# Rates of Change and Multiple Dimensions

• B
• paulo84
In summary: Is there a difference between time and motion?Is there a difference between time and motion?There is a difference between time and motion, but it’s not the difference you think it is. Time is a dimension of space, just as velocity is a dimension of space. But motion is just change of displacement! Or time! So there are an infinite number of dimensions of time?Yes, there are an infinite number of dimensions of time.
lekh2003 said:
A string transports a wave. It can act as a medium.

Thank you, I'm already more clear.

Another question - is there a part in physics which deals with strings carrying beta waves? Hope I don't get eaten!

paulo84 said:
is there a part in physics which deals with strings carrying beta waves?
What is a beta wave?

Dale said:

Thanks. Relative to the 'strings' article - I think I should revisit my textbook first! It's of course far beyond my current learning, I'm just hoping to get a somewhat correct understanding of more complex ideas.

Dale said:
What is a beta wave?

Sorry I meant beta ray. I could have sworn they were called 'beta waves' in school. Woops.

I withdraw my last question.

I'm starting to think Sophie is right.

paulo84 said:
I'm starting to think Sophie is right.
Yes, @sophiecentaur usually is right!

lekh2003, sophiecentaur and paulo84
Dale said:
Yes, @sophiecentaur usually is right!

That somehow doesn't surprise me. :) One final thought (for now) - lekh2003's answer gave me a very basic understanding of one aspect of string theory. A wikipedia article would have been far, far harder to decipher.

paulo84 said:
OK, so time is change of displacement. Speed is change of change of displacement.
It has already been discussed, but IMO bears repeating. Time is NOT change of displacement. If s represents the displacement of some object, then a change in displacement is usually represented as ##\Delta s##. Velocity is the instantaneous rate of change of displacement, and can be written either as s' or s'(t) or ##\frac {ds}{dt}##. This last notation is the derivative of s with respect to t. "Change of change of <whatever>" is not good terminology. We always talk about the "rate of change" of some variable with respect to some other variable. In this context, the "other variable" is time.

Without getting too deep into the weeds of calculus (which is what we're really talking about when we are discussing derivatives), ##\frac {ds}{dt}## is defined in terms of a limit. IOW, ##\frac{ds}{dt} = \lim_{\Delta t \to 0}\frac{\Delta s}{\Delta t} = \lim_{h \to 0}\frac{s(t_0 + h) - s(t_0)}{h}##. Suffice it to say, that we can approximate the velocity by taking smaller and smaller time increments in doing the calculation.

Speed and velocity are different. Velocity is usually taken as a vector quantity, as it indicates a rate of motion in some direction. Speed, on the other hand, is a scalar quantity, with speed = |velocity|. A car's speedometer records the magnitude of the car's velocity, but doesn't indicate the direction.

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, accleleration the rate of change of the velocity with respect to time. Again, if s is displacement, then s'(t) is velocity, and s''(t) or ##\frac {d^2s}{dt^2}##, also a vector quantity, as direction is significant.

paulo84 said:
It seems to me, with each new layer of change you're adding a new dimension.
No. Dimension has nothing to do with any of this.

paulo84 said:
Therefore there must be an infinite number of dimensions of space. Or am I getting space mixed up with motion?
Yes.

I agree with most of your post, but I don't understand how that proves that time is not change of displacement. But as has been noted, I'm not a physicist, I really don't know what I'm talking about.

I'm sorry. I just don't understand the difference between time and space. As far as I can fathom, they're the same thing.

paulo84 said:
I'm sorry. I just don't understand the difference between time and space. As far as I can fathom, they're the same thing.
Duration is what clocks measure, distance is what rulers measure. Clocks and rulers are different. If you are getting so far out in the weeds that the distinction escapes you, it's time to come back to the house.

Dale
jbriggs444 said:
Duration is what clocks measure, distance is what rulers measure. Clocks and rulers are different. If you are getting so far out in the weeds that the distinction escapes you, it's time to come back to the house.

Thanks, I am able to distinguish between space and time for the practical purposes of everyday living. I stand by my point.

paulo84 said:
I am able to distinguish between space and time for the practical purposes of everyday living. I stand by my point.
This is logically inconsistent. If they were the same thing then you could not distinguish between them.

Which one of us is making a circular argument?

Neither of us.

OK. So should I give up?

I retract my previous statement. I am not able to distinguish between space and time. I just think I can due to an illusion caused by consciousness.

There is not much we can do to help you then. If you can’t even distinguish between a clock and a ruler then you will have a very hard time with physics.

I think it is time to close this thread. If you wish to learn physics then please open a new thread with a substantive question

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