# What fundamentally is acceleration?

## Recommended Posts

Usually when I have these long trains of thought, I've gone off the rails early and rest is nonsense.  Hopefully this all makes sense, but I at least hope someone can put me back on the rails so I can try again.

The precursor to all this was thinking about the twin paradox.  I get it - sort of.  I believe the math works out, and I believe that there isn't really a paradox.  But I feel like I'm watching shadows - I get the general idea, but I can't see the finer details.

I don't like the explanation that one twin was in a single inertial frame and the other went through multiple frames.  Why would that be a given?  Why can't it be the other twin that stayed in place the whole time, and the rest of the universe accelerated away and back, and moved through multiple frames?  So that leads me to the acceleration formulation of the answer to the paradox - one twin underwent acceleration leaving, turning around, and stopping as it arrived back to the other twin.  Same problem.  There must be something about acceleration that is more fundamental that simply a change in velocity.

That led me to thinking that there's something more subtle about the asymmetry.  How does one accelerate?  Well in many formulations, one twin leaves in a rocket ship.  A rocket produces a chemical reaction, heat, expanding gas, equal and opposite reactions, yada yada.

But what, fundamentally about that process, is acceleration?  If there is no "cosmic stage", medium, etc, if motion is entirely relative, what about being in a rocket and changing your velocity relative to the rest of the universe is different than the rest of the universe changing it's velocity relative to you?

Did I miss the boat at the beginning - does the twin paradox not imply there is something different about you accelerating away from the whole universe than the whole universe accelerating away from you?  Am I putting the cart before the horse here (in other words, is coming back together and seeing which twin is older the only way to prove which one actually underwent acceleration)?

The thoughts that pop into my head are things like entropy - the chemical reaction of the rocket is increasing entropy - is entropy fundamentally related to acceleration and/or time dilation?

Is there something deeper here about force, about the underlying quantum mechanics and virtual particles that convey forces that produce what we perceive as force (and time dilation).

Is perhaps time dilation the cause of what we perceive as acceleration, and not the other way around?

I think I'm lost.  Help.

##### Share on other sites
8 minutes ago, sgabc123 said:

Is perhaps time dilation the cause of what we perceive as acceleration, and not the other way around?

The example of a geostationary satellite which contains an atomic clock will not give the same time as the atomic clock on earth. And this being motionless.

##### Share on other sites

The thing about accelerated frames of reference is that there is an inertia change, so you can always tell when you are in one.

You accelerating away from the universe is only equivalent to the universe accelerating away from you if you subscribe to a Machian viewpoint.
( see Ernest Mach and the 'Newton's pail" thought experiment )

They could very well not be equivalent.
Try accelerating the universe and let me know how you make out

##### Share on other sites
1 hour ago, sgabc123 said:

There must be something about acceleration that is more fundamental that simply a change in velocity.

That's metaphysics. If you look at just the physics, you can see in the equations how the change in velocity adds up (given enough time and distance). The "something more", if it isn't in the equations, is probably not going to be something measurable (unless you discover something new experimentally), so you can interpret it however you want and invent whatever "something more" you want, without it having any bearing on observed reality, which in my opinion is why metaphysics is philosophy, not science.

1 hour ago, sgabc123 said:

Why can't it be the other twin that stayed in place the whole time, and the rest of the universe accelerated away and back, and moved through multiple frames?

There are 2 possible results. One is, you manipulate the universe so that the two twins experience the exact same thing as they do in the simpler case, for example using gravitational fields and gravitational time dilation instead of just Lorentz time dilation. You might also use frame dragging and calculate the effect of all the mass in the entire universe on the twins. In this case, by making the twins experience exactly the same thing as before, by definition they're going to experience the same difference in aging, and you end up with the same result. Even though you moved the entire universe around instead of the twin to get an exact equivalent of simple acceleration, you still get that the twin that felt the effect of acceleration is the one that ages less.

Second possibility is that you modify things so that they don't have the same experience as in the simpler case. In this case, depending on gravitational time dilation etc., you can get different results, eg. make it so the other twin ages less. But that should be expected; if you change the experiment you can change the results.

If "something moving relative to the rest of the universe" is measurably exactly the same as "the universe moving relative to something", then you can't experimentally say that one is really happening and the other isn't. To say they're different would be metaphysics. I think this would be the Machian viewpoint that MigL mentioned. I think an anti-Machian viewpoint would be that speculatively, there must always be a measurable difference between accelerating something around the universe, vs. accelerating the universe around the something?

