What speed and direction are we actually traveling?

[Amazingly Andrew]

I'm thinking about flying off in a spaceship that travels half the speed of light so I can, in effect, travel into the future, since everyone stuck on Earth will be going relatively slow and aging relatively faster than me. But my concern is that I don't know which way to go.

Right now the Earth is traveling in one direction around the sun, but in 6 months it will be the opposite direction. So is the Earth's actually the speed and direction that the sun is traveling around the galaxy? But then, in 115 million years the sun will be traveling the opposite direction. So is our speed actually the overall speed that the galaxy is moving through space? How is that measured? There isn't exactly a fixed point to refer to for speed.

I guess I just don't want to fly off for 10 years, hoping that 1000 years will pass on Earth, and find that I went the wrong direction and unwittingly reduced my speed that whole time and so I was the one who got old fast, while only 10 minutes passed on Earth.

I am not a scientist at all, and I've never taken a physics class, so pardon my ignorance when you respond!

 

[PeroK]

I'm thinking about flying off in a spaceship that travels half the speed of light so I can, in effect, travel into the future, since everyone stuck on Earth will be going relatively slow and aging relatively faster than me. But my concern is that I don't know which way to go.

Right now the Earth is traveling in one direction around the sun, but in 6 months it will be the opposite direction. So is the Earth's actually the speed and direction that the sun is traveling around the galaxy? But then, in 115 million years the sun will be traveling the opposite direction. So is our speed actually the overall speed that the galaxy is moving through space? How is that measured? There isn't exactly a fixed point to refer to for speed.

I guess I just don't want to fly off for 10 years, hoping that 1000 years will pass on Earth, and find that I went the wrong direction and unwittingly reduced my speed that whole time and so I was the one who got old fast, while only 10 minutes passed on Earth.

I am not a scientist at all, and I've never taken a physics class, so pardon my ignorance when you respond!

All motion is relative, so there is no absolute speed at which the Earth is moving through the universe. It doesn't matter, therefore, which direction you travel. It's only your motion relative to the Earth that matters.

Note also that at half the speed of light (relative to the Earth), the relative time dilation would only be about $1.15$. So, you're not going to get a lot of differential ageing with a 10-year flight - about 1.5 years.

 

[RC_AstroAqua]

Right now the Earth is traveling in one direction around the sun, but in 6 months it will be the opposite direction. So is the Earth's actually the speed and direction that the sun is traveling around the galaxy? But then, in 115 million years the sun will be traveling the opposite direction. So is our speed actually the overall speed that the galaxy is moving through space? How is that measured? There isn't exactly a fixed point to refer to for speed.

Watch the end of this video, explains what you are asking about, traveling aboard the good-ship Earth (and your real journey in life).
Great channel, also.

 

[russ_watters]

Welcome to PF!

So is our speed actually the overall speed that the galaxy is moving through space? How is that measured? There isn't exactly a fixed point to refer to for speed.

You've really hit the nail on the head with your last remark and given half of the answer: The other half is that since there isn't a fixed point to provide a reference for speed, there is no "speed through space". All speeds we can measure are with respect to arbitrarily chosen "stationary" (by choice/definition) references.

There are two sides to this coin:
1. In actuality, the universe doesn't have a definable coordinate system from which to calculate your speed.
2. Even if it did, you wouldn't be obligated to use it. You can/do/have chosen whatever seems relevant to you at the time (often rotating surface of the Earth centered, but not always).

 

[JMz]

1. In actuality, the universe doesn't have a definable coordinate system from which to calculate your speed.

Well, the rest frame of the microwave background provides a pretty good one, doesn't it? (But no, you're not obligated to use it. :-)

 

[rootone]

I guess that from the rest frame of CMB, Earth would seem as more or less stationary and only a short lived event.

 

[JMz]

Yes, close to stationary (as are the Sun, the MW, and even the Virgo Cluster). Short-lived, I'm not sure, though the OP didn't ask about that.

 

[Amazingly Andrew]

Thanks for the answers! I think what's still confusing me is what's the difference between me zooming away from Earth at 1/2 light speed vs. Earth and me booth zooming away from each other at 1/4 light speed? If there is no fixed reference, doesn't that look either way like the same thing, and therefore we are all experiencing time the same way? Sorry, I'm starting from scratch here!

@RC_AstroAqua That video was good, I had actually watched the first half of it before!

