Rates of Change and Multiple Dimensions

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Discussion Overview

The discussion revolves around the concepts of rates of change, particularly in relation to displacement, velocity, acceleration, and the nature of time and motion. Participants explore the implications of these concepts in both theoretical and conceptual contexts, questioning the relationships between them and the dimensionality of space and time.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that with each layer of change (e.g., displacement, velocity, acceleration), a new dimension is added, leading to the idea of infinite dimensions of space or time.
  • Others argue that time and motion are distinct, suggesting that time is not simply a measure of change in displacement.
  • A participant questions whether time can be defined as the rate of displacement, leading to confusion about the definitions of velocity and acceleration.
  • There are claims that acceleration is the second derivative of position, while some participants mistakenly refer to it as the third derivative.
  • One participant suggests that rates of change may be limited by the number of dimensions, questioning if there can be a rate of change beyond acceleration that is not instantaneous.
  • Concerns are raised about the speculative nature of some contributions, with calls for grounding ideas in established physics.
  • Another participant reflects on the challenge of contributing meaningfully without a strong background in physics, expressing a desire to understand mainstream concepts better.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement, with some supporting the exploration of rates of change and dimensions, while others challenge the validity of certain claims and the speculative nature of the discussion. The conversation remains unresolved on several key points, particularly regarding the nature of time and the dimensionality of change.

Contextual Notes

Some discussions involve misunderstandings of mathematical definitions and relationships, particularly concerning derivatives and their physical interpretations. There is also a noted tension between speculative ideas and established physics principles.

Who May Find This Useful

This discussion may be of interest to those exploring foundational concepts in physics, particularly in relation to motion, time, and mathematical representations of change.

paulo84
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OK, so time is change of displacement. Speed is change of change of displacement. Acceleration is change of change of change of displacement (or of distance, sorry I'm not sure whether acceleration is a vector or a scalar). Then you get change of change of change of change etc. ad infinitum.

It seems to me, with each new layer of change you're adding a new dimension. Therefore there must be an infinite number of dimensions of space. Or am I getting space mixed up with motion? But motion is just change of displacement! Or time! So there are an infinite number of dimensions of time?

Is there a difference between time and motion?
 
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paulo84 said:
Is there a difference between time and motion?
I think you have already pointed out the difference as long as you change the first "change" to "rate".
I think you may be trying to make up your own Maths here(?)
 
Sorry, it has just been a long time since I did maths at school. Are you saying you can use change for every example apart from the first one? OK then, can we reapproach this saying 'time is rate of displacement'?
 
I'm sorry, is this one of those 'noone knows what time is?' Read and understand carefully, I know what time is.
 
Look up definitions of velocity, acceleration etc.
Velocity is rate of change of position
Accn. is rate of change of velocity or rate of change of rate of change of position
And you can go as far as you like with the derivatives.
But time is not space, is it? and displacement is a spatial quantity.
Read around this site - starting here.
 
paulo84 said:
I'm sorry, is this one of those 'noone knows what time is?' Read and understand carefully, I know what time is.
You may know 'what time IT is' but, if you think you know what time is, you had better write a paper about it and submit to Scientific American. I think you may be out of your depth here and there are not many PF members who would claim they know what you claim you know.
 
You see, this is my problem. I am not a physicist with a phd, but I know what time is. Obviously no one will take me seriously. I just thought I'd try.
 
paulo84 said:
Obviously no one will take me seriously.
But why should they? To convince people, you need evidence from real experiments or measured observations. You have just made an assertion - a bit like they used to do, hundreds of years ago. Science has moved on since then,
 
I agree. I was just following a logical thought process.

If you like we can forget about whether or not I know what time is and see if what I'm saying in opening post even makes sense?
 
  • #10
paulo84 said:
I agree. I was just following a logical thought process.

If you like we can forget about whether or not I know what time is and see if what I'm saying in opening post even makes sense?
It doesn't - to me.
 
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  • #11
I had another thought. Rates of change again. Is the rate of change one up from acceleration 'instantaneous'? Perhaps rates of change are limited by the number of dimensions, and you can't actually go infinitely. Is there a scientific test which has proved a rate of change above acceleration to exist, without being 'instant'?
 
  • #12
paulo84 said:
I had another thought. Rates of change again. Is the rate of change one up from acceleration 'instantaneous'? Perhaps rates of change are limited by the number of dimensions, and you can't actually go infinitely. Is there a scientific test which has proved a rate of change above acceleration to exist, without being 'instant'?
You are not making any sort of sense at all and, instead, seem to be stringing heard-of-somewhere buzzwords around without heed to any meaning they might have. It doesn't work that way. Further, these forums have rules against such speculation.
 
  • #13
paulo84 said:
time is change of displacement
No.

paulo84 said:
Speed is change of change of displacement.
No. speed is the magnitude of the rate of change of position with respect to time. Or, more briefly, the first derivative of position.

paulo84 said:
Acceleration is change of change of change of displacement (or of distance, sorry I'm not sure whether acceleration is a vector or a scalar).
No. Acceleration is the second derivative of position, not the third.

paulo84 said:
It seems to me, with each new layer of change you're adding a new dimension. Therefore there must be an infinite number of dimensions of space.
Each order of derivative is indeed mathematically orthogonal to the previous, so it can be considered a dimension in a vector space. But this vector space is not the same as space, so it doesn’t add dimension to space.
 
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  • #14
Both are relative and change depending on you view point.new information can change the change and leave you spending all your time without getting any change to spend on new change.so having no change after having change leaves you with change without having any change.
 
