# Force due to acceleration and time flowing differently

• I
• HansH
In summary, Special relativity predicts that a moving clock as measured against an array of "stationary" clocks all synchronized according to the standard of a chosen rest frame will appear to tick slowly by comparison. Meanwhile, a "stationary" clock as measuerd against an array of "moving" clocks all synchronized according to the standard of the chosen moving frame will also appear to tick slowly by comparison. It is not about the clocks. It is about the standard of comparison.f

#### HansH

TL;DR Summary
is there re reason for feeling a force due to acceleration and the resulting time going slower after that?
in special relativity we have moving reference frames resulting in a different flow of time in each reference frame. This we can explain because we use the fact that the speed of light is the same in all reference frames, leading to the Lorenz transformation giving the amunt of slowdown of time.

If you start with a second reference frame having the same speed as the first frame then there is no difference in flow of time. so the fact that the second frame is accellarated and the first frame is not should be the reason for time to flow slower in the second frame after that accelaration.

On the other hand, while accelerating one feels a force proportial to the mass times the accelaration.
so then for me the question arises if there is a deeper link between the force you feel due to accelleration and the fact that time flows slower in your moving reference frame as seen by the observer in the not moving frame.

so put different: does the fact that the speed of light is the same in all reference frames has something to do with the force we feel due to accelaration?

Summary: is there re reason for feeling a force due to acceleration and the resulting time going slower after that?

in special relativity we have moving reference frames resulting in a different flow of time in each reference frame.
Unfortunately, the notion of "time flowing slower" is incorrect to begin with. So everything that follows is nonsense. Time flows at a rate of one second of proper time per second of proper time always.

What Special Relativity predicts is that a moving clock as measured against an array of "stationary" clocks all synchronized according to the standard of a chosen rest frame will appear to tick slowly by comparison.

Meanwhile, a "stationary" clock as measuerd against an array of "moving" clocks all synchronized according to the standard of the chosen moving frame will also appear to tick slowly by comparison.

It is not about the clocks. It is about the standard of comparison.

Tertius, dextercioby, PeroK and 3 others
Unfortunately, the notion of "time flowing slower" is incorrect to begin with. So everything that follows is nonsense. Time flows at a rate of one second of proper time per second of proper time always.

What Special Relativity predicts is that a moving clock as measured against an array of "stationary" clocks all synchronized according to the standard of a chosen rest frame will appear to tick slowly by comparison.

Meanwhile, a "stationary" clock as measuerd against an array of "moving" clocks all synchronized according to the standard of the chosen moving frame will also appear to tick slowly by comparison.

It is not about the clocks. It is about the standard of comparison.
ok I assume you know what I mean. probably I expressed myself a bit unlucky. I mean the factor gamma in the lorenz transformation of course. so does that make the rest of the question still nonsense? so let's try to make this topic converge instead if diverge.

Not Force in non inertial frame of reference but its Potential Energy decides time rate there.

ok but you can calculate the potential energy from the force working over a distance, so that makes the question not basically different I suppose.

You are forgetting that the logic of Special Relativity has a lot of symmetry. If two observers are moving with respect to each other, each observer thinks that the other's clocks are ticking slower than they should. This is true regardless of how they reached their velocities and who accelerated.
You might want to take a hard look at the problem of synchronizing clocks in an inertial reference frame when the speed of light is c no matter what your velocity is. The Lorentz geometry of space-time allows that to happen.

PeroK
Perhaps you should get a bit more comfortable with the basics of SR before moving on to accelerations?
Just a friendly tip.

phinds, Dale, Vanadium 50 and 2 others
so put different: does the fact that the speed of light is the same in all reference frames has something to do with the force we feel due to accelaration?
Forces are familiar concepts in Newtonian physics. That would seem to imply that you would feel forces and accelerations in a Newtonian universe too, which has no time dilation effects.
Lorenz
Lorentz. Lorenz was a different physicist, who has an electromagnetic gauge named after him.

vanhees71
Perhaps you should get a bit more comfortable with the basics of SR before moving on to accelerations?
Just a friendly tip.
yes of course, but I cannot prevent that the question pops up in my head at the wrong moment. So I hoped for a clear high level answer already from people who are already comfortable with the matter.

Are you even comfortable with Newtonian forces and accelerations to begin with?
You are starting at the wrong end. Don't be your friend who have an entire bookshelf with unread GR books :)

vanhees71
Are you even comfortable with Newtonian forces and accelerations to begin with?
You are starting at the wrong end. Don't be your friend who have an entire bookshelf with unread GR books :)
Yes I think so.

Forces are familiar concepts in Newtonian physics. That would seem to imply that you would feel forces and accelerations in a Newtonian universe too, which has no time dilation effects.
ok but we are dealing with one universe that works as is and does not bother about Newton or Einstein. It simply shows both effects. So therefore my question: can we understand that relation?

Lorentz. Lorenz was a different physicist, who has an electromagnetic gauge named after him.
Ok thanks for reminding me being a bit inaccurate in names. That makes the question however not different.

