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

[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".

 

[harrylin]

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? [...]

Yes in free fall the two effects together are zero: one can interpret it as -9.8+9.8=0 (no resulting force on the beam due to free fall) or as 0+0=0 (no resulting force due to "inertial" motion). "Inertial motion" has a different meaning in GR than in SR. As PAllen also noticed, this thread is being muddled up by the mixing of GR with SR while this thread is about SR.