I Force due to acceleration and time flowing differently

[PeroK]

Then the next thing to focus on is basic special relativity ...

... like the first postulate?

 

[HansH]

Do you understand Lagrangian mechanics?

I don't think that was part of my study somewhere.

 

[PeterDonis]

What do you mean by 'proper accelleration'

The acceleration measured by an accelerometer attached to the object.

When i am in freefall does that mean my proper accelleration is zero?

Yes.

 

[Dale]

I don't think that was part of my study somewhere.

If you want something useful, nothing you can study in relativity will be more useful than learning Lagrangian mechanics. And when you do learn the Lagrangian approach it will eventually make studying non-inertial reference frames easier. However, it isn't as "exciting" a topic as relativity.

 

[HansH]

Yes.

ok that helps. Then it means that I am not referring to the tem ''proper acceleration' but to the accelleration as result of an applied force such as a rocket engine. But then I think you are going to say that an observer cannot discriminate between gravity in curved spacetime and a rochet engine in flat spacetime due to the principle of equivalence. But at least for the acceleration he could isolate the effect of a rocket when he knows he has his rocket on or off as this gives the same relation between acceleration mass and force. so you could probably calculate the worldline with and without external forces and calculate only the contribution due to the external force to the difference in time between the watches. at least that should be easy for situations with flat spacetime as there ony the rocket could cause a change in speed.

 

[HansH]

If you want something useful, nothing you can study in relativity will be more useful than learning Lagrangian mechanics. And when you do learn the Lagrangian approach it will eventually make studying non-inertial reference frames easier. However, it isn't as "exciting" a topic as relativity.

thanks I will keep in mind.

 

[Dale]

Then it means that I am not referring to the tem ''proper acceleration' but to the accelleration as result of an applied force such as a rocket engine.

That is proper acceleration. An accelerometer does detect the acceleration as a result of a rocket engine. It seems like you may have a Newtonian physics misunderstanding here.

 

[HansH]

Yes. that would probably mean that the main idea of the topic cannot be united with general relativity due to the equivalence principle that cannot isolate an external acceleration from the effect of curvature on the path of a worldline? also based on the earlier statement that 2 different worldlines can exist with proper acceleration=0 over the whole worldline.

 

[Dale]

Yes. that would probably mean that the main idea of the topic cannot be united with general relativity due to the equivalence principle that cannot isolate an external acceleration from the effect of curvature on the path of a worldline?

I understand all of the words you are using but not the way you are using them.

Proper acceleration is the acceleration measured by an accelerometer. Both GR and Newtonian physics can describe the acceleration measured by an accelerometer. The difference between GR and Newtonian physics is not regarding proper acceleration. It is that Newtonian physics considers gravity to be a real force that is just coincidentally undetectable by accelerometers while GR considers gravity to be locally a fictitious force that is undetectable just like all other fictitious forces.

 

[HansH]

I understand all of the words you are using but not the way you are using them.

Proper acceleration is the acceleration measured by an accelerometer. Both GR and Newtonian physics can describe the acceleration measured by an accelerometer. The difference between GR and Newtonian physics is not regarding proper acceleration. It is that Newtonian physics considers gravity to be a real force that is just coincidentally undetectable by accelerometers while GR considers gravity to be locally a fictitious force that is undetectable just like all other fictitious forces.

I assume I am not talking about the difference between GR and Newtonian physics but the difference between GR with curved spacetime and special relativity with only flat spacetime. probably it helps to draw the worldlines in special relativity with the 2 rockets I used earlier and then calculate the difference between the stopwatches and compare that with the summed up product (integral) of acceleration times the time that the accelaration took at a certain value so integral(a(t)dt) (or probably a more relativistic equivalent that I cannot produce now) and divide that integral by the calculated timedifference between the stopwatches and see if this is a constant or not. But I agree that this should also work in general and for GR because otherwise it is not a valid theory. But proving that a theory is wong only needs one example.

 

[PeterDonis]

Then it means that I am not referring to the tem ''proper acceleration'

Yes, you are. See below.

but to the accelleration as result of an applied force such as a rocket engine.

Such an "applied force" causes proper acceleration.

I think you are going to say that an observer cannot discriminate between gravity in curved spacetime and a rochet engine in flat spacetime due to the principle of equivalence.

Not at all. Remember, in relativity "gravity" is not a force. The force you feel when you stand at rest on the surface of the Earth is not "gravity". It's the force of the Earth's surface pushing up on you. Just as, if you stand at rest on the floor of a rocket accelerating at 1 g, the force you feel is the force of the rocket's floor pushing up on you. The principle of equivalence says that you cannot distinguish these two cases by local observations, but that is not the same as saying that you can't distinguish "gravity" from the effects of a rocket engine in flat spacetime.

