

Of course you mean the may be coordinate acceleration in free fall. It depends on the coordinates.

 

[DaveC426913]

So you think that the acceleration would be felt by the whole water simultaneously? We are talking about a rocket here. Water is not a rigid body. How does having different forces on each of the little H20 molecules, as peaks and valleys of sound waves pass through it, violate the equivalence principle?

I am simply saying that there is no test you can do in a closed room that will distinguish between uniform acceleration and gravity. That is the very essence of EP.

Under uniform acceleration, the water will be compressed normally, and will stay that way throughout the acceleration, just as if the beaker of water were sitting on Earth.

For ease of imagining, picture the water molecules as bunch of large soft plush balls stacked 6ft high vertically. While at rest, the balls exert no pressure on each other. You begin accelerating to 1g, causing all the balls to push on each other (yes, at the speed of sound), which compresses them.

But you have not yet reached full acceleration.

By the time you reach you 1g acceleration gthe balls are fully compressed to 3ft. They will remain that way, stacked on top of each other, 3 ft high and motionless as long as your acceleration remains 1g. The uniform force results in uniform compression, and does not require any "transmission of force from ball to ball at the speed of sound".

 

[ItsDaveDude]

I am simply saying that there is no test you can do in a closed room that will distinguish between uniform acceleration and gravity. That is the very essence of EP.

What about tidal forces? Although they could be incredibly small (and I don't think anyone denies they exist) you could conceive of a test in a closed room that detects tidal forces (if it is gravity) and when it doesn't detect them it is uniform acceleration. Isn't this an effect that makes it misleading to say gravity and uniform acceleration are equivalent, because tidal forces are a detectable force that exist in one case (gravity) but not in the other (uniform acceleration), therefore making them not equivalent effects?

 

[DaveC426913]

What about tidal forces? Although they could be incredibly small (and I don't think anyone denies they exist) you could conceive of a test in a closed room that detects tidal forces (if it is gravity) and when it doesn't detect them it is uniform acceleration. Isn't this an effect that makes it misleading to say gravity and uniform acceleration are equivalent, because it is a detectable force that exists in one case (gravity) but not in the other (uniform acceleration)?

Yes. Which is why the closed system is defined as small. Small enough to not include tidal forces.

 

[ItsDaveDude]

Yes. Which is why the closed system is defined as small. Small enough to not include tidal forces.

Really? I hate being correct. To me, this means uniform acceleration and gravity are not equivalent then, and the equivalence principle is just some happenstance of physics that happens to work if we don't look too closely, but in reality these are totally different physical laws/effects from different fundamental processes, and we shouldn't be going on about how they are they same effect or equivalent. Is this a fair statement? Is the equivalence principle just a convenience/artifice for thinking about physics but doesn't hold in reality if you want to think about physics fundamentally?

I know this is getting off topic so I put it in a new post: https://www.physicsforums.com/showthread.php?p=3344706#post3344706

 

[Dale]

What do you think the equivalence principle says? There is nothing wrong with the equivalence principle, you can't blame it if you thought it applied to tidal gravity.

 

[harrylin]

I've seen so many descriptions of the twin paradox that mention the equivalence principle (and thus GR), but I never was told, until you stated the above, that the legit twin paradox totally ignores it.

Sorry I should have said it differently. What I meant was that the twin paradox ignores the gravitational effect of mass on clock rate.

But no single sound bite can catch the whole history. In a nutshell:

The original setting (by Langevin) was a straightforward SR problem of two people, one staying on Earth and the other making a space travel.
However, the twin problem can also be solved with GR, using the equivalence principle: then the traveler has the POV to be "in rest" and so "induced gravitational fields" appear. That solution (by Einstein, about two clocks) is much less obvious, or "paradoxical".