General and special theory of relativity in few words

I appreciate your indulgence, but I am not asking about equality. I am asking about the truth, or possible truth, of competing observations.

It is true that Smith claims the pattern of the bouncing ball is straight. It is true that Jones claims the pattern of the bouncing ball is not straight. Here we agree. Is it true that the pattern is both straight and not straight?

Here's an example. Smith and Jones observe a criminal suspect. Smith says the suspect is male; Jones says the suspect is not male. No one reports that the suspect is (in fact) male and not male.

Matterwave
Gold Member
A better analogy would be that Smith and Jones are both looking at a suspect from two sides. Smith says "I see a face", Jones says "I see the back of a head". Do you want to say that one or the other is wrong? They see the same thing, from two different perspectives, and have two different ways of describing the same situation.

Nugatory
Mentor
It is true that Smith claims the pattern of the bouncing ball is straight. It is true that Jones claims the pattern of the bouncing ball is not straight. Here we agree. Is it true that the pattern is both straight and not straight?

When Smith says "the pattern of the bouncing ball is straight up and down", I understand that statement as Smith meaning "the ball is moving on a path that takes it up and down but not left and right or forwards and backwards relative to me"

When Jones says "the pattern of the bouncing ball is straight up and down", I understand that statement as Jones saying "the ball is moving on a path that takes it up and down but not left and right or forwards and backwards relative to me".

It's possible, because of that all-important phrase "relative to me" for the ball to be bouncing up and down according to Smith but not Jones, or vice versa, without requiring that one of them be wrong.

Here's an example. Smith and Jones observe a criminal suspect. Smith says the suspect is male; Jones says the suspect is not male. No one reports that the suspect is (in fact) male and not male.

Suppose that Smith reported that "the suspect and I are the same gender" and Jones reported that "the suspect and I are not the same gender". Now we have (Thomas) Smith saying P and (Audrey) Jones saying not-P, yet they are both right and there is no contradiction.

The "straight up-and-down bounce" report works the same way; the notion of up and down is defined relative to an observer so different observers can make different statements about whether the motion is up-and-down without contradiction.

Perhaps the most important thing for understanding physics is learning the difference between frame-dependent quantities ("Is the bouncing ball moving straight up and down?", "Is the suspect of the same gender as you?") and frame independent quantities ("What is the world-line of the bouncing ball?", "What is the gender of the suspect?").

A better analogy would be that Smith and Jones are both looking at a suspect from two sides. Smith says "I see a face", Jones says "I see the back of a head". Do you want to say that one or the other is wrong? They see the same thing, from two different perspectives, and have two different ways of describing the same situation.

Thank you. With your analogy, we know that both judgments can be true: the suspect has a face and a back to his head. But suppose Smith says, "The face has a mole between his eyes," and Jones says, "The [same] face has no moles on it." Here, both cannot be true. (There might be confusion about what a mole is, but we still know that both cannot be true no matter our understanding of moles. That is Smith says, "The face has X on it," and Jones says "The face has no X on it.")

Again, using your analogy, and back to the bouncing ball, Smith says, "The ball has a red stripe on it," and Jones says, "The ball has a blue star on it." Both judgments can be true. But if Smith says, "The ball bounces in a straight line," while Jones says, "The ball does not bounce in a straight line (because it bounces in a W pattern)," both judgments cannot be true.

Thank you. With your analogy, we know that both judgments can be true: the suspect has a face and a back to his head. But suppose Smith says, "The face has a mole between his eyes," and Jones says, "The [same] face has no moles on it." Here, both cannot be true. (There might be confusion about what a mole is, but we still know that both cannot be true no matter our understanding of moles. That is Smith says, "The face has X on it," and Jones says "The face has no X on it.")

Sure, both cannot be true because this is a frame-independent statement.

Again, using your analogy, and back to the bouncing ball, Smith says, "The ball has a red stripe on it," and Jones says, "The ball has a blue star on it." Both judgments can be true. But if Smith says, "The ball bounces in a straight line," while Jones says, "The ball does not bounce in a straight line (because it bounces in a W pattern)," both judgments cannot be true.

Here we have a frame-dependent statement. This is why both statements can be simultaneously correct. This also means that "bouncing in a straight line" is not an absolute statement, but a relative one.