 

[PeroK]

Thanks for the answers! I think what's still confusing me is what's the difference between me zooming away from Earth at 1/2 light speed vs. Earth and me booth zooming away from each other at 1/4 light speed? If there is no fixed reference, doesn't that look either way like the same thing, and therefore we are all experiencing time the same way? Sorry, I'm starting from scratch here!

In terms of that constant state of relative motion, `yes there is no difference. All you have is a relative velocity between you and the Earth.

But, if you change your reference frame (in general by accelerating), then that is absolute: you can measure your acceleration. And, if you turn round and return to Earth, then when you get back you will have experienced "differential ageing" compared to those who have stayed on Earth.

It's the change of inertial reference frame (acceleration) that creates an asymmetry.

 

[Arkalius]

I think what's still confusing me is what's the difference between me zooming away from Earth at 1/2 light speed vs. Earth and me booth zooming away from each other at 1/4 light speed?

Well, if you and Earth flew away from some point in opposite directions, both at 0.25c, then from your perspective Earth would only be moving away from you at about 0.47c because velocities don't add linearly in special relativity.

But that's the primary idea behind the principle of relativity. There is no privileged inertial frame of reference. The laws of physics work the same in all valid inertial frames of reference, and thus there is no frame that special in any objective sense.

 

[JMz]

In terms of the OP, I think @PeroK said it best: It is the change of inertial frame (acceleration, when you turn around) that makes the difference.

That isn't exactly a statement of physics, but it gives your answer. In physics, if you & the Earth just go in opposite directions, then you will never see your friends again to compare your ages, so the question is moot. (In physics, things that are distant from each other can't meaningfully compare durations or lengths.) But if either of you reverses course to catch up with the other -- that's where the acceleration occurs -- then that's the person or planet that will age less.

 

[A.T.]

Sorry, I'm starting from scratch here!

There are hundreds of threads on the "twin paradox" here. Try the search function.

 

[stevendaryl]

I have perhaps the opposite perspective about motion and relativity. It's often thought that relativity is about what is relative, as opposed to absolute. And that is the source of the name, "relativity". However, there is another way of looking at relativity, according to which, it restores a notion of absolute motion---but not motion through space as a function of time. Instead, the motion of an object through spacetime as a function of proper time (or some other parameter) is absolute.

Every massive object has a unique velocity through spacetime. When I travel from New York City at 1:30 on March 23, 2018 to London at 11:30 the same day, I am traveling through both space and time. My starting point is a unique point in space and time, and my ending point is another point in space and time. Along the way, at each moment, I have a unique velocity through spacetime, where I measure my progress according to the watch on my wrist.

Now, while my velocity is unique and unambiguous, the way that I describe that velocity is dependent on a coordinate system. I can, for instance, use the coordinate system:

• $\phi$: My longitude
• $\theta$: My lattitude
• $h$: My height, or altitude
• $t$: The GMT time (the local time, corrected back to the time in London through adding hours for the local time zone)

If $\tau$ is the time on my watch, then I can describe my velocity using a coordinate-dependent description: $V = (\frac{d\phi}{d\tau}, \frac{d\theta}{d\tau}, \frac{dh}{d\tau}, \frac{dt}{d\tau})$, where $\frac{d\phi}{d\tau}$ is the rate, according to my watch, at which my longitude is increasing or decreasing, etc.

Obviously, instead of using $\phi, \theta, h$, I could, if I wanted to, come up with a solar-system based coordinate system $r, A, z$ where $r$ is the distance from the sun, $A$ is the angle between the line from me and the sun and some arbitrary axis through the sun in the plane of the Earth's orbit, and $z$ is my height above the plane through the Earth's orbit. With this coordinate system, its clear that the components of my velocity will be different than the latitude/longitude based coordinate system. Nobody is surprised that the velocity components are different when you use a different coordinate system.

What's surprising about special relativity, compared with Newtonian physics, is not that velocity (components) are relative to a coordinate system, but that one particular component, $\frac{dt}{d\tau}$, is. Newton's theory had a universal time coordinate, and clocks and watches (if they were running correctly) kept track of this coordinate. So in Newton's theory, $\frac{dt}{d\tau}$ was always equal to 1, which is the reason it never shows up in any calculations---it's boring. With special relativity, there is no longer a unique time coordinate. There can be many different time coordinates, just like there can be many different spatial coordinates, and $\frac{dt}{d\tau}$ can be equal to 1 for some of them, but not for others. (It's a fact about SR that if $t$ is the time according to any standard inertial coordinate system, $\frac{dt}{d\tau} \geq 1$.)