That said, I think it would be very difficult to figure out how to manipulate the entire real universe so that there's no measurable difference from just accelerating a twin. In a toy universe containing only the twins, it should be easier.

Edited by md65536

##### Share on other sites

The accelerating twin is changing their position with respect to the rest of the universe, so the two won't be perfectly symmetric in that sense.

##### Share on other sites
5 hours ago, sgabc123 said:

But what, fundamentally about that process, is acceleration?

An accelerated observer is one who traces out a world line that is not a geodesic of the underlying spacetime. It is thus fundamentally geometric in nature, and has nothing to do with forces, virtual particles etc. Thinking of it in terms of varying velocity - though formally correct - isn't especially helpful in understanding the actual physics at play, IMHO. Acceleration is simply a measure of a test particle's failure to be in free fall.

5 hours ago, sgabc123 said:

Did I miss the boat at the beginning - does the twin paradox not imply there is something different about you accelerating away from the whole universe than the whole universe accelerating away from you?

An accelerating observer will measure a non-zero reading on a comoving accelerometer, someone in an inertial frame will show zero on his instrument. So these two situations are physically distinct, and easily distinguishable - there is no symmetry.

1 hour ago, moth said:

Is the moon still considered to be in freefall even though the distance between Earth and moon is increasing due to tidal forces?

Yes.

##### Share on other sites

I simply don't understand the fundamentals of acceleration, time dilation, differential aging, to really grasp what the twin paradox and the solutions actually mean.

Thanks for the replies, lots to think about.

Scott

Perhaps this will inch me forward.  It's my understanding that all motion is relative.  That there is no cosmic 'stage' by which absolute motion can be measured.

Say I'm the only thing in the universe, just floating in space.  I have a baseball, and I throw it.  What actually changed?

I should have undergone a slight change in velocity (acceleration), but only relative to the ball.  Is there any remaining evidence of the acceleration?  Is there anything fundamentally different about me that proves I underwent acceleration?

The only thing different is that where there was once one mass bound together, there are now two masses (the ball and myself), and the distance between us is forever growing.

Scott

##### Share on other sites
3 hours ago, sgabc123 said:

I simply don't understand the fundamentals of acceleration, time dilation, differential aging, to really grasp what the twin paradox and the solutions actually mean.

Thanks for the replies, lots to think about.

Scott

Perhaps this will inch me forward.  It's my understanding that all motion is relative.  That there is no cosmic 'stage' by which absolute motion can be measured.

Say I'm the only thing in the universe, just floating in space.  I have a baseball, and I throw it.  What actually changed?

I should have undergone a slight change in velocity (acceleration), but only relative to the ball.  Is there any remaining evidence of the acceleration?  Is there anything fundamentally different about me that proves I underwent acceleration?

The only thing different is that where there was once one mass bound together, there are now two masses (the ball and myself), and the distance between us is forever growing.

Scott

If your mass is greater than that of the ball then I think you will experience proportionally less acceleration than the ball.

And vice versa.

I don't think though that you experience acceleration relative to the ball as acceleration is absolute even though the magnitude of your initial acceleration was relative to the magnitude of the initial acceleration of the ball.

##### Share on other sites
3 hours ago, sgabc123 said:

I simply don't understand the fundamentals of acceleration, time dilation, differential aging, to really grasp what the twin paradox and the solutions actually mean

There is no 'paradox' at all. It quite simply means that the two twins connect the same two events by two different world lines in spacetime - and since the accumulated reading on a clock is always identical to the geometric length of the world line traced out by that clock, their respective ages at the end of the experiment will differ. That is all there is to it - two world lines of differing length connecting the same two events. It's purely down to geometry.

3 hours ago, sgabc123 said:

It's my understanding that all motion is relative.

Yes, but acceleration is not. When you hold an accelerometer in your hand, the reading it shows is a proper quantity, it is not relative to anything else. Speed on the other hand is not a proper quantity, it is a relationship between frames, so it is relative to some reference point.
What instruments measure locally in their own local frames without reference to anything else are called proper quantities; quantities calculated with respect to some other reference point are called coordinate quantities. For a thorough grasp on the theory of relativity, it is crucially important to understand the difference between these.

3 hours ago, sgabc123 said:

I should have undergone a slight change in velocity (acceleration)

Indeed - this is essentially like firing a rocket thruster.

3 hours ago, sgabc123 said:

but only relative to the ball

No, it's not relative to anything. An accelerometer carried along with you would have registered and recorded that acceleration locally in your own frame, irrespective of how it physically came about.