So therefore my question: can we understand that relation?
My point is that you can have forces and accelerations in systems of physics that do not include time dilation. That's a pretty strong hint that the one doesn't cause the other.

dextercioby, FactChecker, Vanadium 50 and 2 others
Ok thanks for reminding me being a bit inaccurate in names.
You see the same mistake in actual textbooks, but it's good to talk about the right person.

malawi_glenn
Summary: is there re reason for feeling a force due to acceleration and the resulting time going slower after that?

If you start with a second reference frame having the same speed as the first frame then there is no difference in flow of time. so the fact that the second frame is accellarated and the first frame is not should be the reason for time to flow slower in the second frame after that accelaration.
You need to be careful here. The Lorentz transform is between inertial reference frames only. If you have an accelerating reference frame then it is non-inertial and the Lorentz transform does not apply. In that case you have to be more specific about the exact details for your reference frame since there is not a standard non-inertial reference frame.

My preferred non-inertial reference frame is the radar coordinates which were popularized by Dolby and Gull. One thing that is nice about radar coordinates is that there is a known procedure for determining the metric given only the proper acceleration of the non-inertial observer. This procedure is a concrete answer to your question about the link between acceleration and the metric (which includes the "flow of time")

I have linked to two simple papers on this topic. I would recommend that you read both of them. If you cannot understand these papers then you are probably not yet ready for this question and should focus on the basics first.

vanhees71
My point is that you can have forces and accelerations in systems of physics that do not include time dilation. That's a pretty strong hint that the one doesn't cause the other.
Do we then have any idea where the fixed relation between force, mass and acceleration comes from? Because if you say that the one does not cause the other then I assume there are 2 options:
1) we don't know
2) we can prove that it is not the case for a good reason.

My point is that you can have forces and accelerations in systems of physics that do not include time dilation. That's a pretty strong hint that the one doesn't cause the other.
Like here:

car is moving relative to the ground with velocity v to the right and is accelerated to the right with acceleration a.
@HansH determine the magnitude and direction of the forces which the person in the car, sitting on that chair, is "feeling".
This is Newtonian physics, forget about Lorentz and Lorenz for a minute.

You need to be careful here. The Lorentz transform is between inertial reference frames only.

My preferred non-inertial reference frame is the radar coordinates which were popularized by Dolby and Gull. One thing that is nice about radar coordinates is that there is a known procedure for determining the metric given only the proper acceleration of the non-inertial observer. This procedure is a concrete answer to your question about the link between acceleration and the metric (which includes the "flow of time")

I have linked to two simple papers on this topic. I would recommend that you read both of them. If you cannot understand these papers then you are probably not yet ready for this question and should focus on the basics first.
OK, I will check, but before understanding the details: is what you say that there is indeed a relation? because it is not always needed to know al the details to have a high level overview. (any engineer reporting to his management should be able to recognize that. At this moment I am more or less in the role of the management trying to get the picture only and not all the details)

OK, I will check, but before understanding the details: is what you say that there is indeed a relation? because it is not always needed to know al the details to have a high level overview. (any engineer reporting to his management should be able to recognize that. At this moment I am more or less in the role of the management trying to get the picture only and not all the details)
If you do not want the details then the answer to your question:
Summary: is there re reason for feeling a force due to acceleration and the resulting time going slower after that?
is a simple "no".

Understanding "time going slower" involves grasping the details.

before understanding the details: is what you say that there is indeed a relation?
I don't think that the answer can be understood without the details in this case.

"There is indeed a relation" is an overly broad and un-nuanced statement that I cannot answer either yes or no to. I can only explain with details. If I simply answer yes or no then you will unavoidably come out with an understanding that will be wrong.

jbriggs444
Like here:
View attachment 312622
car is moving relative to the ground with velocity v to the right and is accelerated to the right with acceleration a.
@HansH determine the magnitude and direction of the forces which the person in the car, sitting on that chair, is "feeling".
This is Newtonian physics, forget about Lorentz and Lorenz for a minute.
he feels a force F=m*a pointing to the left pushing him in his chair to the back , where m is the mass of his body. Of course when he hets the back of his chair the chair creates the same force tothe right preventing the person from moving backwards related to the car. for this example v does not make a difference in what the person feels.

If you start with a second reference frame having the same speed as the first frame then there is no difference in flow of time. so the fact that the second frame is accellarated
You don't accelerate frames. You accelerate objects. You can have a frame that is not an inertial frame, but talking about accelerating a frame doesn't make sense; accelerating a frame would mean the frame changes with time, but a frame already has to include time, so talking about it changing with time doesn't make sense.

Also, you can't compare "rate of time flow" between objects unless they meet up twice. But you're not talking about that. The "rate of time flow" you are talking about is frame-dependent and doesn't have any physical meaning.

does the fact that the speed of light is the same in all reference frames
It isn't. It's only the same in all inertial frames.

has something to do with the force we feel due to accelaration?
Only in the sense that both of them are consequences of spacetime geometry. The usual relativistic view is that a force is felt due to proper acceleration because proper acceleration means the object is not following a geodesic worldline through spacetime; whether a worldline is geodesic or not is a consequence of the spacetime geometry.

