Can A Slow Shuttle Leave A Fast Ship Safely?

I am traveling in a Generational spaceship that has, over time, been accelerated to 0.4 light speed. The ship can not slow down until it nears its destination in 50 years. The ship has a small, conventionally powered shuttle craft whose top speed is 0.1 light speed. Can that shuttle leave the ship and maneuver about the ship without being left behind? I am thinking that when it leaves the ship it is moving at the same relative speed as the ship, and as long as it does not ever go below that speed, it can safely return.
The Space Shuttle orbiter Atlantis, framed by the California mountains, as it rides on the back of one of NASA's Boeing 747 Shuttle Carrier Aircraft (SCA) en route from California to the Kennedy Space Center, Florida. Image credit: NASA

The Space Shuttle orbiter Atlantis, framed by the California mountains, as it rides on the back of one of NASA's Boeing 747 Shuttle Carrier Aircraft (SCA) en route from California to the Kennedy Space Center, Florida. Image credit: NASA

Originally posted on Forbes!

It’s easier to get your head around this scenario if we start with a much simpler version of this, moving at much slower speeds. So let’s say we have a convertible, driving at 40 miles an hour, and a passenger in that car can throw a ball at 10 miles an hour. If the passenger throws the ball straight up while the car is moving, the passenger can catch that ball when it comes back down. Someone observing this scene from the side of the road would say that the ball is moving to the side along with the car, while the passenger inside the car would tell you that the ball didn’t move horizontally relative to the car. (This means that when the ball came back down, it landed in the hands of the person throwing it, instead of hitting the front or back of the car.) Both statements are perfectly correct, and both the side of the road watcher and the passenger in the car would tell you that the ball flew upwards at 10 miles an hour, and then back down.

This kind of thought experiment illustrates an important point in physics - motion in the horizontal direction and motion in the vertical direction can be treated completely separately from each other. If I’m just interested in describing the motion of the ball up and down, that can be done regardless of what the horizontal motion of that ball is doing - any horizontal motion simply takes a vertical path up and down and stretches it out sideways.

Once we speed things up to fractions of the speed of light, the concepts of special relativity begin to apply, but this basic division of motion remains constant. Two things do change, though, and the first is that we need to be much more careful with where our watchers are when we describe what it is that they see. The other change is that the conversion from what the passenger in the convertible sees to what the person on the side of the road sees is more complex than simply remembering to add in the motion of the car.

Flying some 500 feet behind NASA's DC-8 flying laboratory, NASA Langley's heavily instrumented HU-25 Falcon measured chemical components of the exhaust streaming from the DC-8's engines burning a 50/50 mix of conventional jet fuel and a plant-based biofuel during the 2013 ACCESS biofuels flight tests. Image credit: NASA/Lori Losey

Flying some 500 feet behind NASA's DC-8 flying laboratory, NASA Langley's heavily instrumented HU-25 Falcon measured chemical components of the exhaust streaming from the DC-8's engines burning a 50/50 mix of conventional jet fuel and a plant-based biofuel during the 2013 ACCESS biofuels flight tests. Image credit: NASA/Lori Losey

If our shuttle exits the larger spaceship, and has two rockets on it, one on each end, so that it can move at a speed of one-tenth the speed of light at a perfect 90 degrees, and then stop, and go in reverse back to the spaceship, we have effectively replicated our slower situation. A person on the spaceship would say that the shuttle isn’t moving at all horizontally (in the direction the spaceship is traveling) but is bouncing outwards and back without shifting along the spaceship from its berth. Because it’s moving at 90 degrees to the direction the spaceship is traveling, there isn’t anything that would prevent the shuttle from coming straight back to its dock on the main spaceship.

An observer on a nearby planet would see the spaceship passing by at four tenths the speed of light, and they would see a shuttle leave the main craft, appear to drift outward at an angle, and then drift back inwards, meeting back up with the main craft. That planet based observer would measure the speed of the shuttle to be higher than 0.1c, because it’s got a horizontal speed that the observer on the spaceship doesn’t see, along with its motion at a right angle to the spaceship.

