Force due to acceleration and time flowing differently

[Ibix]

Hmm, I thought he was asking about a relationship between acceleration and time dilation.

Depends which paragraph in the OP you read, I think...

 

[HansH]

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.

 

[PeroK]

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.

 

[Dale]

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.

 

[malawi_glenn]

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.

 

[HansH]

True, the he feels normal force mg upwards.

The concept "feeling" a force is very fuzzy.

ok so what is it you wanted to reach with your question? my knowledge of basic physics? that is pre university level with a mark 9 for physics and 2 years of physics during the study of 4 years of electical engineering. Dutch HTS which could be compared to batchelor I believe.

 

[malawi_glenn]

ok so what is it you wanted to reach with your question? my knowledge of basic physics? that is pre university level with a mark 9 for physics and 2 years of physics during the study of 4 years of electical engineering. Dutch HTS which could be compared to batchelor I believe.

Rather what the concept of "feeling a force" means. It is fuzzy.

 

[vanhees71]

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?

Indeed, "a force", seems to be best defined by the equation of motion of a particle in an external field,
$$\mathrm{d}_{\tau} p^{\mu}=F^{\mu}(x,p), \quad \mathrm{d}_{\tau} x^{\mu}=\frac{1}{m} p^{\mu},$$
where $m$ is the invariant mass. The "Minkowski force" $F$ must obey the contraint
$$p_{\mu} F^{\mu}=0,$$
such that the equation of motion is consistent with
$$p_{\mu} p^{\mu}=m^2 c^2 =\text{const}.$$
Of course, all this even holds within GR. Then you only have to use the covariant derivative wrt. $\tau$,
$$\mathrm{D}_{\tau} p^{\mu} = \mathrm{d}_{\tau} p^{\mu} + {\Gamma^{\mu}}_{\rho \sigma} p^{\rho} \mathrm{d}_{\tau} x^{\sigma}.$$
Note that then on the right-hand side you only have the forces but not gravity, which is contained on the left-hand side of the equation. In GR gravity is not a force to begin with of course. Perhaps it's anyway best to first concentrate on SRT only, excluding the discussion of gravity at this stage...

 

[HansH]

Rather what the concept of "feeling a force" means. It is fuzzy.

not sure how that relates to the answer the topic question. What actually happens is not fuzzy but well defined.

 

[malawi_glenn]

not sure how that relates to the answer the topic question

Topic question used the phrasing "feeling a force".

 

[vanhees71]

Feelings are anyway not subject of the natural sciences (except in brain research, maybe ;-)).

 

[PeterDonis]

gravity gives a force downwards

Not in relativity, no. In relativity gravity is not a force. It's just spacetime geometry. In relativity the Earth pushes up on you, causing you to have nonzero proper acceleration. That's why you feel a force (an upward force) when you are at rest on the Earth's surface.

 

[PeroK]

not sure how that relates to the answer the topic question. What actually happens is not fuzzy but well defined.

One of the things the principle of relativity implies is that an acceleration phase has no material or physical effect on a particle. This is equivalent there being "no such thing as a state of absolute rest".

It's clear that in your knowledge of physics the concept of absolute rest and absolute velocity is deeply embedded. And, everything you try to ask or understand about relativity is distorted by this misconception.

 

[HansH]

Topic question used the phrasing "feeling a force".

Ok I see. I did not want to talk about my feelings and especially not when it makes the topic diverge instead of converge as it now seems to do. So shall I change it to 'experiencing or what is the best word'? so let's discuss the essential parts.

 

[PeterDonis]

he feels a force F=m*a pointing to the left pushing him in his chair to the back

No. He feels a force F = ma to the right because the car is accelerating to the right.

or the person this feels like a force backwards as he resists to the acceleration

No, it feels like a force in the direction of the proper acceleration. The Earth pushes up on you giving you an upward proper acceleration, so you feel an upward force. The car pushes you to the right giving you a rightward proper acceleration, so you feel a rightward force.

 

[PeterDonis]

what would you suggest as the origin of force as a concept? It remains the rate of change of four momentum with respect to proper time

With the bolded addition above, this answers the question.

fouromentum is a normalised tangent to the worldline

No, 4-velocity is the normalized tangent vector. 4-momentum is not normalized; its norm is the invariant mass, not a constant number.