 

[vanhees71]

I guess that from the rest frame of CMB, Earth would seem as more or less stationary and only a short lived event.

Well, it's not that slow after all. One can measure the speed of our "local group" (or us on Earth for that matter) against the fundamental observers' rest frame (relative to which the CMBR is by definition at rest) by measuring the (dipole part) of the variation of its temperature with direction. That's, by the way the largest deviation from homogeneity an thus usually subtracted from the pictures shown about the flucutations of the CMBR temperature. It was first accurately determined by the satellite COBE, then by WMAP and PLANCK. The latter's finding is that we move with a speed of ($384 \pm 78 \;\text{km}/\text{s}$) towards the Leo constellation.

https://arxiv.org/abs/1303.5087

 

[JMz]

Well, that's pretty slow compared to the speed that the OP needs to accomplish much time dilation. :-)

 

[Thecla]

I think a good question would be if the rocket ship left the Earth at 19 miles /second, the speed of the Earth around the sun. I grant that this is not a relativistic speed, but let's say you leave Earth for a long time.Do you have to include in your time calculations that your relative speed with respect to the Earth is changing every 6 months i.e. half the time the Earth in orbit around the sun is moving toward you(slowing the relative speed) and half the time the Earth is moving away from you(increasing your relative speed)

 

[Ibix]

I think a good question would be if the rocket ship left the Earth at 19 miles /second, the speed of the Earth around the sun. I grant that this is not a relativistic speed, but let's say you leave Earth for a long time.Do you have to include in your time calculations that your relative speed with respect to the Earth is changing every 6 months i.e. half the time the Earth in orbit around the sun is moving toward you(slowing the relative speed) and half the time the Earth is moving away from you(increasing your relative speed)

No. It isn't really your relative speed that matters, although it simplifies to that in the usual twin paradox case. What matters is the interval along your worldline, which is the 4d spacetime generalisation of the length of your path through space. The interval turns out to be the elapsed time on your watch. So what you need to do is work out the interval along each path and compare them.

In the particular case you are considering, both paths turn out to be the same "length" (give or take general relativity), so both twins would be the same age.

 

[pervect]

I have perhaps the opposite perspective about motion and relativity. It's often thought that relativity is about what is relative, as opposed to absolute. And that is the source of the name, "relativity". However, there is another way of looking at relativity, according to which, it restores a notion of absolute motion---but not motion through space as a function of time. Instead, the motion of an object through spacetime as a function of proper time (or some other parameter) is absolute.

Does this boil down to saying that a 4-velocity is a tensor? And that you regard tensors as absolute?

I'm not too sure how I feel about the wording and the definitions of the later point. I tend to regard tensors as being a fundamental representation of reality, but I'm not sure this is the same thing as being absolute, and we're getting into philosophical realms rather than scientific ones here.

 

[PeterDonis]

In terms of the OP, I think @PeroK said it best: It is the change of inertial frame (acceleration, when you turn around) that makes the difference.

This is true in flat spacetime, but not in curved spacetime, i.e., when gravity is present. In curved spacetime, you can have multiple geodesic worldlines (i.e., zero proper acceleration) between the same pair of events, and they can have different lengths.

In the particular case you are considering, both paths turn out to be the same "length"

I'm not sure this is true. What path through spacetime do you envision the traveling spaceship as following?

 

[PeterDonis]

I guess I just don't want to fly off for 10 years, hoping that 1000 years will pass on Earth, and find that I went the wrong direction and unwittingly reduced my speed that whole time

This way of thinking of it assumes that "speed" is something absolute. It isn't.

What matters, as others have pointed out, is not "speed" but the relative lengths of your path through spacetime and the Earth's. Since you are looking for a time dilation factor of 100, your path through spacetime will need to be 100 times shorter than the Earth's. To do that, you would need to travel at a speed very close to the speed of light relative to the Earth for 10 years by your clock. At that speed relative to the Earth, the motion of the Earth in its orbit around the Sun is negligible, and you might as well just treat the Earth as at rest for the purpose of determining your trajectory. So it won't matter which direction you go out and come back.

 

[kent davidge]

This way of thinking of it assumes that "speed" is something absolute. It isn't.

isn't the meaning in english of speed "the scalar product of the velocity vector with itself". if so it should be invariant.

