Rates of Change and Multiple Dimensions

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  • #1
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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  • #2
sophiecentaur
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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(?)
 
  • #3
paulo84
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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'?
 
  • #4
paulo84
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I'm sorry, is this one of those 'noone knows what time is?' Read and understand carefully, I know what time is.
 
  • #5
sophiecentaur
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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.
 
  • #6
sophiecentaur
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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.
 
  • #7
paulo84
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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.
 
  • #8
sophiecentaur
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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,
 
  • #9
paulo84
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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
sophiecentaur
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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
paulo84
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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
jbriggs444
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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
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time is change of displacement
No.

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.

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.

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
ZHIHZ
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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
paulo84
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OK that makes a lot of sense. So is time the magnitude of change of position? Because that makes sense to me.
 
  • #16
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Rates of change again. Is the rate of change one up from acceleration 'instantaneous'?
The third derivative of position is called “jerk”.

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
paulo84
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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
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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
paulo84
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Oh...ok apologies for the arrogance. I try harder next time.
 
  • #20
paulo84
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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
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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.

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
lekh2003
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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
sophiecentaur
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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.
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
paulo84
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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
lekh2003
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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
paulo84
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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
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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
sophiecentaur
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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
sophiecentaur
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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
lekh2003
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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.
 
  • #31
sophiecentaur
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I often hear of teaching tactics where people ask questions first and then the teacher begins the class.
That's far too vague to prove things one way or another. It is not unusual for a teacher to ask students to prepare questions for next lesson but then the questions need to be within limits and they will be the result of some targeted homework.
Anything else would be idle chat and would risk wasting the other students' time.
I have a feeling that the OP expects to get a deep knowledge of Physics without any of the graft. He is destined to be disappointed - like many other 'visitors' we have had to PF.
 
  • #32
paulo84
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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.

What is the fundamental difference between a string and a wave?
 
  • #33
lekh2003
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What is the fundamental difference between a string and a wave?
A string transports a wave. It can act as a medium.
 
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  • #34
sophiecentaur
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What is the fundamental difference between a string and a wave?
Here we go; you have just made my point. Have you read about the two and what would your own conclusion be?
 
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