What are the energy implications of time travel into the future?

[Suraj M]

I'm new to all these concepts so sorry if i make any mistake in advance !
I watched a video on Nat Geo a few months ago it was about time travel into the future which is quite possible.
They talked of building a track that goes around the earth. A train would go around the Earth at a very high speed so hence slowing down time for the passengers. They said that 1 week in the train would be equal to 100 years on the earth.
My question is regarding the energy for the train.
I f you power it from the outside then you'll have to supply energy to the train for a 100 years and if you supply the energy from inside it would be just for a week! What am i missing here? Don't say change in mass!

 

[DaveC426913]

The concept, of course, is fantasy.
The train would circumscribe the planet and pass through its one station seven times every second.
The system would contain so much kinetic energy that it would turn the planet into a ticking bomb.
Not to mention that the Earth does not contain enough energy to power it.
There's no physical way to contain it against the colossal forces involved.
And the g-forces on the passengers and somewhere around one billion g's.

But the principle is sound. Moving at .99999998c (the speed of light to within one part in 100 million) would let you experience only one week as a century passed on Earth.

I'm still working on a way to describe the solution to your question: why the discrepancy in energy.

 

[Dale]

What am i missing here?

Energy is different in different frames. It is frame-variant.

 

[CRT]

The basic difference is only in the passage of time.If we talk of Earth we are living at the rate of 1 hour per hour and when moving close to (c) the speed being considered here which is hard to attain,we are living at 1week per 100 year.so if we use energy say E on Earth to accelerate that train.It is equivalent to much more energy calculated by you for 1 week sitting inside the train.Even if you use that energy for 1 week,a person on Earth will say that you have used the same amount of energy E for 100 years.As also stated by dale spam sir previously that energy is different in different frames.

 

[Nugatory]

The basic difference is only in the passage of time.If we talk of Earth we are living at the rate of 1 hour per hour and when moving close to (c) the speed being considered here which is hard to attain,we are living at 1week per 100 year.

That is not right. You are always "living at one hour per hour". Consider that right now, even as you're reading this, you are moving at .99c according to an observer in some far distant galaxy but also about one km/sec relative to someone on the other side of the rotating earth. Which if either of these speeds should determine how fast time is passing for you? The answer, of course, is "neither".

 

[CRT]

yes you are correct sir but i was considering the passage of time as noticed according to a third viewer in free space.when he looks at me on Earth he should say mr.crt you are living 1 hour per hour.but if i were in that train orbiting Earth a speed of .99 c the third person would say mr .crt you are living 1 week per 1century with respect to earth.I forgot to mention it previously.
if its still wrong then please sir reply to it.A big thanks in advance sir.

 

[Suraj M]

Energy is different in different frames. It is frame-variant.

What does that mean? Are you referring to the magnitude?

 

[Suraj M]

When i took this question to my physics teacher, he said something about the path of the train getting shortened because of his speed! How does that come in?

 

[DaveC426913]

I was working on that angle.

It is true. The path of the train is so dramatically shortened by length contraction that it only takes a week to reach the finish line. Essentially, the Earth shrinks so much that all 22 billion round-the-world trips (that's 7 per second for 100 years to everyone else) only take the train one week to complete.

That is one way of answering your conundrum.

It's easier to see when you examine a one-way trip to a distant star. Say it's 100 light years away. On Earth we see the trip take 100 years, but in the ship, traveling at .99999998c, the distance is contracted to a mere light-week away. Thus, for the occupants, it takes only a week to arrive - which only requires one week's worth of fuel.There are many ways of looking at this problem, some are more intuitive than others.

 

[Nugatory]

Energy is different in different frames. It is frame-variant.

What does that mean? Are you referring to the magnitude?

A bullet weighing .1 kg strikes a 1000 kg elephant with a velocity of 1000 meters per second.

It's natural to analyze this problem using a frame in which the elephant is at rest and the bullet is moving. The total kinetic energy of the system (elephant and bullet) is, by ##E_k=mv^2/2##, ##5\times{10}^4## joules. (That's the classical formula - the speed is small enough that I don't need to worry about relativistic effects).

However, we could choose to use a frame in which the bullet is at rest and the elephant is moving. In that frame, we have a one-metric-ton elephant moving at one kilometer per second, and the kinetic energy is ##5\times{10}^8## joules.

There's no violation of conservation of energy going on here. Whatever frame we choose will have a certain amount of energy, and it won't change. However, that amount may be different in different frames so we call it a "frame-variant" (as opposed to "frame-invariant") quantity.

 

[Dale]

What does that mean? Are you referring to the magnitude?

Energy is not a vector so it only has a magnitude.

Consider an ordinary train moving at more normal velocities, like 30 m/s, and a 1 kg ball thrown by a passenger at 10 m/s relative to the train. Relative to the train the ball has 50 J of KE, but relative to the tracks it has 800 J of KE.

Energy is different in different frames. The exact same ball in the exact same scenario has different KE depending on if you are doing the analysis for the train or for the earth. This is not just something that happens at speeds close to c.

 

[Suraj M]

But change in KE is absolute right? so It would still require the same energy to power it from outside and inside.