 

[Ibix]

I'm not sure this is true. What path through spacetime do you envision the traveling spaceship as following?

I think it depends on unstated assumptions. I assumed the question was stated in a sun-centred inertial frame with the Earth and the ship always doing 19km/s in varying directions in this frame (I did explicitly neglect GR). In that case the path doesn't actually matter - the proper time is $\gamma$ times the coordinate time.

If you interpret the question differently, your answer may well be path dependent.

 

[Ibix]

If you interpret the question differently, your answer may well be path dependent.

That's not well phrased. The answer is always path dependent. It's just that, given my assumptions about what the question meant, all possible paths it specifies have the same proper time. Other interpretations may not have that property.

 

[PeroK]

isn't the meaning in english of speed "the scalar product of the velocity vector with itself". if so it should be invariant.

Well, speed is not invariant in classical physics either. How could it be?

 

[stevendaryl]

Does this boil down to saying that a 4-velocity is a tensor? And that you regard tensors as absolute?

"Absolute" is perhaps not the best adjective, because that can be ambiguous, but a 4-velocity is independent of coordinate systems. It is an observer-independent mathematical object.

 

[Ibix]

isn't the meaning in english of speed "the scalar product of the velocity vector with itself". if so it should be invariant.

Speed is the magnitude of the three-velocity, which isn't covariant in either Newtonian nor Einsteinian relativity. The magnitude of the four-velocity is invariant, but it's always c, which isn't very informative.

 

[JMz]

This is true in flat spacetime, but not in curved spacetime, i.e., when gravity is present. In curved spacetime, you can have multiple geodesic worldlines (i.e., zero proper acceleration) between the same pair of events, and they can have different lengths.

Quite right. The OP seems to be more concerned with simply using SR effects to wait for all his friends to die, but he could just as well hang out near a BH for a while.

 

[PeroK]

Quite right. The OP seems to be more concerned with simply using SR effects to wait for all his friends to die, but he could just as well hang out near a BH for a while.

https://www.physicsforums.com/threads/using-black-holes-to-time-travel-into-the-future.938858/

 

[stevendaryl]

The paradoxical aspect of the twin paradox is this: If all frames are equivalent, and all motion is relative, then what basis is there for saying that one twin will be older than the other when they get back together. To me, it ceases to be paradoxical (although it might still be puzzling) from the point of view of 4-dimensional spacetime.

The three-dimensional analogy: Two people travel from New York City to London by different routes. There is nothing at all surprising about the fact that the elapsed time on one person's watch might be different than the elapsed time on the other person's watch. If you travel by different routes, then your velocities will be different, and it's likely that you will arrive after different amounts of elapsed time.

If instead of traveling through space, you're traveling through spacetime. The starting point is New York City at 1:00. The ending point is London at 11:00. How long (according to your watch) does it take to travel from the starting point to the ending point? Just as the case with 3-dimensional travel, how long it takes you depends on the path you take, and particular your velocity through spacetime.

 

[pervect]

I like to use a purely spatial analogy similar to stevendaryl's. Two people travel from New York to Los Angeles by different routes. One goes directly from New York to LA, the other goes through Albuquerque.

One finds that the total distance traveled is shorter along the direct path.

Nobody finds it "paradoxical" that the shortest distance between two points is a straight line (or, more generally, and that if you don't take a straight line path, you travel a longer distance.

Space-time geometry has very similar rules to the Euclidean geometry that says that the shortest distance between two points is a straight line. But it's not quite the same. For space-time geometry, the equivalent of a straight-line path has the _longest_ elapsed (or proper) time, not the shortest. This can be traced to a simple sign change in the space-time geometry, though spelling it out with all the details gets somewhat technical.

There are several important things that need to be grasped in the context of special relativity, and I will try to communicate the facts, but not necessarily the "why" of them briefly. The first is a matter of terminiology. We call a path through space-time a worldline. We draw worldlines on space-time diagrams. We can start thining about how to draw space-time diagrams by thinking about how to draw time on a diagram. The solution is well-known, we draw time on a diagram via a timeline, something that should be familiar to most readers. We extend the concept of the time-line by adding another dimension to the diagram, making it a 2 (or higher) dimensional diagram by including one or more spatial dimensions on the diagram. We call the result a space-time diagram. An event is a point in space that occurs at a particular time. We use the name "event" to talk about somethign that happens at a particular point in space and a particular instant of time to avoid confusing the space-time concept of events with a "point" in space.

