Relative Velocity

[Mart]

Imagine X and Y moving at a steady non-zero velocity relative to each other. X might claim that he is stationary and that Y is moving. Y could reverse the claim. We scratch our heads and say that provided we stick to steady motion we do not know any way of distinguishing between moving and stationary. But this raises a problem. Although a huge number of different claims about the velocities of X and Y can be made (none, apparently, provable) it can't be the case that both X and Y are stationary. The steady non-zero velocity they experience relative to each other would vanish. It has to be true that at least one of them is moving. Is there a solution?

[5614]

The steady non-zero velocity they experience relative to each other would vanish.

 

i agree with most of the post, except the bit i quoted... so they are both moving relative to one another, or one is moving relative to the other, so why would the non-zero veolcity they experience relative to each other vanish?

 

by the way, you asked for the solution, but you didnt state a question, only a scenario.... the solution to what?

[ed84c]

Is this a H/W question?

 

If not, I think you may be confusing relative apearance with reality. Anyway X and Y would both experience (tiny) amounts of time slow, due to special relativity. therefore theoretically the model is not water tight because you may be able to work it out from this (theoretically)

 

wait till Martin comes along, he seems to be an expert on these things.

[Mart]

X and Y are assumed to be moving at a steady non-zero velocity relative to each other (first line of post). If both X and Y are stationary then how can the distance between them be changing steadily? No changing distance = zero relative velocity. That's the problem.

[5614]

that's impossible!

 

look:

 

X and Y are assumed to be moving at a steady non-zero velocity relative to each other (first line of post).

ok, they are moving at a non-zero velocity relative to each other, therefore if one is moving at speed 'q' the other is moving at more than 'q', there is a non-zero velocity relative to each other, so one MUST be moving faster than the other and therefore

 

If both X and Y are stationary

they cannot be, you said so yourself!

 

how can the distance between them be changing steadily

because one is moving faster than the other.

 

No changing distance = zero relative velocity

but you've already said:

 

non-zero velocity relative to each other

 

therefore they do have a velocity relative to each other.

 

so whilst:

"No changing distance = zero relative velocity"

is correct, they DO have a relative velocity so:

changing distance between x and y = non-zero relative velocity

which is what we have!

[Mart]

You say one MUST be moving faster than the other. What do X and Y have to do in order to determine their relative velocity?

[JaKiri]

If both X and Y are stationary then how can the distance between them be changing steadily?

 

They're not both stationary. Either one is stationary and the other isn't, or neither are. And all of these options are true.

[5614]

You say one MUST be moving faster than the other. What do X and Y have to do in order to determine their relative velocity?

to determine the relative velocity of x and y you must know their individual velocities.

 

if x is moving at 50 units of speed and y is moving at 75 units of speed their relative velocity is 25 units of speed.

[[Tycho?]]

X and Y are assumed to be moving at a steady non-zero velocity relative to each other (first line of post). If both X and Y are stationary then how can the distance between them be changing steadily? No changing distance = zero relative velocity. That's the problem.

 

What are you talking about. If the distance between two objects is changing steadily they are obviously not both stationary, you said this.

 

Its like saying "An apple is moving at 1m/s. Why is the apple not moving?" The problem is that its a contradiction, they cannot both be happening.

[Mart]

to determine the relative velocity of x and y you must know their individual velocities.

 

What do X and Y have to do to know their individual velocities?

[5614]

that's a strange question.

 

if X and Y are speedometers, or mass's which have a speedometer or a method of measure then you just read that.

 

its like asking "what do i have to do to know my speed?"

 

you measure the speed.

 

maybe using the equation

s=d/t

speed = distance / time

 

X and Y have to be measured by you so you know their velocity, they can only know thier own velocity if you feed them the data (if they are a computer of some sort) or you tell it to them (if they are a human or animal which you communicate to).

[Mart]

'']An apple is moving at 1m/s.

 

What does an apple (you) have to do to know that it is moving at 1m/s. Remember, there is no absolute velocity.

[JaKiri]

Hey guys, what's this!

 

They're not both stationary. Either one is stationary and the other isn't, or neither are. And all of these options are true.

[5614]

yeah JaKiri, my post #5 said the same thing!