 

[vanhees71]

<Pedantic mode on> The Lorentzian fundamental form doesn't induce a metric, because it's not positive definite. For a classical particle, $p_{\mu} p^{\mu}=m^2 c^2=\text{const}$ with $m$ the (invariant) mass of the particle and $c$ the speed of light.

 

[Dale]

So shall I change it to 'experiencing or what is the best word'? so let's discuss the essential parts.

Perhaps talk about measurements with an accelerometer. That is why I brought in the second of the two suggested references, the one which determines the metric in a radar-coordinates non-inertial frame using an accelerometer as the input.

 

[HansH]

I don't know, what you mean by "one does not cause the other".

That came from Ibix in #14 I assume indicating the possible relation being the main subject.

 

[malawi_glenn]

Not in relativity, no.

Which is why I wrote "forget about relativity for a while" or something along those lines

experiencing

Being exerted on.

 

[PeterDonis]

Which is why I wrote "forget about relativity for a while" or something along those lines

I'm not sure that's a good idea. The OP is asking about relativity, and the treatment of gravity in Newtonian mechanics vs. relativity is very different, so I'm not sure trying to start with a Newtonian treatment will be helpful.

If the scenario were modified to eliminate gravity (for example, taking place out in deep space far away from all gravitating bodies), then starting with a Newtonian treatment might work better.

 

[Dale]

The Lorentzian fundamental form doesn't induce a metric, because it's not positive definite

Physicists nevertheless call it a metric, even knowing that technically it is not

 

[malawi_glenn]

Physicists nevertheless call it a metric, even knowing that technically it is not

Not all of them ;)

 

[vanhees71]

Given the confusion of the OP, I think we should be a bit more pedantic. Our sloppy physicists' slang is not helpful!

 

[PeterDonis]

Given the confusion of the OP, I think we should be a bit more pedantic. Our sloppy physicists' slang is not helpful!

I'm not sure harping on the pedantic difference between a metric and a pseudometric is going to be the silver bullet that resolves the OP's confusion. IMO it's more likely to increase it.

 

[Dale]

Given the confusion of the OP, I think we should be a bit more pedantic. Our sloppy physicists' slang is not helpful!

Understood. That is where we differ. Given the confusion of the OP, I think the OP should study the basics some more and then come back to this question. I don't think being pedantic will resolve the confusion, but I do think studying the basics will.

 

[vanhees71]

That's of course true ;-). I still think that sloppy slang adds to the confusion. When I started to study relativity in high school this particular example of calling an indefinite quadratic form "a metric" took me quite some time to sort out again.

 

[HansH]

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 .....

I see that I have to be much more accurate in my descriptions to prevent that the discussion drives away from the subject. as I understand An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed. so what I mean is then probably 2 rockets in space with an observer in each rocket going with relative speed =0 close to each other. Then they both synchronze their clocks and then one rocket accelerates for a certain amount of time with say 1g. so this gives a force of 1 Newton per kg mass at that mass during this amount of time. then after some time the same rocket accelerates for (I assume) a same amount of time with -1g so that after that there is no speed difference between the 2 rockets but only a certain distance in between. now they come together again by slow acelleration en de-aceleration and after that compare their watches. This means there is now a time difference between their watches related to the amount of time and acceleration that one of them acellerated. if I would use the double accellaration or the double time while acelerating finally the difference between their clocks would also be different. so therefore I suppose there could be an uderlying reason why both are related. (at least that both are related is clear and could be calculated)

 

[Vanadium 50]

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.

No, but you can't expect to start in the middle rather than the beginning and understand. That's why we call it the "beginning".

 

[HansH]

Understood. That is where we differ. Given the confusion of the OP, I think the OP should study the basics some more and then come back to this question. I don't think being pedantic will resolve the confusion, but I do think studying the basics will.

That sounds as a good compromise. For sure we differ as I am an engineer interested in the physics from pure interest relarted to topics I never studied so far (ok you have to make choices in your life) and most of you are professional physics guys. Only point for me is that I have a question about a possible relation that I see but no idea if or what underlying theory supports that, so what basics should I study then? looks like a chicken and egg. so there I need your advice. What I can do is study the links Dale gave and see if that makes sense, as I think that was a good advice.