But what if the shuttle doesn’t go out at a right angle to the spaceship’s direction of travel? In that case, what the watching people see on the spaceship and on the planet they’re zipping past might differ a little more. If our shuttle can reverse directions instantaneously, going from 0.1c “forwards” with the spaceship to 0.1c “backward” right away, then someone on the spaceship would simply see the shuttle moving at 0.1c relative to the ship, which is stationary under their feet. As long as the shuttle is always moving at a fixed speed, it should be able to reverse course and catch back up to its dock.

The planetary observer, meanwhile, would observe a whole host of things changing. (And if we wanted to make things super complicated, we could look at how much time each set of observers is dealing with.) Velocities don’t add in the same way when you’re moving at significant fractions of the speed of light, and so the shuttle would appear to be moving at different speeds relative to the planet, depending on whether the shuttle was moving against the flow of the spaceship (0.29c) or along with it (0.48c).

The shuttle could wind up in a situation where it couldn’t reach the spaceship again if it could slow itself down enough. In the above scenario, I’ve assumed that that shuttle is always moving at a fixed speed, but if the shuttle could change its speed so that instead of being stationary relative to the spaceship, it were stationary relative to the planet, it would not be able to accelerate back up to the speed of the spaceship. Then it would be stuck, lagging ever further behind the spaceship it came from.

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If Time Doesn't Exist For Photons, How Does Anything Happen To It?

Images showing the expansion of the light echo of V838 Monocerotis. Image credit: NASA, ESA, H.E. Bond (STScI) and The Hubble Heritage Team (STScI/AURA)

Images showing the expansion of the light echo of V838 Monocerotis. Image credit: NASA, ESA, H.E. Bond (STScI) and The Hubble Heritage Team (STScI/AURA)

Originally posted at Forbes!

The concept of photons running with stopped clocks is something that is pulled straight out of relativity; the faster you’re moving, the slower your onboard clocks are moving, and the closer to the speed of light you’re operating, the more sluggish they get. Once you reach the speed of light, your clock runs infinitely slow - for practical purposes, we can say that time doesn't flow for the photon. As with all things relativity, this isn’t an absolute statement- light still has a finite speed, and we can observe light taking fixed amounts of time to traverse large distances.

When light goes zipping around our Universe, it is physically moving through space at a speed of 186,000 miles every second.  But if you could affix a clock to it, an observer that’s not moving at the speed of light would not see the clock moving forwards the way their own clocks do. A hypothetical person moving at the speed of light wouldn’t notice anything weird with their clock, but what they might notice is that the Universe is full of things to smash into.

This artist's impression shows how photons from the early universe are deflected by the gravitational lensing effect of massive cosmic structures as they travel across the universe. Image credit: ESA

This artist's impression shows how photons from the early universe are deflected by the gravitational lensing effect of massive cosmic structures as they travel across the universe. Image credit: ESA

No matter how fast you’re going, if there’s something in front of you, and you can’t dodge it, you will hit it. This is as true for humans as it is for light, and light is even less capable of dodging an oncoming object than we humans are.  Light always travels in locally straight lines - the only way to bend light is to make a curve in the shape of space. A photon will then follow that curve, but there’s no onboard navigation.

Photons are effectively stuck playing the world’s most obnoxious game of bumper cars, continually bouncing from impact to impact. From our non-speedy perspective, the clocks on photons do not tick forward between impacts, so if the photon has the good fortune to get re-emitted by whatever it ran into, it will, from our viewpoint, instantaneously smash directly into something else without its onboard clock ticking onwards at all.