 

[CRT]

Energy is not a vector so it only has a magnitude.

Consider an ordinary train moving at more normal velocities, like 30 m/s, and a 1 kg ball thrown by a passenger at 10 m/s relative to the train. Relative to the train the ball has 50 J of KE, but relative to the tracks it has 800 J of KE.

Energy is different in different frames. The exact same ball in the exact same scenario has different KE depending on if you are doing the analysis for the train or for the earth. This is not just something that happens at speeds close to c.

Energy is not a vector so it only has a magnitude.

Consider an ordinary train moving at more normal velocities, like 30 m/s, and a 1 kg ball thrown by a passenger at 10 m/s relative to the train. Relative to the train the ball has 50 J of KE, but relative to the tracks it has 800 J of KE.

Energy is different in different frames. The exact same ball in the exact same scenario has different KE depending on if you are doing the analysis for the train or for the earth. This is not just something that happens at speeds close to c.

This example given by dale spam clearly defines everything.50J energy of ball with respect to train is 800 J if seen relative to track and is something different value if seen relative to a car moving at say 5 Km/ hr.So value of energy is not absolute.
Hats off.

 

[A.T.]

But change in KE is absolute right?

No.

 

[Suraj M]

No.

 

[Nugatory]

But change in KE is absolute right? so It would still require the same energy to power it from outside and inside.

No. Consider a one-kilogram object that starts at rest relative to you and is accelerated to 20 meters/second, for a net change in kinetic energy of 200 joules in your frame. I, moving at 10 meters/second relative to you and seeing the object accelerate from -10 meters/sec to 10 meter/sec, will find that the kinetic energy was 50 joules before and after so the net change is zero.

There's still no violation of energy conservation here. Suppose the object is a rocket, and the energy came from burning its fuel. The amount of fuel burned is of course the same in both frames and it has the same chemical characteristics in both frames, so the total amount of energy released is the same in both frames. So you might expect the change in kinetic energy of the rocket is the same in both frames... But it's not. You'll find the "missing" energy in the rocket's exhaust gasses, which are moving in the opposite direction and with frame-variant speeds.

Even if the object isn't a rocket and it was accelerated by some external force, Newton's third law requires that there will have been an equal and opposite force on something, and you'll find your missing energy in the change of speed of that something.

 

[Dale]

But change in KE is absolute right? so It would still require the same energy to power it from outside and inside.

As Nugatory explained, no, it is not the same.

It is important to understand that "frame invariant" and "conserved" are two entirely different concepts. "Frame invariant" means that different reference frames agree on the value. "Conserved" means that the value does not change over time.

Energy is conserved, but it is not invariant. So, going back to your OP, the train frame and the Earth frame will disagree about the amount of energy, but in each frame the energy will be conserved.

 

[jbriggs444]

Consider a one-kilogram object that starts at rest relative to you and is accelerated to 20 meters/second, for a net change in kinetic energy of 200 joules in your frame. I, moving at 10 meters/second relative to you and seeing the object accelerate from -10 meters/sec to 10 meter/sec, will find that the kinetic energy was 50 joules before and after so the net change is zero.

However, if you close the system...

Consider a one kilogram object accelerated from 0 to 20 meters per second (delta KE 200 Joules as above) together with a 10 kg platform from which it was launched (delta KE = 20 Joules). That's a total of 220 Joules.

Now shift to a frame of reference in which this is an acceleration from -10 to 10 meters per second (delta KE 0 Joules as above) together with the 10 kg platform from which it was launched (delta KE = 220 Joules). That's also a total of 220 Joules.

 

[Dale]

That does work in Newtonian mechanics, but not in relativistic mechanics.

EDIT: Oops. I sat down and actually worked it out and it does work in relativistic mechanics also. jbriggs444 is correct. For a closed system the energy of each particle and the energy of the system as a whole is frame variant, but it seems that the change in kinetic energy is not. At least not for one particle splitting into two particles.

 

[bubblewrap]

That does work in Newtonian mechanics, but not in relativistic mechanics.

EDIT: Oops. I sat down and actually worked it out and it does work in relativistic mechanics also. jbriggs444 is correct. For a closed system the energy of each particle and the energy of the system as a whole is frame variant, but it seems that the change in kinetic energy is not. At least not for one particle splitting into two particles.

So the change in Kinetic energy is frame invariant and absolute?

 

[bubblewrap]

I was working on that angle.

It is true. The path of the train is so dramatically shortened by length contraction that it only takes a week to reach the finish line. Essentially, the Earth shrinks so much that all 22 billion round-the-world trips (that's 7 per second for 100 years to everyone else) only take the train one week to complete.

That is one way of answering your conundrum.

It's easier to see when you examine a one-way trip to a distant star. Say it's 100 light years away. On Earth we see the trip take 100 years, but in the ship, traveling at .99999998c, the distance is contracted to a mere light-week away. Thus, for the occupants, it takes only a week to arrive - which only requires one week's worth of fuel.There are many ways of looking at this problem, some are more intuitive than others.