3 hours ago, sgabc123 said:

Is there any remaining evidence of the acceleration?  Is there anything fundamentally different about me that proves I underwent acceleration?

Yes, you would have accumulated less proper time (aged less) between two fixed events, in comparison to some other reference clock which connects the same events, but without throwing a ball. In other words - you would have traced out a shorter world line between the same set of events.

##### Share on other sites
4 hours ago, sgabc123 said:

Perhaps this will inch me forward.  It's my understanding that all motion is relative.  That there is no cosmic 'stage' by which absolute motion can be measured.

Yes. The same is not true for acceleration.

4 hours ago, sgabc123 said:

Say I'm the only thing in the universe, just floating in space.  I have a baseball, and I throw it.  What actually changed?

I should have undergone a slight change in velocity (acceleration), but only relative to the ball.  Is there any remaining evidence of the acceleration?  Is there anything fundamentally different about me that proves I underwent acceleration?

The only thing different is that where there was once one mass bound together, there are now two masses (the ball and myself), and the distance between us is forever growing.

Scott

There are instruments that would be able to show that you underwent an acceleration, even if you could not look out into space for references to show that you had relative motion. Nobody else in the universe would detect this, as they did not undergo an acceleration.

##### Share on other sites
5 hours ago, Markus Hanke said:

Yes, but acceleration is not. When you hold an accelerometer in your hand, the reading it shows is a proper quantity, it is not relative to anything else. Speed on the other hand is not a proper quantity, it is a relationship between frames, so it is relative to some reference point.
What instruments measure locally in their own local frames without reference to anything else are called proper quantities; quantities calculated with respect to some other reference point are called coordinate quantities. For a thorough grasp on the theory of relativity, it is crucially important to understand the difference between these.

This is what's breaking my brain.  If there is no cosmic stage, if speed is only meaningful relative to other things, how can change in speed be absolute/not relative?  What really is changing?

I'll look up proper quantities and coordinate quantities.

Is this concept one of those things that can be understood intuitively, or is it one of those things that the math works, and there really isn't much to be gleaned by asking why?

Thanks a bunch, it's very fun for me to explore this stuff, even if it doesn't come easily!

Scott

##### Share on other sites

The link to proper acceleration, and differences from coordinate acceleration, was, unfortunately, split off to the hijack thread.
Here it is again ...

It is easily understandable at first, but does get quite mathematical later on.

##### Share on other sites
42 minutes ago, MigL said:

The link to proper acceleration, and differences from coordinate acceleration, was, unfortunately, split off to the hijack thread.
Here it is again ...

It is easily understandable at first, but does get quite mathematical later on.

A good presentation, for those who already know some Physics.  +1

##### Share on other sites
1 hour ago, sgabc123 said:

If there is no cosmic stage, if speed is only meaningful relative to other things, how can change in speed be absolute/not relative?

Coordinate speed is relative, but proper speed is absolute. Coordinate acceleration is relative, but proper acceleration is absolute.

Even relative speeds can have absolute consequences. For example, if two objects have a relative speed and they collide, that collision is absolute. When things have a speed relative to other things, that can be measured. Acceleration can involve different parts of things having different relative speeds at different times. For example, if a cantilever in an accelerometer momentarily has a non-zero speed relative to the rest of the device, the device measures a proper acceleration. If you think of a "cosmic stage" there may be a mystery, but the practical measurements aren't mysterious.

##### Share on other sites
17 hours ago, sgabc123 said:

This is what's breaking my brain.  If there is no cosmic stage, if speed is only meaningful relative to other things, how can change in speed be absolute/not relative?

Acceleration is not change in speed, but change in velocity. That's an important difference - velocity is a vector that, at a given instant, is tangential to the world line of the test particle at that instant in time. Speed is the magnitude of that vector, so it is just a real number.

Consider two frames in spacetime, which are initially inertial. You can go from one frame to another by performing a Lorentz transformation; geometrically speaking, such a transformation is simply a hyperbolic rotation in spacetime. So in other words, the relative speed between two inertial frames can be geometrically interpreted as a rotation angle - you (hyperbolically) rotate space into time, and vice versa, as you go from one frame to another. This is where length contraction and kinematic time dilation come from. Applying acceleration to one of the frames means you are changing that rotation angle - and while the original angle itself depends on the relationship between the frames (so it is relative to the frames), the change in that angle is not relative to anything.