The photon may not get re-emitted by whatever it ran into, (this is one way to get rid of a photon). The energy of whatever it hit will increase, so the energy isn’t lost. However, if it hits something particularly cold, the object won’t be radiating much, and the photon’s energy will be a convenient donation.  More commonly, after some amount of time, a new photon will be produced, at a different energy level, carrying energy away from whatever the photon punched itself into earlier. That new photon has an equally short apparent flight until it smashes into something else.

It’s not the most glamorous of paths through the Universe, but a continual ricocheting from solid matter to solid matter is how photons in our Universe go about it.

The bright cloud is a reflection nebula known as [B77] 63, a cloud of interstellar gas that is reflecting light from the stars embedded within it. There are actually a number of bright stars within [B77] 63. Image credit: ESA

The bright cloud is a reflection nebula known as [B77] 63, a cloud of interstellar gas that is reflecting light from the stars embedded within it. There are actually a number of bright stars within [B77] 63. Image credit: ESA

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Can The Mass Of An Object Ever Change?

What is the difference between “mass” and “rest mass” ? Does this mean that mass is not always the same?
Nuclear particle tracks in the ten-inch bubble chamber mounted inside a superconducting magnet at Argonne show what happened to two negative K mesons that entered the bubble chamber from Argonne's ZGS. c.1966 Image credit: US Department of Energy, public domain

Nuclear particle tracks in the ten-inch bubble chamber mounted inside a superconducting magnet at Argonne show what happened to two negative K mesons that entered the bubble chamber from Argonne's ZGS. c.1966 Image credit: US Department of Energy, public domain

Originally posted on Forbes!

This is a good question, and also a good reminder to be careful with one’s language when writing about physics!

Most of the time, if you’re reading an article, what we mean by mass and rest mass is exactly the same. Rest mass is a slightly more precise term in its phrasing, meaning specifically the mass of that object when it is at rest, relative to the person measuring its mass. This is almost always how we measure mass. If you’re in a lab (or a kitchen), and you measure an object’s weight on a scale, that object is not moving at any speed. If it is moving at a speed, you should probably catch it, because it’s rolling off your scale.

If you’re on Earth, you take the weight — which is the force with which that object is pressing on your scale, within our Earth’s gravitational field – and can then convert it into a mass. This mass you’ve measured is the “rest mass”, since nothing’s moving in this scenario. Generally this number — the rest mass — is the most useful metric of how much material is assembled into whatever you’ve measured, so “rest mass” is often abbreviated into just regular old “mass”.

However, there is a way to make an object sort of behave as if it has a much larger mass than its rest mass, and given my pointing out how nothing’s moving in the definition of rest mass, you will rightly guess that it has something to do with motion. However, it’s not just any motion — an egg rolling off your kitchen scale isn’t any heavier than the egg that managed to stay balanced.

You’d have to accelerate that egg to a significant fraction of the speed of light before the egg started behaving as though it were heavier (and if you can do that without crushing the egg, you’ve won the world’s most difficult Egg Drop Challenge). It’s critical to note that the egg itself is not intrinsically heavier, and so we’re careful to keep “rest mass” separate from this relativistic speed effect. However, because the egg now has so much kinetic energy from moving so fast, and there is an equivalence between mass and energy (hello E=mc²), the energy of the object can masquerade as additional mass by adding to that object’s momentum.

A Newton’s Cradle toy in Darlington-Park in Mülheim an der Ruhr. Image credit: Frank Vincentz, CC BY SA 3.0

A Newton’s Cradle toy in Darlington-Park in Mülheim an der Ruhr. Image credit: Frank Vincentz, CC BY SA 3.0

The faster our relativistic egg is moving, the larger this energy-mass bonus gets, and the egg gains more and more momentum. The relevant feature of momentum here is that it resists changes to its speed. In particular, for our relativistic egg, the faster and faster it goes, the more momentum it has, so the harder it is to speed it up any more – you need to start expending truly ludicrous amounts of energy to speed it up even a little bit. This is one half of the reason it’s physically impossible to accelerate an object all the way to the speed of light — the closer you get, the closer to infinite energy you need to continue speeding it up.

