Hypothetical time travel & time dilation

[EvagelosEuler]

Homework Statement

<Q1> “Super Ted”, a famous children’s TV cartoon character, has
just leant of an evil deed carried out by “Texas Pete” who had opened a
farm gate at A and let all the sheep out onto the
train tracks and roads. It shows that everything was normal until Super Ted boarded the train at B and did some magic
to make sure that the train arrived at A before Texas Pete
opened the farm gate. Note : At A, departure was at 16:13 and at B, at 16:45

(a) Assuming that the distance D between B and A
is 30 km (in ref frame S), and Super Ted can break the law of
Physics about being able to get mass up to (and beyond the
speed of light), how many times faster than the speed of light
must the train travel to achieve the arrival time at A ?



(cool.gif (b) Now “Texas Pete”: is captured and given a community service
order to round up all the sheep using a
giant vacuum cleaner. If there are 3000 million sheep and these
have an average separation between them of 10m (in stationary
reference frame S), then at what sub-light speed (V wrt S) must
“Texas Pete” travel in order to capture all the sheep in t’=60
seconds of his time in reference frame S’? Note: you may
completely ignore the relativistic mass increase resulting from
cumulative inelastic collisions (captures of) with sheep.

<Q2> Consider two alien creatures, a senile old green Soup Dragon that
lives close to the centre of a 600m diameter asteroid and a relativistic-
velocity capable Iron Chicken. The Soup Dragon is in the rest reference
frame S. The Iron Chicken is in reference frame S’ and when triggered
can jump up to a speed of 0.8C instantly, and likewise can stop
immediately from 0.8c down to 0c. However despite its speed, the Iron
Chicken is not a very clever animal. The Iron Chicken is initially at rest
wrt S, however when it sees an explosion it will immediately make flight
at 0.8c directly towards the explosion, and if it sees a second explosion then it will stop immediately. Now the Soup Dragon needs a change in
diet and decides it wants some chicken ingredient to go into its soup pot,
situated very close to the centre of the asteroid. If the soup dragon has
some very precise timed detonator explosives, that it has synchronized
from its central position, what time difference δt between two explosions
will bring the Iron Chicken to rest at the precise centre of the asteroid?
Hint: a Minkowski diagram will simplify the solution to the problem.




THANKS

Homework Equations

Q1 VELOCITY TRANSFORMS, TIME DILATION, LORENTZ TRANSFORMS

Q2 TIME DILATION, LORENTZ CONTRACTION?

The Attempt at a Solution

Q1 Part a) is a hypothetical question about
time travel. I say hypothetical because we cannot accelerate matter
up to the speed of light. But suppose we could, and had a velocity
> c e.g. 2c, or 5c etc. What effect would this have on the time
dilation effect? Does it actually lead to time travel or not?
If not then I'd like to explain why not, as you see it. I Tried drawing a Minkowski
diagram, to see if this helps? Part b) of 1 I looked at the equation for time dilation, to see if that is of any use but I'm still confused.



Q2 I draw four vertical world lines, one for the Chicken's initial position,
one for the centre of the asteroid, and two others for the
explosive devices.I know that If something is stationary it moves along a vertical
line. Information of the explosion travels at the speed of light - this
is a 45deg line. The chicken must see the light of the explosion before
it can jump to sub light speed. Anything at sub light speed travels along a line that lies between the
vertical and the 45 deg light cone. However, I am unsure about which equation gives the correct δt?

 

[Jhero]

For Q1, the concept of time travel is not possible according to our current understanding of physics. The speed of light is the fastest speed at which anything can travel, and it cannot be exceeded. This means that no matter how fast the train travels, it will still experience time dilation, but the time dilation factor will approach infinity as the speed approaches the speed of light. This means that the train will appear to take less time to reach its destination from the perspective of an observer on the train, but from an outside observer's perspective, the train will still take the same amount of time to reach its destination. This means that time travel is not possible, even at speeds faster than the speed of light.

For Q2, the equation for time dilation is t' = t/γ, where t' is the time in the moving frame of reference, t is the time in the stationary frame of reference, and γ is the Lorentz factor, given by γ = 1/√(1-v^2/c^2), where v is the velocity of the moving frame of reference and c is the speed of light.

In this case, we know that the Iron Chicken can travel at 0.8c, so we can plug this value into the equation and solve for the time dilation factor, γ. Once we have this value, we can use it to calculate the time difference, δt, between the two explosions. This can be done using the formula δt = γΔt, where Δt is the time difference in the stationary frame of reference.

It is important to note that the Lorentz contraction does not play a role in this problem, as it only affects the length of objects in the direction of motion, not time. The Minkowski diagram may help to visualize the problem, but it is not necessary to solve it.