It's like an oven - when you first turn it on and set a temperature (say e.g. 200 degrees), then that temperature is always relative to the room temperature it started off at. So for example, if you set it at 200 degrees starting at 20 degrees room temperature, you are actually setting it at 493K relative to absolute zero. So it's a relative value. But when you later on decide to dial up the temperature by another 20 degrees, then that change is not relative to anything - you simply add an absolute amount of 20 degrees, regardless of what the original temperature was. The change is by an absolute amount of 20 degrees, it isn't relative.

17 hours ago, sgabc123 said:

Is this concept one of those things that can be understood intuitively

Yes - once you 'get' it for the first time, the concept is very intuitive.

17 hours ago, sgabc123 said:

What really is changing?

Velocity in spacetime is a 4-vector, which has 1 component for time, and 3 components for space. When you apply acceleration, what you are effectively doing is changing the 'mix' of time and space components, so in general terms you are changing the relationship between 'motion in time' and 'motion in space', or (if the magnitude of the vector remains constant) you are changing the mix of the three spatial components only (=change in spatial direction). While this change is happening, the test particle is not in free fall, so the geometry of the world line it traces out in spacetime is different from that of an inertial frame, until acceleration is zero again.

Edited by Markus Hanke

##### Share on other sites
1 hour ago, Markus Hanke said:

Yes - once you 'get' it for the first time, the concept is very intuitive

Agreed.

On 10/6/2020 at 11:41 PM, sgabc123 said:

But what, fundamentally about that process, is acceleration?

Here is a slightly different point of view, especially since you mention chemical reactions.

Acceleration is a second order measure of something which is already a function of time.

In your case you are talking about velocity, which is a spatial function of time. (velocity is time rate of change of a line in space.)

I think your difficulty comes because you are concentrating on the 'something' not the time rate of change.

I know that all sound pompous but here is a chemical example that may help.

In Chemistry we talk about the rate of a chemical reaction, meaning the time rate of change of the quantity or concentration of  a reactant or product.

We also talk about an accelerating ( or decelerating) rate of reaction as as the measured quantity builds up or reduces whilst the reaction is taking place.

So in keeping with my definition, acceleration of the rate of a chemical reaction is the time rate of change of the time rate of increase in the quantity of product.
Thus it is second order because the rate with respect to time is invoked twice.

##### Share on other sites
6 hours ago, Markus Hanke said:

Acceleration is not change in speed, but change in velocity.

I was trying to keep things as simple as possible.  But if motion is relative, is not the direction of motion relative, only relevant in relation to a specific observer, the same as the magnitude?

I think I'm too hung up on a strict adherence to the idea of relativity.

I haven't had time to really digest some of the answers, particularly proper speed, proper acceleration, proper vs coordinate quantities.  I think that's the next thing I'll try to explore to see if I can understand what/why some things are absolute.

Thanks all!

Scott

##### Share on other sites

I feel like I'm challenging my betters here, but forgive me, I'm still hung up on this relativity thing.

I see no reason why acceleration would ever be absolute.

My first misstep here was assuming acceleration has something to do with resolving the apparent twin paradox.  I have come to believe it doesn't, not directly anyway (Dr. Lincoln from Fermilab):  https://www.youtube.com/watch?v=GgvajuvSpF4

I also incorrectly believed that acceleration causes time dilation, but it doesn't (again, at least not directly).  https://www.physicsforums.com/threads/does-acceleration-cause-time-dilation.237212/.

An accelerometer works because there is a differential in acceleration between the housing and sprung mass.  I don't believe a particle with no internal structure 'experiences' anything from acceleration.  Anything inferred as absolute about acceleration is emergent from the interactions of many particles.

I'm feeling a lot better about what acceleration is and isn't.  So unless I got something grossly wrong here....

##### Share on other sites
57 minutes ago, sgabc123 said:

I feel like I'm challenging my betters here, but forgive me, I'm still hung up on this relativity thing.

I see no reason why acceleration would ever be absolute.

Velocity is relative, but if it changes, only one of the objects will feel the acceleration.

If you and I move relative to each other in cars, and you slam on the brakes, my beverage doesn’t get spilled.

##### Share on other sites
52 minutes ago, swansont said:

Velocity is relative, but if it changes, only one of the objects will feel the acceleration.

If you and I move relative to each other in cars, and you slam on the brakes, my beverage doesn’t get spilled.

I would say that if velocity changes NO objects will "feel" the acceleration, at least not at the fundamental particle level.