Comparison of Newtonian and relativistic momentum. 1 on the x axis is the speed of light. As you approach the speed of light, in a relativistic framework, momentum rapidly approaches infinity. Image credit: Wikimedia user D.H, CC BY-SA 3.0

Comparison of Newtonian and relativistic momentum. 1 on the x axis is the speed of light. As you approach the speed of light, in a relativistic framework, momentum rapidly approaches infinity. Image credit: Wikimedia user D.H, CC BY-SA 3.0

So you can safely substitute “mass” anytime you see anyone mention a “rest mass,” but there are situations in which an object might behave as though it has more mass than its “rest mass” — these are, however, limited to objects traveling a significant fraction of the speed of light.

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Does time dilation affect light itself?

I understand the concept of light years; for example, if one states that some celestial object is 100 light years away, then it takes 100 years for light to reach it. But according to Einstein, as you approach the speed of light, there is time dilation. Does this also apply to light itself (i.e. it might appear 100 light years away to us but in reality, it takes the light a lot less time to reach it)?

The idea of time dilation depends very strongly on who’s doing the observing. The general idea is that the faster you go, the more your clocks appear to move slowly from the perspective of someone not moving at that speed. However, from the perspective of the person moving quickly, your clock is fine; relatively speaking, it’s the people not moving who have odd clocks.

We can observe this happening at small-ish velocities with the clocks on the International Space Station. I say small-ish because they’re not going that fast (nowhere near the speed of light), but they are still orbiting just fast enough to make it into minuscule time dilation territory - the clocks on the space station are fast by a few milliseconds, relative to the control team on the ground. If you spent a year on the ISS (which is rare, most people only spend a few months up there), you would have aged a grand total of 0.007 seconds less than your family on the ground. This is a very small number because the ISS is orbiting at around 7.7 km/s, and the speed of light is about 39,000 times faster than that.

Now, if we put an imaginary person on a much faster ship and have them observe time passing, the difference between their time and the time at home on Earth will increase. This difference in the time both people have observed to have passed is called the Lorentz factor. The Lorentz factor is named after Hendrik Lorentz, who wrote down some of the equations helping to relate differences in length and in time perceived by two observers of the universe. This factor is also what’s plotted on the vertical axis of the figure above.

This factor increases like an exponential as you start moving faster and faster (it’s not actually an exponential, but it’s close in shape). Importantly, the closer you get to the actual speed of light, the more dramatic the discrepancy between the traveller and the Earthbound becomes. This tells you that the closer to the speed of light you move, the longer and longer your Earthbound observers will wait for one of your seconds to pass.

But what happens if we attach an imaginary observer to a photon of light, or to a hypothetical speed-of-light ship? At the speed of light, time dilation gets a little weird(er). The exact relation magnitude of the difference between the fast traveller and someone back home on Earth is determined by the ratio of one over the square root of the following:

(1 - (velocity squared/ speed of light squared))

If the velocity is equal to the speed of light (as it would be, for our imaginary photon hitchhiker), then that second ratio is equal to 1. Now subtract 1 from 1, and you get zero. The square root of 0 is still zero, and then we run into a problem, mathematically. Now we have to divide 1/0, but any number divided by 0 is infinity. This is why the Lorentz factor suddenly shoots off the top of the figure when you reach the speed of light.

According to our current understanding of this physics, a person on Earth would therefore have to wait an infinite amount of time to observe any amount of time passing on the photon. As far as the Earthbound observer is concerned, time has stopped for the photon-rider.

The trick to answering your question is that there isn’t really an “in reality” here. We would observe the photons to not feel the passage of time, but the photon wouldn’t notice anything different about the way its own time is passing. We observe photons to have finite speed - and that’s a real measurement of the physics of the universe, and our determinations of light years are still good, impartial, measuring sticks for the universe. It’s just that the photon (as we see it) won’t feel those 100 years passing.

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