So the passengers of that train would see a shortened track of the train as well as shortened circumference of Earth?

 

[Suraj M]

So the passengers of that train would see a shortened track of the train as well as shortened circumference of Earth?

I realized that Taking Earth for this example,is just not realistic. Thanks to all of them who replied here.
And yes the distance would contract.
I haven't officially studied these topics but when i was discussing this with my physics teacher he gave me an example of of some muons, je said they dro tp the ground really quickly and should decay before they drop, but they don't because the distance shrinks for them and time for us or vice versa I'm not sure.
He also said that if length contracts time won't slow down, only one of them can happen! Is that true? If it is then, we can't consider the angle of distance contraction as we are already talking of time!

 

[Ronzinem]

Well its like this... Let's say the life span of a muon is half a second but it would take a muon one second for it to reach from the top of the atmosphere to the ground at the speed with which it moves... So a muon should not reach the ground without having decayed on the way... But it does reach the ground intact... This paradox canbe explained by relativistic consideration... One observer sees length contraction and the other sees time dilation, but neither sees both...A physicist looking at the muon standing on the ground will see it reach the ground before it decays because for him, the time on the muon is running slowly... Somebody sitting on the muon will see it reach the ground before it decays, because for that person the distance from the top of the atmosphere to the ground is shorter... So the two observers experience different effects but agree on the end result

 

[Suraj M]

But what about my original question?

 

[Dale]

So the change in Kinetic energy is frame invariant and absolute?

I don't know. For a plastic collision between two particles and for boosts along the direction of the collision I have not found a counterexample. If that holds in general I don't know.

 

[Suraj M]

So is post #5 the answer?? or still debatable?

 

[Dale]

I think that every post has been correct with the exception of part of 4 and part of 19, both of which were corrected later.

The basic point is that energy is frame variant, so there is no expectation that it should be the same for the train and the earth. Anything more detailed would require working out the math which is complicated by the fact that the train is non inertial.

 

[Suraj M]

Oh ok thank you!

 

[arsenal1607]

I was working on that angle.

It is true. The path of the train is so dramatically shortened by length contraction that it only takes a week to reach the finish line. Essentially, the Earth shrinks so much that all 22 billion round-the-world trips (that's 7 per second for 100 years to everyone else) only take the train one week to complete.

That is one way of answering your conundrum.

It's easier to see when you examine a one-way trip to a distant star. Say it's 100 light years away. On Earth we see the trip take 100 years, but in the ship, traveling at .99999998c, the distance is contracted to a mere light-week away. Thus, for the occupants, it takes only a week to arrive - which only requires one week's worth of fuel.There are many ways of looking at this problem, some are more intuitive than others.

Not for a second am i suggesting you're wrong, rather me trying to interpret something. When you say it's 100 light years away, how would you get there in a week? Ie doesn't that mean it also takes light 100 years to get there? Assuming you're correct which you are, I'm missing something aren't i?

 

[DaveC426913]

Not for a second am i suggesting you're wrong, rather me trying to interpret something. When you say it's 100 light years away, how would you get there in a week? Ie doesn't that mean it also takes light 100 years to get there? Assuming you're correct which you are, I'm missing something aren't i?

The occupants experience the passage of a week during the entire trip.

When they look out the window of their spaceship, they see Earth and the target star only one light-week apart (as well as extremely flat along their direction of travel). Thus, it only takes them a week to journey there, as they expect.

 

[Rene Manzano]

What happens if inside the train we build another track that goes in circles, and we repeat this process over and over, would that mean that theoretically we can we can travel all the age of the unvierse in less than a second or a infinitesimal amount of time?

 

[DaveC426913]

What happens if inside the train we build another track that goes in circles, and we repeat this process over and over, would that mean that theoretically we can we can travel all the age of the unvierse in less than a second or a infinitesimal amount of time?

That would be adding an implausibility on top of an implausibility.

The way to avoid all this implausibility is to just get in a spaceship and leave poor Earth in peace. Your ship has a engine that can run indefinitely. In theory, you could continue to accelerate until the universe flashes by at a billion years a second or faster. There's really no upper limit.

 

[bubblewrap]

That would be adding an implausibility on top of an implausibility.

The way to avoid all this implausibility is to just get in a spaceship and leave poor Earth in peace. Your ship has a engine that can run indefinitely. In theory, you could continue to accelerate until the universe flashes by at a billion years a second or faster. There's really no upper limit.

Why wouldn't it work though?

 

[jbriggs444]

In principle, it would work. But it is implausible that we can build a train to go around the Earth at 99.99+% of the speed of light. Building a nested sequence of such trains is more implausible still. Why make a thought experiment complicated when one can simply imagine the original train going faster and achieving an identical effect?

 

[Suraj M]

In principle, it would work. But it is implausible that we can build a train to go around the Earth at 99.99+% of the speed of light. Building a nested sequence of such trains is more implausible still. Why make a thought experiment complicated when one can simply imagine the original train going faster and achieving an identical effect?

It would actually complicate the part of my question about powering the train from outside. Won't it? What if i considered a different planet with a huge radius(compared to earth) so will it be possible then?