Basically what the principle of equivalence is saying is that proper acceleration is proper acceleration, and by itself it doesn't tell you want kind of spacetime geometry the proper acceleration is occurring in.

the equivalence principle that cannot isolate an external acceleration from the effect of curvature on the path of a worldline?

There is no such thing as "the effect of curvature on the path of a worldline" if by "curvature" you mean "spacetime curvature". That is getting things backwards. It's not that you start out with a worldline, and then you put it in one spacetime geometry or another and see what happens to it. You have the spacetime geometry first, and then you look at the behavior of worldlines in it. There is no way to pick out "the same worldline" in two different spacetime geometries and compare the effects of one spacetime geometry vs. another on "the worldline". There is no way to even define a "worldline" at all independently of a spacetime geometry.

 

[PeterDonis]

I assume I am not talking about the difference between GR and Newtonian physics but the difference between GR with curved spacetime and special relativity with only flat spacetime.

If you want to put gravity in your scenario, yes, that would be the usual assumption in this forum since it is the relativity forum.

probably it helps to draw the worldlines in special relativity with the 2 rockets I used earlier and then calculate the difference between the stopwatches

If this means "calculate the difference in arc lengths of the worldlines", then yes, this is the general method that always works, whether spacetime is flat or curved.

and compare that with the summed up product (integral) of acceleration times the time that the accelaration took at a certain value so integral(a(t)dt) (or probably a more relativistic equivalent that I cannot produce now) and divide that integral by the calculated timedifference between the stopwatches and see if this is a constant or not.

I'm not sure what you are trying to accomplish with all of this. But whatever it is, as I have already pointed out several times now, it would only be applicable to this scenario and nothing it might tell you would generalize usefully to other scenarios.

 

[Dale]

the difference between GR with curved spacetime and special relativity with only flat spacetime

I am not sure that there is any reasonable way to compare the lengths of two worldlines in different spacetimes. I mean, you can certainly compare their lengths, but trying to say the difference in length was caused by something seems impossible. Two different spacetimes are causally disconnected by definition.

 

[HansH]

I can produce scenarios where this is not true. You can have double the acceleration with the same difference between clocks.

I talked about acceleration during a certain time interval. so not ony the acceleration but also the duration of the accelleration. so it is about the combination of acceleration during a certain time interval (causing a speed difference between the 2 rockets) and the building up rate of the difference between the clocks. of course the difference in clocks builds up over the time that the speed difference remains, so the interval of keeping th speed difference before going back to same speed for both rockets also is in the relation. So I would expect you could write this down in a total equation something like :

difference in clocks= k1 x F1(build up speed difference) x F2(duration that the speed difference remans)

difference in clocks= k1 x F3(accelaration) x F4(duration the acceleration) x F2(duration that the speed difference remans)
so the question is: can we

 

[HansH]

I'm not sure what you are trying to accomplish with all of this. But whatever it is, as I have already pointed out several times now, it would only be applicable to this scenario and nothing it might tell you would generalize usefully to other scenarios.

The point is that mass curves spacetime and mass also resists against a change in speed. and a change in speed is acceleration and aceleration also plays a role in curvature of spacetime. So as I assume these are both properties of mass, it could well be that there is an underlying common reason for both properties to behave like this that we possibly cannot see because it could be in the machinery behind nature that we cannot see. so if this is the case there should be some relation so that was where I was looking for and if this was probably already known in the physics community.

 

[PeterDonis]

The point is that mass curves spacetime and mass also resists against a change in speed.

These are two different concepts of "mass". The precise term for the first one is "stress-energy", and the mathematical entity that embodies it in relativity is the stress-energy tensor.

The precise term for the second one (which actually is not properly described as "change in speed"--see below) is "invariant mass", which is a scalar, the norm of an object's 4-momentum vector.

In some particular cases there are relationships between these two things, but they're not the same.

a change in speed is acceleration

No. Proper acceleration is not a "change in speed", it's path curvature of a worldline.

The "change in speed" concept of acceleration is called "coordinate acceleration" in relativity, and it is not an invariant (whereas proper acceleration is). IMO this concept should simply be ignored when trying to learn relativity; it causes far more problems than it helps to solve. This is an instance of the general rule that frame-dependent quantities in relativity don't have any physical meaning and should not be focused on. They can be useful as conveniences to simplify calculations but they should not be focused on conceptually to try to understand what is happening.

The rest of your post just builds on the above misconceptions.

 

[PeterDonis]

I talked about acceleration during a certain time interval. so not ony the acceleration but also the duration of the accelleration. so it is about the combination of acceleration during a certain time interval (causing a speed difference between the 2 rockets) and the building up rate of the difference between the clocks.

Your approach here is based on some fundamental misconceptions (see my post #106 just now). As I have already commented multiple times now, you might be able to get something like this to work in certain particular scenarios, but nothing you learn from that will generalize. IMO you would be far better served by dropping this entirely and focusing on the geometric approach.