 

What does an apple (you) have to do to know that it is moving at 1m/s. Remember, there is no absolute velocity.

 

remember there is no absolute velocity, you said it yourself... this apple is moving at 1m/s.... relative to what is it moving at that speed?

 

an apple cannot know its speed because an apple cannot know much, it doesnt have brain!

 

you can know the apple's speed is 1m/s relative to a ruler by seeing that the apple moves 10cm in 10 seconds, then you say

s=d/t

s=10cm / 10seconds

s=10/10

s=1

s=1m/s

[Mart]

 

if X and Y are speedometers' date=' or mass's which have a speedometer or a method of measure then you just read that.

 

[/quote']

 

Can't do that. No absolute frame of reference. Like no road surface. Like no surface at all.

 

Speed = distance/time. Yes. Ok. Where does X (now assumed sentient) measure distance to and time to and how does he do it?

[Mart]

you can know the apple's speed is 1m/s relative to a ruler

 

I need to make something clear. This is happening in empty space apart from the apple (and any other apples). Where's the ruler come from? We'll allow apples to be sentient. It could be a person.

[5614]

so this is in a universe where nothing but a few apples exist?

 

Where does X (now assumed sentient) measure distance to and time to and how does he do it?

 

you are asking, in an empty universe where nothing but human-intelligent apples exist, how would an apple measure an apple's speed?

 

well you cant, you need a human measurement system such as meters and time measured in seconds and speed, like meters per second.... and then you can calculate a speed.

 

you cant measure 'speed' unless the word has a definition, you cant use s=d/t unless both 'distance' and 'time' have a definition.

[Mart]

you cant use s=d/t unless both 'distance' and 'time' have a definition.

 

I'm not sure what you mean by a definition. Distance is measured with rulers and time is measured with clocks. Forget apples. Think two people moving relative to each other. In space. How could they each measure their individual velocities?

[5614]

I'm not sure what you mean by a definition. Distance is measured with rulers and time is measured with clocks. Forget apples. Think two people moving relative to each other. In space. How could they each measure their individual velocities?

 

there is no such thing as absolute velocity.

 

remember that!

 

"How could they each measure their individual velocities?"

you ask... well, relative to what i ask!

[Mart]

In your earlier post #8 you said

to determine the relative velocity of x and y you must know their individual velocities

.

 

So how do get to know their individual velocities? What experiment can you do? Tell me.

[5614]

So how[/b'] do get to know their individual velocities? What experiment can you do? Tell me.

 

in another thread JaKiri said: "circular logic is so fun", he said that just today, its very relevant to this thread!

 

to know their individual velocity you need to measure their velocity relative to something else.

on earth you measure the speed of your car relative to the road.

 

in space you measure your space ship's speed using s=d/t where distance starts at where you started and speed starts at 0, until the current point in time, you see 5 minutes after you started your journey from mars youve travelled 50 meters, therefore you are going at a speed of 10meters per minute.

 

in a space where only two humans exist you measure human X relative to human Y, there's nothing else to measure them again, you can only know the relative speed, you cannot know their individual speed as there's nothing else to measure them against!

[Mart]

in a space where only two humans exist you measure human X relative to human Y' date=' there's nothing else to measure them again, you can only know the relative speed, you cannot know their individual speed as there's nothing else to measure them against![/quote']

 

OK. But HOW would YOU go about measuring their relative speeds if YOU were X? A simple explanation will do.

[5614]

if you were X and you wanted to know your speed relative to Y you would use a speedometer and use Y as the absolute frame of reference.

 

you say:

 

right, Y is totaly still, starting NOW... *timing* 10 seconds later, right, *measuring* (instanteously) at 10 seconds in time i've moved 10meters away from Y, therefore s=d/t s=10/10 s=1 therefore i (X) have a speed relative to Y of 1m/s (meter per second).

[Mart]

right, Y is totaly still, starting NOW... *timing* 10 seconds later, right, *measuring* (instanteously) at 10 seconds in time i've moved 10meters away from Y

 

OK. We've got a clock to measure time. 10 metres? What about the ruler? How's that used? A bit of detail please.

[5614]

ok, Y holds one end of a measuring tape or ruler, X sees how far along it he has gone.