Special Relativity spaceship problem

[Mathematicsresear]

Homework Statement

Mavis boards a spaceship and zips Stanley on Earth a constant speed of 0.600c at the instant mavis passes, both start timers.

At the instant mavis reads 0.400 s on her timer, what does Stanley read on his?

Homework Equations

The Attempt at a Solution

since time from an stationary observer = gamma proper time, so the dilated time is 0.400s/the gamma factor which gives 1/2, why is this wrong?

 

[BvU]

Check your relevant equation (oops, it was erased ?) How do you calulate $\gamma$ ?

 

[TSny]

Hello.

The question is ambiguous to me. You could interpret the question in at least two non-equivalent ways:

(i) What is the reading of Stanley's timer at an instant that is simultaneous with Mavis' timer reading 0.400 s according to simultaneity as defined by Mavis?

(ii) What is the reading of Stanley's timer at an instant that is simultaneous with Mavis' timer reading 0.400 s according to simultaneity as defined by Stanley?

 

[Mathematicsresear]

Hello.

The question is ambiguous to me. You could interpret the question in at least two non-equivalent ways:

(i) What is the reading of Stanley's timer at an instant that is simultaneous with Mavis' timer reading 0.400 s according to simultaneity as defined by Mavis?

(ii) What is the reading of Stanley's timer at an instant that is simultaneous with Mavis' timer reading 0.400 s according to simultaneity as defined by Stanley?

Whats the difference between the two? The answer considers 0.400seconds as the one that is not dilated, which is what I'm confused about.

 

[Mathematicsresear]

Hello.

The question is ambiguous to me. You could interpret the question in at least two non-equivalent ways:

(i) What is the reading of Stanley's timer at an instant that is simultaneous with Mavis' timer reading 0.400 s according to simultaneity as defined by Mavis?

(ii) What is the reading of Stanley's timer at an instant that is simultaneous with Mavis' timer reading 0.400 s according to simultaneity as defined by Stanley?

I said thatAccording to Stanley, Marvis passes him, and according to Marvis, Stanley passes her. Therefore according to Marvis the dilated time is Stanleys time, is that correct?

 

[TSny]

I said thatAccording to Stanley, Marvis passes him, and according to Marvis, Stanley passes her. Therefore according to Marvis the dilated time is Stanleys time, is that correct?

Each person would say that the other person's timer runs slow compared to their own.

 

[TSny]

Whats the difference between the two? The answer considers 0.400seconds as the one that is not dilated, which is what I'm confused about.

As I read it, there is nothing in the statement of the problem that implies that the 0.400 seconds is not dilated. For Mavis, this time is not dilated (i.e. it is not "slowed"). But for Stanley, it is dilated (or slowed).

 

[Mathematicsresear]

Each person would say that the other person's timer runs slow compared to their own.

I said thatAccording to Stanley, Marvis passes him, and according to Marvis, Stanley passes her. Therefore according to Marvis the dilated time is Stanleys time is that correct?

 

[TSny]

I said thatAccording to Stanley, Marvis passes him, and according to Marvis, Stanley passes her. Therefore according to Marvis the dilated time is Stanleys time is that correct?

Yes, that's correct. But, according to Stanley, Marvis' time is dilated. Both views are valid.

 

[TSny]

For these types of problems, it's a good idea to think in terms of specific "events". Events occur at specific locations. The instant that Mavis' clock "strikes" 0.400 s is an event and this event occurs at the location of Mavis' timer (that she is carrying with her). We can label this event "E1". Likewise, each specific reading of Stanley's timer is an event located at Stanley's location. The question asks for the time that Stanley reads on his timer when Mavis reads 0.400 s on her timer. This is the same as asking for which event at Stanley's location is simultaneous with event E1 (which occurs at a different location). But Mavis and Stanley are not going to agree in general on the simultaneity of events. In particular, they are not going to agree on which reading of Stanley's clock is simultaneous with Mavis' clock striking 0.400 s.

The wording of the question is, "At the instant mavis reads 0.400 s on her timer, what does Stanley read on his?" I suppose that this could imply that we are asking Stanley to look at his timer at the instant he would consider Mavis' timer as reading 0.400 s. If so, then there is no ambiguity and there is a definite answer. But, it seems to me that the question could also be interpreted as asking for what time Mavis would say that Stanley sees on his timer at the instant her own timer reads 0.400 s. Perhaps most people would take one of these interpretations as being the more natural interpretation.

Anyway, if the question had asked, "At the instant Mavis' timer reads 0.400 s, what does Stanley's timer read?", then it would definitely be ambiguous.