 

[Vanadium 50]

@HansH, you are not on the path to success.

You complain you don't want to spend years studying this. Fair enough, but this will limit what you will be able to learn - as Euclid said 2300 years ago, "There is no royal road to understanding mathematics".

You also want to start in the middle. OK, but there is a reason that normally people start at the beginning. You need to lay a proper foundation. If you tried to build the top floor of your house building the lower floors what is going to happen?

You need to seriously think about the replies you are getting. I can tell you aren't doing this because of your speed in responding. Fully half of your messages post in under 5 minutes since the message you are responding to. The most common case? Zero minutes - you post a reply in the same minute that the message you are replying to is posted.

If you want to learn, you need to do things differently than you are - especially more thinking about what people are saying to you. You have to put in the work. We can't do it for you.

 

[HansH]

in#105 I am asked what I am trying to accomplish.
I give a fair and open answer of my way of thinking and already indicated several times that I am not a professional physicist but eager to get answers on things that bother me and then as result I am given twice a shot in the back.
I appreciate your opinion and understand that you want everyone to learn physics, but in this way you block people to ask any question and show what keeps them busy
sorry for that, but this gives me a really bad taste in my mouth. Next time I am only asking a question after studying the full theory. Then I am at least prepared to understand al your reactions. If this is what (the way of commuinicating within) physics is about, then I am really happy I made the right decision in my study.

 

[PeterDonis]

I am given twice a shot in the back.

No, that's not what you have been given. What you have been given is an honest response telling you that what you say you want is not possible. What you say you want to accomplish in #105 cannot be done. If you don't want to accept that answer, that's up to you, but to characterize it as "a shot in the back" is wrong. We can't help it if the actual physics doesn't allow you to do what you want to do.

 

[HansH]

No, that's not what you have been given. What you have been given is an honest response telling you that what you say you want is not possible. What you say you want to accomplish in #105 cannot be done. If you don't want to accept that answer, that's up to you, but to characterize it as "a shot in the back" is wrong. We can't help it if the actual physics doesn't allow you to do what you want to do.

I think you still do not understand my point. of course I can agree on your conclusion that things are not possible and that there is not such relation as I brought into the discussion. You are the expert here. But when you are saying I react within 5 minutes and keep a stopwatch to see how fast I respond then I feel that as not respectfull and intimidating. and if I dare to ask a question that comes into my mind because I am a creative person in life helping technology forward with 75+ patents on my name helping my company to be the world leader, then you probably also can imagine that I have enaugh esperience to not letting anyone intinidate me. also not if I ask a question that does not fit into the logical sequence how normally a physics study is organized and get that back as my fault.

 

[PeterDonis]

when you are saying I react within 5 minutes and keep a stopwatch to see how fast I respond

If that specifically is what you are concerned about as being "a shot in the back", you should reference it specifically. (You can also use the Report button to report posts that you think violate PF rules.)

You might also want to consider that the criticism might be making a valid point. Bear in mind that everyone here who is an expert in this was once in the same position that you are in. Nobody is born knowing these things. We all have to learn them. And those of us who have learned them took years to do it, and made plenty of false starts and went down plenty of blind alleys in the process. You might want to consider that that experience gives us knowledge not just about the physics you are asking about, but about what works and what doesn't when trying to learn it.

if I dare to ask a question that comes into my mind

Nobody is saying you can't ask questions that come into your mind. But in this thread, you have repeatedly been asking questions that are based on fundamental misconceptions of yours, and the answers you have gotten are trying to tell you that--which amounts to telling you that in order to learn what you say you want to learn, you are first going to have to unlearn things that you think you already know. It's not clear that you've grasped that and considered its implications.

also not if I ask a question that does not fit into the logical sequence how normally a physics study is organized and get that back as my fault.

It's not a matter of "fault". It's a matter of what works and what doesn't in learning these things. See my comments above.

 

[HansH]

ok I will make one final remark about this. I think I already indicated several times that my knowledge level is not sufficient at this specific topic. Therefore I am not going into discussions about if something what an expert says is true or not, but instead I ask additional questions to get the picture more clear and to better prepare the picture what I still need to do. That probalby is the point of asking 5 questions in 1 minute.get things clear and get the way forward clear. That there are misconceptions seems locical, because that is the reason why I involve this forum becausing I want to test my thoughts with experts that can rapidly hit the essentials. I also indicated somewhere that I thought I was loading your team too mucht and already indicated on my own initiative that perhaps I should do more study first. And then I still get 10 reactions back that challenge me to use that to come further. I also asked advice what topics to study and at least Dale gave good advice there I think. but that is not a matter of a few days work.

