Clocks & Boxcars: Get Solution to Problem

[Dreads]

Can someone look at the attachment and tell me where I went wrong thanx

 

[JesseM]

Let's start with fig. 1 in those attachments. The text file starts out saying:

Referring to Fig 1
There is a boxcar traveling along train tracks at a constant velocity.

In the box car there are two lightning rods located at point A and B

There are a series of points G, D, H, E marked on the floor of the boxcar.

For those who don't want to download the diagram, G and D are on either side of the lightning rod at A at equal distances from it, and H and E are on either side of the lightning rod at B at equal distances from it.

length GA = length DA = length HB = length EB

In the boxcar there is a person named Dash

In the boxcar there are two identical clocks X and Y. The clocks stop when they are struck by photons from lightening

Dash is at rest wrt the boxcar as are the clocks

External to the boxcar is Still Bill who is not at rest wrt the boxcar

Dash positions the clocks at points D and E as shown and then synchronises clock X and Y. Dash now concludes that the clocks are synchronised within his frame.

So, clock X is to the right of lightning rod B at point E, and clock Y is to the right of lightning rod A at point D.

Dash then goes and stands at position J. Length JA = length JB.

A lightning bolt then strikes the two lightning rods at time T0. [/quote]
"At time T0" is too vague--do you understand that because of the relativity of simultaneity, if the two strikes happen at the same time in Dash's frame then they happen at different times in Still Bill's frame, and vice versa? If so, in whose frame do they both strike simultaneously at T0? You go on to say:

At time T0 Still Bill is a distance L from points A and B. As Still Bill is equidistant from points A and B the photons from A and B will strike his eyes simultaneously and he will conclude that the lightning bolts struck simultaneously.

The light will only reach his eyes simultaneously if the strikes occurred simultaneously in Still Bill's frame, i.e. if T0 referred to Still Bill's time coordinate. If the strikes occurred simultaneously in Dash's frame, then the light from the strikes will reach Still Bill's eyes at different moments.

Theory states that the photons from the lightning bolts travel at C and for spheres about points A and B

As length DA = length EB I don’t think I need to drive the fact that the time on the clocks X and Y will be the same. Going off the clocks Dash will also conclude that the lightning struck simultaneously.

But here you are assuming something incompatible with the above. If the strikes occurred simultaneously in Still Bill's frame, then they occurred non simultaneously in Dash's frame, therefore the time on the clocks X and Y will be different.

Do you understand that the relativity of simultaneity means if the strikes were simultaneous in one frame, they were non-simultaneous in the other? If so, you should be able to understand why only one of your two assumptions could be true--either Still Bill sees both strikes at the same time (because the strikes occurred simultaneously in Still Bill's frame), or Dash's clocks X and Y read the same time when the light hits them (because the strikes occurred simultaneously in Dash's frame), but both these assumptions cannot possibly be true.

 

[Dreads]

I agree T0 is too vague replace it with lightning bolts strike at points A and B. Dash and Still Bill want to know if they were simultaneous or not.

I don't assume anything different from any explanation you will find for simultenaiety.

 

[Dreads]

you say "Do you understand that the relativity of simultaneity means if the strikes were simultaneous in one frame, they were non-simultaneous in the other?"

Yes I understand that is the theory I mean that is very basic. If you don't know that then I think you shouldn't be posting here in the first place.

The problem I have is the results I get appear to be paradoxical with this concept

 

[Dreads]

Even if you ignore what Still Bill sees all together and concentrate on just what Dash observes I seems to get paradoxical results

 

[Dale]

Ignore Dash for a moment. Write down the t and x coordinates of the following events: the two lightning strikes and when Bill sees them.

 

[Dreads]

sorry there was an error in fig 1 I didnt have Dash positioned at point J the correct pic is attached

 

[Dreads]

FYI the round circles under the boxcar are its wheels they are a little confusing

 

[JesseM]

I agree T0 is too vague replace it with lightning bolts strike at points A and B. Dash and Still Bill want to know if they were simultaneous or not.

I don't assume anything different from any explanation you will find for simultenaiety.

In a standard explanation of simultaneity using train cars and lightning strikes, they always specifically state which frame the strikes are simultaneous in (usually the Earth's rest frame). You can't just say two strikes happen at A and B because it isn't enough information to answer your questions, it might be they were simultaneous in Still Bill's frame (Still Bill sees light from both strikes at same moment, Dash's clocks show different readings when light reaches them), it might be that they were simultaneous in Dash's frame (Still Bill sees light from both strikes at different moments, Dash's clocks show same reading when light reaches them), or it might be they weren't simultaneous in either frame (Still Bill sees light at different moments and Dash's clocks show different readings). These are all physically different scenarios, and they are all physically possible.

 

[Dreads]

referring to fig 1 Just a question. If Still Bill perceives the bolts as simultaneous will the photons from A strike clock Y simultaneously as the photons from B to clock X?

 

[Dreads]

OK let's say the strikes are simultaneous in Still Bills frame

 

[Dreads]

referring to fig 1 Just a question. If Still Bill perceives the bolts as simultaneous will the photons from A strike clock Y simultaneously as the photons from B to clock X? from Still Bills perspective

 

[JesseM]

referring to fig 1 Just a question. If Still Bill perceives the bolts as simultaneous will the photons from A strike clock Y simultaneously as the photons from B to clock X? from Still Bills perspective

Yes, in Still Bill's frame. However, in Still Bill's frame these two clocks are not synchronized, so they will show different times when the light hits them despite the fact that the light hits them simultaneously in this frame.