# Problem with understanding of relative motion.

• withoutn
In summary, the conversation revolves around the confusion about the concept of relative velocity and its measurement. The speakers discuss the example of two observers, K and K', who are moving with uniform velocity with respect to each other, and how they perceive each other's motion. They also bring up the concept of spacetime diagrams and the difficulty in measuring absolute velocity. The issue of gravitational fields and the idealization of observers as points is also mentioned.

#### withoutn

Hi everyone,
I have a problem with understanding a few lines from the book on Relativity I am using. Let me first quote my troubles,

"Let us express these facts algebraically, for two observers, K and K', who are moving with uniform velocity relatively to each other, thus:
K writes x = ct,
and K' writes x' = ct',
both using the same value for the velocity of light, namely, c, and each using his own measurements of length, x and x',
and time, t and t', respectively.

It is assumed that at the instant when the rays of light start on their path, K and K' are at the same place, and the rays of light radiate out from that place in all directions.

Now according to equation x = ct, K who is unaware of his motion through the ether (Since he cannot measure it), may claim that he is at rest and that in time, t, K' mus have moved to the right and [vice versa (K' thinks same about K)"

My question is, if K and K' are in the same place at an instant, how come either of them moves while the other stays in place? As is written, K thinks that K' moved, while K' thinks K moved, but wait a minute, since they're at the same place, don't they both move or stay?

withoutn said:
My question is, if K and K' are in the same place at an instant, how come either of them moves while the other stays in place? As is written, K thinks that K' moved, while K' thinks K moved, but wait a sminute, since they're at the same place, don't they both move or stay?

Consider a traffic accident, but a non-violent one in which the two cars are able to move through each other. The cars are only together at the instant of the collision; before and after the colliion, the cars are separated.

Hey, thanks
However, I can't quite imagine a guy standing on a piece of matter, and another passing right through him - Wouldn't that result in a colission? I need somewhat a better explanation. If these two guys are in spacecraft s, and let's say K passes by Point O where K' is parking at that moment and emitting a ray of light too, then, These two as long as they are in the same medium and same working spacecraft s, then I'm pretty sure it'd be possible to calculate the velocity of either one based on how far they recede from one another in time t, but on the other hand it's condradictory to experimental data which A. Einstein proposed (according to the book) where velocity of moving object cannot be measured.
Case 2, if they're not in Spacecrafts but for example at some distant planets, each moving through space with unknown velocity v (since it cannot be measured according to the data), Wouldn't the two fall into each others' gravitational fields while passing by? I don't know... It's so confusing and I suck in physics, Help Me...

withoutn said:
If these two guys are in spacecraft s, and let's say K passes by Point O where K' is parking at that moment and emitting a ray of light too, then, These two as long as they are in the same medium and same working spacecraft s, then I'm pretty sure it'd be possible to calculate the velocity of either one based on how far they recede from one another in time t, but on the other hand it's condradictory to experimental data which A. Einstein proposed (according to the book) where velocity of moving object cannot be measured.
There's no problem with either observer measuring their relative velocity. But an "absolute" velocity has no meaning; velocity is always with respect to something.

Can you draw a position vs. time graph [a spacetime diagram] of two objects traveling with different constant velocities?

withoutn said:
Hey, thanks
However, I can't quite imagine a guy standing on a piece of matter, and another passing right through him - Wouldn't that result in a colission? I need somewhat a better explanation. If these two guys are in spacecraft s, and let's say K passes by Point O where K' is parking at that moment and emitting a ray of light too, then, These two as long as they are in the same medium and same working spacecraft s, then I'm pretty sure it'd be possible to calculate the velocity of either one based on how far they recede from one another in time t, but on the other hand it's condradictory to experimental data which A. Einstein proposed (according to the book) where velocity of moving object cannot be measured.
Case 2, if they're not in Spacecrafts but for example at some distant planets, each moving through space with unknown velocity v (since it cannot be measured according to the data), Wouldn't the two fall into each others' gravitational fields while passing by? I don't know... It's so confusing and I suck in physics, Help Me...
Usually in physics when you talk about two observers passing next to each other, for convenience you're treating the observers as mathematical points, so their paths are just 1-dimensional lines, and the point where the lines intersect is where they pass. Of course this is an idealization, but if the scale of the problem is in light-years and the two ships pass within a few meters of each other, the error in treating them as points which pass at a single point is negligible.

## What is relative motion?

Relative motion refers to the movement of an object in relation to another object. It is the difference in position, velocity, and acceleration between two objects, taking into account their frames of reference.

## Why is understanding relative motion important in science?

Understanding relative motion is important in science because it allows us to accurately describe and predict the behavior of objects in motion. It also helps us to understand the laws of physics, such as Newton's laws of motion, which are based on the concept of relative motion.

## What are some examples of relative motion?

Some examples of relative motion include a car moving on a road, a person walking on a moving train, and a satellite orbiting around the Earth. In each of these cases, the motion of the object is described in relation to another object or frame of reference.

## How do you calculate relative motion?

To calculate relative motion, you need to determine the velocity and acceleration of each object involved, as well as their frames of reference. You can then use mathematical equations, such as the velocity and acceleration formulas, to determine the relative motion between the objects.

## What are the common challenges in understanding relative motion?

One common challenge in understanding relative motion is identifying the correct frames of reference for each object. Another challenge is visualizing the movement of objects from different frames of reference. It can also be difficult to accurately calculate the relative motion if there are multiple objects involved with varying velocities and accelerations.