You can discuss about the technical things being true of not, but you can't discuss about how someone should experience the way of communicating. When that is experienced as intimidating it is what it is. posting that should ring a bell at the people concerned at the level of intelligence we have here. so using the report button to me sounds more like being anonimous not daring to mention the things as they are and hiring other to solve that. That is not how I am.

for me this topic is sufficiently answered to be able to continue for a while with the input I got. so probably I will come back later with some more knowledge. (If I am allowed after mentioning things by name as I just did)

 

[PeterDonis]

for me this topic is sufficiently answered to be able to continue for a while with the input I got

Ok, good. That's the ultimate goal.

so probably I will come back later with some more knowledge.

Good.

(If I am allowed after mentioning things by name as I just did)

That's not an issue. By all means come back with further questions once you have continued for a while on your own.

 

[Sagittarius A-Star]

thanks I will keep in mind.

Here you can find good lecture videos from Leonard Susskind as introduction:
https://theoreticalminimum.com/courses

You can find there a lecture video about the Lagrangian for classical mechanics under

• "Classical Mechanics": Lecture 3

You can find lecture videos about Special Relativity (including relativistic laws of motion) under

• "Special Relativity and Electrodynamics": Lectures 1 to 3

Related textbooks:

• https://www.amazon.de/dp/0465075681/
• https://www.amazon.de/dp/0141985011/

 

[HansH]

Here you can find good lecture videos from Leonard Susskind as introduction:
https://theoreticalminimum.com/courses

You can find there a lecture video about the Lagrangian for classical mechanics under

• "Classical Mechanics": Lecture 3

You can find lecture videos about Special Relativity (including relativistic laws of motion) under

• "Special Relativity and Electrodynamics": Lectures 1 to 3

Related textbooks:

• https://www.amazon.de/dp/0465075681/
• https://www.amazon.de/dp/0141985011/

Thanks. 1 or 2 years ago I already followed the lecture video's about special relativity and also a part of the lectures about general relatvity. alt a certaim monent I lost the overview over the general relativity part and after some time started from scratch again. Then I saw that whe I viewed it for the second time I could follow more than the first time. so it seems difficult to to get this clear from video's alone. I think however more exersices would be needed as following a video only doesn't give the problems one runs into when doing yourself. so that is a thing I need to solve in some way also.

 

[malawi_glenn]

@HansH Lenny is releasing GR book end of this year/ beginning of next :) same series "the theoretical minimum"

 

[vanhees71]

Thanks. 1 or 2 years ago I already followed the lecture video's about special relativity and also a part of the lectures about general relatvity. alt a certaim monent I lost the overview over the general relativity part and after some time started from scratch again. Then I saw that whe I viewed it for the second time I could follow more than the first time. so it seems difficult to to get this clear from video's alone. I think however more exersices would be needed as following a video only doesn't give the problems one runs into when doing yourself. so that is a thing I need to solve in some way also.

The problem with such online-movies is that you tend to just watch the movies and think you have understood the material. This is particularly true for well-presented movies like the Susskind movies. The important point is that you have to sit down and do something actively with the material to see, whether you can work with the material, particularly solve problems for yourself. This holds, of course, true also for textbooks, manuscripts, and papers.

 

[HansH]

be comfortable using the Lagrangian for classical physics.

2 questions at this stage:
-From the given reference to the lectures of Leonard Susskind I understand that this method allows you to optimize something to a minimum value such as calculate the shortest trajectory between 2 points. Is that the reason why it is important for relativity?
-I also understood from one the reactions in this topic that the time dilatation is defined by the length difference between 2 worldslines. So then I assume that that length is the sum of ds over such trajectory. but for calculating ds pythagoras cannot be applied as we need to take the difference of the squares of the time and the space component. But from the lecture of Susskind I also understand that the Lagrangian method includes a part where pythagoras is used. So how should I interpret that?

 

[vanhees71]

The main reason to use the "principle of least action" is that it admits an elegant formulation of symmetry principles that underly all of modern physics. E.g., the form of the equations of motion in Newtonian mechanics look the way they look, because of the symmetry of the underlying Galilei-Newtonian spacetime model. As well the relativistic field equations of motion (in the classical realm that means classical electrodynamics) look the way they do in a similar way because of the symmetry of the spacetime model underlying special relativity (Minkowski spacetime). In its "Hamiltonian formulation" in phase space it provides one of the most elegant tools to heuristically "quantize" classical theories, known as "canonical quantization". To make this heuristical hand-waving a bit more rigorous you can refer to the representation theory of Lie groups and algebras, which tell you why the quantum theoretical equations look the way they look too, e.g., it explains why in a wave-mechanical formulation (1st quantization formalism of non-relativistic QM) the self-adjoint operator describing the momentum of a particle is $\hat{\vec{p}}=-\mathrm{i} \hbar \vec{\nabla}$: It's because momentum is the infinitesimal generator for spatial translations, and infinitesimal spatial translations are described by the Nabla-operator in field theory.