What you're describing seems to me an emergent phenomenon.  An accelerometer only "feels" acceleration because of interactions between particles.

An accelerometer works when you apply force to the housing, the housing changes velocity before the sprung mass.  Because of the relative change in velocity between the housing and the sprung mass, there is a measurable difference in the position of the sprung mass relative to the housing.  Individually, all 100% relative.  Macroscopically appearing as absolute.

If you accelerate every particle in an accelerometer uniformly, it doesn't read anything.  It's only because of a non-uniform, relative acceleration between the housing and sprung mass that it "feels" anything.

I believe that if I accelerated every particle in the universe, including your beverage, just not your car, you're spilling your drink, and nobody else notices.  It's still all relative.  The only reason we would never assume such a thing is because we know it's wildly impractical to accelerate the entire universe.

On 10/7/2020 at 11:57 AM, md65536 said:

Coordinate speed is relative, but proper speed is absolute. Coordinate acceleration is relative, but proper acceleration is absolute.

Even relative speeds can have absolute consequences. For example, if two objects have a relative speed and they collide, that collision is absolute. When things have a speed relative to other things, that can be measured. Acceleration can involve different parts of things having different relative speeds at different times. For example, if a cantilever in an accelerometer momentarily has a non-zero speed relative to the rest of the device, the device measures a proper acceleration. If you think of a "cosmic stage" there may be a mystery, but the practical measurements aren't mysterious.

Now that I re-read this, I think we're saying basically the same thing.  I think the idea here is that "proper" involves more than one reference.

When two particles are moving directly toward one another - individually there is no proper way to say which is moving, which is stationary, or what combination.  But the difference in their velocities is an absolute, and we all agree on it.

And the same for acceleration when two particles collide.  The total acceleration that occurs is an absolute on which everyone agrees.  But the new details of the individual particles - the new directions and speeds, are still relative to a reference frame.

So thinking in relative terms regarding acceleration is meaningless - because in the real world, particles don't spontaneously change velocity (quantum mechanics?).  Only interactions with other particles cause changes in velocity, and since there are always multiple entities involved, there are also always proper quantities to be calculated.

Does my lay explanation sound about right?

Thanks all,

Scott

##### Share on other sites

From my first post  ( on Tuesday ), an acceleration involves a change of inertia.
Even fundamental particles ( no internal structure ) will experience a change of inertia.
Non-accelerating frames are called inertial frames, and accelerating frames are called non-inertial, as a consequence.

Inertia is what resists forces that produce accelerations.
And mass is what resists changes in inertia.

##### Share on other sites
22 minutes ago, sgabc123 said:

I would say that if velocity changes NO objects will "feel" the acceleration, at least not at the fundamental particle level.

What you're describing seems to me an emergent phenomenon.  An accelerometer only "feels" acceleration because of interactions between particles.

If I accelerate an electron - a fundamental particle - it will emit radiation. This does not happen with constant velocity. So no. This is fundamental.

22 minutes ago, sgabc123 said:

An accelerometer works when you apply force to the housing, the housing changes velocity before the sprung mass.  Because of the relative change in velocity between the housing and the sprung mass, there is a measurable difference in the position of the sprung mass relative to the housing.  Individually, all 100% relative.  Macroscopically appearing as absolute.

If you accelerate every particle in an accelerometer uniformly, it doesn't read anything.  It's only because of a non-uniform, relative acceleration between the housing and sprung mass that it "feels" anything.

I believe that if I accelerated every particle in the universe, including your beverage, just not your car, you're spilling your drink, and nobody else notices.

No, everybody notices. Light gets deflected in an accelerating frame (another pesky fundamental particle). All of the free charges radiate, as above.

##### Share on other sites
50 minutes ago, sgabc123 said:

What you're describing seems to me an emergent phenomenon.  An accelerometer only "feels" acceleration because of interactions between particles.

An electron does not have to "feel" acceleration due to interaction with other particles. One single isolated electron will accelerate in an electrical field and radiate according to Swansont's description.

##### Share on other sites
22 minutes ago, Ghideon said:

An electron does not have to "feel" acceleration due to interaction with other particles. One single isolated electron will accelerate in an electrical field and radiate according to Swansont's description.

OK, but isn't that an interaction, or at least modeled as an interaction - exchange of virtual photons?

##### Share on other sites

It’s true that an interaction is required to have an acceleration, but that should come as no surprise, as this is described by Newton’s first law.

edit: I don’t think you can argue Newton’s first is an emergent phenomenon

## Create an account

Register a new account