  • #15
OK that makes a lot of sense. So is time the magnitude of change of position? Because that makes sense to me.
 
  • #16
paulo84 said:
Rates of change again. Is the rate of change one up from acceleration 'instantaneous'?
The third derivative of position is called “jerk”.

paulo84 said:
Perhaps rates of change are limited by the number of dimensions, and you can't actually go infinitely.
In principle there is no limit. However, Newton’s laws are about the second derivative, so there is rarely any need to go higher.
 
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  • #17
OK so it doesn't go instant it just goes accelerated of accelerated? Interesting. I'm sorry for the speculation, I don't want to be a trouble maker, I just find myself constantly having somewhat logical thoughts and I don't know where to run other than physicsforums...
 
  • #18
paulo84 said:
OK that makes a lot of sense. So is time the magnitude of change of position? Because that makes sense to me.
No. Written mathematically you are saying: ##t=|\frac{d}{dt}x|## which doesn’t make sense because t appears on both sides. It is a circular “definition “. It also doesn’t make sense physically because most systems don’t obey that relationship.
 
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  • #19
Oh...ok apologies for the arrogance. I try harder next time.
 
  • #20
But why can't you define 'change of position' as either displacement or time? Imagine there is only 1 material object in existence. If it moves or time passes, there will be no visible change as there is no other reference point. Surely this shows either motion or time only become distinguishable when you have 2 or more material objects?

If you have 2 material objects and nothing else, then the 4 fundamental forces can come into play. But does it not make more sense to try and understand things like time and motion in terms of the 4 forces?

Sorry I'm in way over my head. Wish I could contribute better.
 
  • #21
paulo84 said:
Imagine there is only 1 material object in existence.
You certainly can imagine such a barren universe, but physics is about describing this universe and I am highly doubtful of the value of such imaginations for that goal.

paulo84 said:
Sorry I'm in way over my head. Wish I could contribute better
The best way to contribute is to learn mainstream physics. There are some very good reasons why things are done the way they are. Until you learn those your proposals will consistently run into problems that have already been solved. Only then you will be able to look for approaches that improve what doesn’t work without breaking what does.
 
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  • #22
Dale said:
The best way to contribute is to learn mainstream physics. There are some very good reasons why things are done the way they are. Until you learn those your proposals will consistently run into problems that have already been solved. Only then you will be able to look for approaches that improve what doesn’t work without breaking what does.
I think I am beginning to full understand why PF doesn't allow speculations. @paulo84 is coming up with ideas without fully understanding mainstream physics. It is easy to make theories and assertions in modern physics if you don't understand mainstream physics. I have recently finished learning most of classical physics and I now understand that many of the crazy thoughts about physics I had were simply misconceptions.
 
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  • #23
paulo84 said:
I just find myself constantly having somewhat logical thoughts
They may be 'thoughts' but that doesn't make them "logical", I'm afraid.
If you aren't prepared to follow the accepted approach of mainstream Physics then you shouldn't attempt to have a proper conversation about it.
paulo84 said:
Sorry I'm in way over my head. Wish I could contribute better.
Yes, you seem to be. If you really want to contribute better then you need to get up to speed with real Physics. You will never manage to construct one of your own, from scratch. None of the great minds of the past and present have ever done it that way.
 
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  • #24
lekh2003 said:
I think I am beginning to full understand why PF doesn't allow speculations. @paulo84 is coming up with ideas without fully understanding mainstream physics. It is easy to make theories and assertions in modern physics if you don't understand mainstream physics. I have recently finished learning most of classical physics and I now understand that many of the crazy thoughts about physics I had were simply misconceptions.

I would just add that there can be value to speculations. I wish I had the time to learn all of classical physics. Certainly I will be revisiting my high school textbook.
 
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  • #25
paulo84 said:
I would just add that there can be value to speculations. I wish I had the time to learn all of classical physics. Certainly I will be revisiting my high school textbook.
There can be value to speculations but on this forum, we avoid them since they might confuse members not learned in physics.

It's nice to know you will be revisiting the world of classical physics.
 
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  • #26
lekh2003 said:
There can be value to speculations but on this forum, we avoid them since they might confuse members not learned in physics.

It's nice to know you will be revisiting the world of classical physics.

Thanks. I have to admit I'm a little frustrated. If I were allowed to ask as many questions as I liked, I'm pretty sure I could get up to speed relatively quickly. Unfortunately (for me) these forums are stricter than that. I fully understand the approach though.
 
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  • #27
paulo84 said:
If I were allowed to ask as many questions as I liked, I'm pretty sure I could get up to speed relatively quickly
Ask as many questions as you like! The problem isn’t in questions, it is in speculation. Speculation does not accelerate education, we have tried.
 
  • #28
paulo84 said:
I would just add that there can be value to speculations.
Not random ones though. Monkeys and typewriters never produced anything worth reading, did they?
 
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  • #29
paulo84 said:
If I were allowed to ask as many questions as I liked, I'm pretty sure I could get up to speed
It well know that Q and A is not a good way to learn because one doesn't know the appropriate questions to ask. You are 'allowed' to read as many textbooks as you like and use other people's past knowledge about how to get into a subject.
 
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  • #30
sophiecentaur said:
It well know that Q and A is not a good way to learn because one doesn't know the appropriate questions to ask. You are 'allowed' to read as many textbooks as you like and use other people's past knowledge about how to get into a subject.
I often hear of teaching tactics where people ask questions first and then the teacher begins the class. It works, but at the end of the day, the teacher has to fully explain everything about how they were wrong and how they were right.

I don't think this can work on something like PF, there's no guarantee that the member understood everything at the end of the discussion.
 

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