A sequence of connected events, including a sequence of connected events that happen "at the same place" or "at the same point" in space is called a worldline, and is drawn on the space-time diagram as a line.

Getting students or readers to actually draw space-time diagrams seems to be challenging for some reason that I can't fathom. It's not a terribly difficult idea, or hard to do, and most textbooks have pictures of them, as does google images. But if readers can't or won't draw their own diagrams, they seem not to understand or study images of space-time diagrams.

There's another concept that's needed. This is that the particular sort of worldline that someone can carry a clock along is called a "timelike" worldline. By the rules of special realtivity, timelike worldlines alwasys represent objects moving at less than the speed of light, thus the slope of the worldline on the space-time diagram is smaller than the slope of light.

A third concept that's needed is just a matter of semantics. Rather than talking about "straight lines" in space-time, we talk about time-like geodesics. We have already discussed time-like worldlines. When a time-like worldline is "straight" we call it a time-like geodesic to indicate it's straightness.

Given these basics, one might expect the shortest elapsed time between two events (points on the space-time diagram) would be the space-time equivalent of a straight line, a time-like geodesic. One would be wrong. The time-like geodesic is the longest, not the shortest, time-like path in special relativity.

The twin "paradox" is thus seen to be space-times version of the triangle inequality, which says that the shortest distance between two points in a Euclidean space is a straight line. The geometry of space-time is not Euclidean - it's different. We have a name for the sort of geometry it is, but I've introduced too many technical terms already, so I'll leave off giving it unless someone asks.

Operationally, we can tell which observer takes the "straight-line" geodesic path through space-time by looking at their proper acceleration. Sometimes it seems difficult to explain that we can tell observers that are accelerating form observers that are not, that the observers that are not accelerating are called inertial observers, and that they follow time-like geodesics. I'm not sure how to make this any simpller.

Then we can easily tell, in the context of special relativity, which observer will have the longest elapsed time (proper time) reading on their clock when two clocks start out at some event, and end up at the same event, but take different paths through space-time. The unique worldline that is "straight" that connects the two events will be the worldline that has the maximum elapsed time.

 

[JMz]

Sometimes it seems difficult to explain that we can tell observers that are accelerating form observers that are not

I'm curious how this manifests, and what seems successful to get past it. I realize that most students don't have experience traveling at large fractions of the speed of light (as our OP-er wants), but is this any different from telling someone, "Even if we stood in a closet and turned off the lights, we would be able to tell which way is down"? A hypothetical unfamiliar individual might have to accept it on faith, but, really, that's just the way the world works.

 

[PeterDonis]

I'm curious how this manifests

You can measure proper acceleration directly with an accelerometer.

 

[JMz]

To clarify: I'm curious how this difficulty of explaining manifests: What do the students(?) say, and what works for them?

 

[julcab12]

The paradoxical aspect of the twin paradox is this: If all frames are equivalent, and all motion is relative, then what basis is there for saying that one twin will be older than the other when they get back together. To me, it ceases to be paradoxical (although it might still be puzzling) from the point of view of 4-dimensional spacetime.

Frames are never equivalent when measured. If two atomic clocks are started simultaneously(sort of) with one remaining on the ground and the other on a flight 10km above the Earth and its gravity, then the readings show two different results: the one at a distance would have “lived” less long by some nanoseconds than the one on the ground. Same goes with 3 clocks. Both of them move on opposite direction with equal path and distance and the other stationary would still show nano differences between clocks. The effect is very slight and not noticeable.

 

[Ibix]

Frames are never equivalent when measured.

I'm not sure what you mean by this. Frames are not something you can measure; they are a tool to analyse a situation.

If two atomic clocks are started simultaneously(sort of) with one remaining on the ground and the other on a flight 10km above the Earth and its gravity, then the readings show two different results: the one at a distance would have “lived” less long by some nanoseconds than the one on the ground. Same goes with 3 clocks. Both of them move on opposite direction with equal path and distance and the other stationary would still show nano differences between clocks. The effect is very slight and not noticeable.

I think you may have missed Steven's point. He was pointing out that the "paradox" lies in trying to treat this experiment as if all clocks were at rest in an inertial frame at all times. And one way round this is to drop the whole "frame" thing and just use intervals as you would distances in space.