Relativity question (1 Viewer)

[iStudent]

Please answer this and explain your answer:

If the electron in a cathode ray tube was travelling at 0.2c, qualitatively predict how mass and time for the electron would vary in the laboratory frame of reference and the electrons' frame of reference.

any responses would be welcome

 

[anomalousdecay]

It says qualitatively, but because it asks "explain" you should still use calculations. You should also quote the formulas.

In the laboratory's frame of reference, the electron will seem to have a larger mass than when stationary relative to the laboratory. Also, the electron will seem to, in terms of the laboratory's frame of reference, have time passing slower for the electron than the lab.

In the electron's frame of reference, the electron will tend to see no mass change in itself at this velocity relative to its mass when stationary relative to the lab. The electron in its frame of reference will see no difference in time for itself relative to time ticking when stationary relative to the lab.

That's pretty much all the question asked for, but you should put it in the structure necessary for all Physics questions, in context with the question verbs.

Explain means that you need to state what causes something to happen, what effect this has and what happens, and the reason why this happens.
So you should use calculations.

Does this help?

 

[iStudent]

Oh, sorry i made up the "explain" part (included there because I didn't get it)

According to the answer, in the electron's frame of reference, the laboratory's time passes more slowly and the mass of the objects in it increases (than when stationary, relative to the electron). also, the electron never sees its own passage of time change nor does its mass change.

don't really understand why the lab time passes more slowly and the mass in it increases (i understand why time passes slowly for the electron, but not for the lab).

 

[anomalousdecay]

Oh, sorry i made up the "explain" part (included there because I didn't get it)

According to the answer, in the electron's frame of reference, the laboratory's time passes more slowly and the mass of the objects in it increases (than when stationary, relative to the electron). also, the electron never sees its own passage of time change nor does its mass change.

don't really understand why the lab time passes more slowly and the mass in it increases (i understand why time passes slowly for the electron, but not for the lab).

Relative to the lab in its inertial frame of reference, the electron is travelling at a constant speed of 0.2c.

Relative to the electron in its inertial frame of reference, the lab is travelling at a constant speed of 0.2c.

You need both to be in an inertial frame of reference as stated above.

P.S. be careful with these types of questions. It did not ask for the variation in the mass and time of the lab. The mass of the lab would also be seen as an increase relative to the electron's frame of reference. You don't lose marks in the exam for stating extra, but instead lose time to write extra information.

 

[iStudent]

...and that's what's bugging me

how can both the electron's frame and the lab's frame both experience time dilation? what would happen (e.g.) if there were clocks in them? i know why the "clock" in the electron's frame would be slower after it slows to a stop, but how can this explain the one in the lab's frame? (which is, supposedly "slowing down").

I know this is outside the actual question, but if you can, can you explain this to me?

 

[anomalousdecay]

...and that's what's bugging me

how can both the electron's frame and the lab's frame both experience time dilation? what would happen (e.g.) if there were clocks in them? i know why the "clock" in the electron's frame would be slower after it slows to a stop, but how can this explain the one in the lab's frame? (which is, supposedly "slowing down").

I know this is outside the actual question, but if you can, can you explain this to me?

This is also explained by the twin paradox.

Basically, in the electron's frame of reference, someone moving in the lab will seem to be moving in slow motion. This occurs as of the formula:



Jacaranda has a clearer explanation on this.

Now, if you put a clock on each of the frames of reference, the electron will accelerate then decelerate, whereas the lab will stay in an inertial frame of reference at all times. The electron will go in a non-inertial frame of reference a few times.

So if you use a clock, you will not be able to clearly understand the difference.

There is a video on this. If I recall correctly this one:

Skip to about 20 minutes into the video. If it isn't clear, then watch the full video.

 

[studybuddy101]

i remember struggling with the exact same thing in school, the above explanations are really good but just incase i'll add what helped me understand it. The tricky part imo is understanding the fact that both systems can be "moving" relative to each other. Picture a man on the sidewalk and a person driving past, the person in the car sees the man to be moving whilst they sit still in the car, however the man on the sidewalk sees the car to be moving while he stands still. If that same car moved at relativistic speeds then they would both experience time dilation because they are both moving relative to each other. Try your best to visualise that above scenario as well as research the twin paradox suggested above (once you get it it'll bend your mind so don't worry if it doesn't fully make sense, it's not exactly an intuitive idea and is one reason Einstein is considered one of the greats).

 

[anomalousdecay]

i remember struggling with the exact same thing in school, the above explanations are really good but just incase i'll add what helped me understand it. The tricky part imo is understanding the fact that both systems can be "moving" relative to each other. Picture a man on the sidewalk and a person driving past, the person in the car sees the man to be moving whilst they sit still in the car, however the man on the sidewalk sees the car to be moving while he stands still. If that same car moved at relativistic speeds then they would both experience time dilation because they are both moving relative to each other. Try your best to visualise that above scenario as well as research the twin paradox suggested above (once you get it it'll bend your mind so don't worry if it doesn't fully make sense, it's not exactly an intuitive idea and is one reason Einstein is considered one of the greats).

This is very, very true. I didn't understand it until I realised inertial frames of references apply to such a situation. Then the twins paradox just solidified my realisation. Repped.

 

[iStudent]

Oh I think I get it... yeah I think it was because of the inertial/non inertial rule that tripped me over

But just one last thing to clear things up:
If we're looking at things from the electron's frame of reference, would "to" be the time in time in the electron's frame and "tv" be the time in the lab? (which is undergoing dilation)
Or is "to" always the time in the stationary frame (i.e. the lab)

 

[anomalousdecay]

Oh I think I get it... yeah I think it was because of the inertial/non inertial rule that tripped me over

But just one last thing to clear things up:
If we're looking at things from the electron's frame of reference, would "to" be the time in time in the electron's frame and "tv" be the time in the lab? (which is undergoing dilation)
Or is "to" always the time in the stationary frame (i.e. the lab)

If we're looking at things from the electron's frame of reference, would "to" be the time in time in the electron's frame and "tv" be the time in the lab? (which is undergoing dilation).

This is correct. It is in whichever frame of reference you are referring to be observing from, you get "to".

"tv" is always the frame that you are trying to observe.