Do we then have any idea where the fixed relation between force, mass and acceleration comes from?
I think that's a definition. The physical quantity "force" is defined to be the rate of change of momentum. Momentum is a Noether charge, and emerges from the fact that the laws of physics are the same everywhere (and the conservation law that comes with that is why force is intetesting at all).
"There is indeed a relation" is an overly broad and un-nuanced statement that I cannot answer either yes or no to. I can only explain with details. If I simply answer yes or no then you will unavoidably come out with an understanding that will be wrong.
I would say the existence of systems of physics with forces but no light speed invariance strongly suggests that forces and light speed invariance are separate things. However, the invariance of light speed definitely affects the form of the relationship, and can make things more complicated - in relativity you can use force to mean the three-vector force or the four-vector force.

Dale
he feels a force F=m*a pointing to the left pushing him in his chair to the back , where m is the mass of his body.
Wrong.
The motor is in the car. The motor is doing the work and is causing the car to accelerate. The person has no motor in him/her. The person can only accelerate if there is force pushing on him to the right. The back of the chair is pushing on the person with a force ma to the right. Then we also have gravity.
In total, forces on the person are ma to the right and mg down.

Do we then have any idea where the fixed relation between force, mass and acceleration comes from? Because if you say that the one does not cause the other then I assume there are 2 options:
1) we don't know
2) we can prove that it is not the case for a good reason.
As any established physical law we know about the relation between the said quantities from experience. I don't know, what you mean by "one does not cause the other".

The physical quantity "force" is defined to be the rate of change of momentum. Momentum is a Noether charge
This is not correct. Momentum is only a Noether charge in spacetimes with translational symmetry (i.e., with the appropriate Killing vector fields). But a force is felt due to proper acceleration in any spacetime, even one that lacks such symmetry.

nasu, vanhees71 and malawi_glenn
Wrong.
The motor is in the car. The motor is doing the work and is causing the car to accelerate. The person has no motor in him/her. The person can only accelerate if there is force pushing on him to the right. The back of the chair is pushing on the person with a force ma to the right. Then we also have gravity.
In total, forces on the person are ma to the right and mg down.
ok ,but you were asking what the person is feeling. He does not feel gravity because he is already used to that. Of course the gravity gives a force downwards and the chair of the car gives a force forward as I said. and you can sum up both forces to determine a residual force and direction if you like. But for the person this feels like a force backwards as he resists to the acceleration. at least that is what I feel when I am in a car and that was what you asked.

nasu
I would say the existence of systems of physics with forces but no light speed invariance strongly suggests that forces and light speed invariance are separate things
Hmm, I thought he was asking about a relationship between acceleration and time dilation. Since light speed is only generally invariant for inertial frames and he is asking about non-inertial frames the light speed invariance isn't even generally applicable.

This is not correct. Momentum is only a Noether charge in spacetimes with translational symmetry (i.e., with the appropriate Killing vector fields). But a force is felt due to proper acceleration in any spacetime, even one that lacks such symmetry.
Fair point. So what would you suggest as the origin of force as a concept? It remains the rate of change of four momentum, and fouromentum is a normalised tangent to the worldline, but why is that normalisation of interest?

Hmm, I thought he was asking about a relationship between acceleration and time dilation.
Depends which paragraph in the OP you read, I think...

Dale
If you do not want the details then the answer to your question:
then you don't understand. of course I want the details, but as Dale mentioned, it could well be that I first need to digg deeper into the matter before I can understand the details. so wanting to know the details and able to follow them are 2 different things. Therefore a high level answer can be the in between answer. but your high level answer seemsto contradict that of Dale and I cannot judge that at the moment.

Motore
Summary: is there re reason for feeling a force due to acceleration and the resulting time going slower after that?

in special relativity we have moving reference frames resulting in a different flow of time in each reference frame. This we can explain because we use the fact that the speed of light is the same in all reference frames, leading to the Lorenz transformation giving the amunt of slowdown of time.
For every frame where the force increases your speed, there is a frame where the force decreases your speed. Hence, in your terms, speeding your time up.

Compare aircraft taking off east and west. The aircraft flying west measures less time than a clock in the airport. E.g. in one circumnavigation of the Earth.

jbriggs444
but your high level answer seemsto contradict that of Dale and I cannot judge that at the moment
That is the nature of an un-nuanced answer. Different people giving an un nuanced answer will inevitably give different answers due precisely to the nuances that are being avoided. I am sorry, but the details matter here. Please read the two papers I provided.

ok ,but you were asking what the person is feeling.
True, the he feels normal force mg upwards.

The concept "feeling" a force is very fuzzy.

so wanting to know the details and able to follow them are 2 different things
Reminds me of some of my students asking me how to prove that the electric field between two parallell flat charged plates is homgenous. I gave them the derivation. They looked like (students have never seen integrals before). What did that derivation provide them? nothing I guess.