# Measuring velocity in empty space

1. Jun 29, 2013

### pearmtn

Let me preface this by saying I know very little about relativity. Last night a friend and I were discussing a particular scenario that will probably arise when humans begin to be capable of interstellar travel. Say you take off from earth and accelerate to some velocity and then coast until you get to a region of completely empty space with no visual references. Suddenly you decide that you want to bring your ship to a complete stop. To do so you would probably have to fire some reverse thrusters and accelerate opposite the direction you originally got going in. This is where we couldn't figure it out. How would you know when you had come to a complete stop? If you over fire the thrusters you could end up moving backwards rather than stopping.

This led us to the idea that since mass is proportional to velocity under relativity, if you had a very good scale you might be able to determine the lowest possible mass that an object can achieve by trying out a few different directions of deceleration. Thus, to stop the ship you could decelerate until the object has that lowest possible mass.

Does this make sense? I am confused about whether the people on the ship would see the mass of the object change with their velocity, and/or if that is what someone "outside the ship" would see. Also, is velocity only relative to something else, or is it somehow "non-relative" in that the speed of light is a constant value that can never be exceeded even in a completely empty universe? If it's the latter, it seems like you could figure out how to slow down to a complete stop in interstellar space somehow using the relationship between mass and velocity.

Any thoughts?

2. Jun 29, 2013

### jeppetrost

You're on to something, but you learned just enough to confuse yourself.

The concept of relativity is in some sense, that velocity is observer dependant. Say you're you. How ever fast you're going - you're always "standing still" as seen by yourself. Same thing happens in outer space, only it's more manifest. You can only say you're standing still or going at some speed with respect to some thing, say the earth or the road (in your car) or another space ship. -- But be careful, this is not the case with acceleration.

So according to the people on the ship, their mass would always be the same, no matter how fast they're going accoring to people on, say, the earth. But the guys down on earth would indeed see eg. length contraction and (in some sense) the increased mass.

I hope this is somewhat clear.

So yes, velocity is relative.

3. Jun 29, 2013

### Simon Bridge

Welcome to PF;
There is no way to determine your absolute velocity - the best you can do here is match velocities with something else. Then we say that you are "at rest with respect to" the object ... in context, you'd use a star - either the star you just left or the one you are headed for.

Does not work.
The "mass increase" is actually a statement of kinetic energy rather than actual mass increasing ... it applies only to things that are moving with respect to you. Since you are at rest with respect to yourself, you don't see any change in kinetic energy or mass as you accelerate.

Classically, you could record your acceleration through the trip and fire your rockets to reverse the effect of that acceleration ... then you will be at rest with respect to your departure point.

It's probably a good idea to review relativity concepts - "Galilean relativity" (look it up) is all you need for your discussion. The main thing to realize is that there is no such thing as an absolute velocity - everything is in motion with respect to something else. There is no way to know, at constant velocity, if it is you or the scenery that is moving.

4. Jun 29, 2013

### ghwellsjr

Do you really think there exists such a place in our universe?

5. Jun 29, 2013

### nitsuj

If there are truly are no reference points then it truly doesn't mean anything to be stopped. Said different it wouldn't matter if you are stopped or not as compared to "objects" you can't observe here "objects" includes anything. Relative motion is just that. it doesn't only apply to "going" but also applies to "stopped". Same as imagining being in empty space, right?

I think that would be possible, of course by scale you mean an accelerometer and ideally compensating calculations for varying gravity potentials, I'd presume you could measure/observe & reverse the intervals of accelerations. Like when I get in my stopped car and go somewhere and then get out of my stopped car. I'm thinking the directions of accelerations of that trip net to zero. :tongue2: I know then I am "stopped" relative to both my car (always a good idea before getting out) and the Earth.

Long and short of it is kinetic energy is a comparative measure. Mass is not.

It takes "two to tango" for kinetic energy to have any physical meaning. Mass has physical meaning just sitting there.

6. Jun 29, 2013

### nitsuj

Theoretically this is still a physically valid "state" regardless if how impractical it would be to have such a scenario in reality.

7. Jun 29, 2013

### pearmtn

Thanks for all you replies!

It makes sense that velocity can only be measured between two objects. However, I am still confused about how the speed of light is an invariant constant. For instance, let's say you're travelling at the speed of light and you turn on a flashlight in the direction of your travel. Relative to some star that you were wizzing by when you turned on your flashlight it would appear that the light from your flashlight is moving twice as fast as the light emanating from the star, thus seeming to exceed the speed of light.

A related situation would be if rather than moving forward at the speed of light you were moving forward at half the speed of light and passed an object moving half the speed of light in the opposite direction. Now your relative speed is the speed of light, but neither object is moving at the speed of light relative to some third object (e.g. the earth). I don't see why you couldn't continue to speed up so that your relative speed begins to exceed the speed of light.

From this it seems like at best the limit in relative velocities is actually twice the speed of light--an example being just holding two flashlights back to back. If it's the acceleration that's the problem and not the actually speed of light itself, then for a massless object like a photon there should be no reason why they can't go "faster than light."

So to bring it back to the initial question, what would be the frame of reference for the ship and which frame of reference would limit the ship's total velocity?

8. Jun 29, 2013

### ghwellsjr

Sure, but not in the OP's scenario where he said:

His scenario is inconsistent with itself and so the variety of answers he got were all dependent on which details were ignored--all good answers, by the way.

9. Jun 29, 2013

### pearmtn

The situation could arise in a variety of ways, such as if the ship has no windows, or the instruments for measuring the positions and intensities of nearby stars were disabled. Practically, it wouldn't be that surprising if the situation did actually occur.

10. Jun 29, 2013

### Staff: Mentor

The velocity of B relative to A is defined as the velocity of B as measured in a frame in which A is at rest; or equivalently the negative (because it's in the other direction) of the velocity of A as measured in a frame in which B is at rest. Using this definition, the relative velocity between two massive objects can never be greater than c.

However, you are right that a third observer moving relative to both of them can see the distance between them changing by as much as twice the speed of light. The more you think about it, the more you will realize that this third observer's picture isn't very useful - it's not as if you can move things around, travel from one point to another, or send messages between two points at twice the speed of light using this observational effect.

You'll hear people speaking about "the frame of reference of <something>" all the time. However, you need to be careful about using that phrase, because it's not strictly correct; it is a convenient shorthand for the correct "a frame in which the <something> is not moving". So for a spaceship zooming by the earth at .5c, "its frame" is one in which the spaceship is at rest while the earth is receding into the distance at .5c.

Last edited: Jun 29, 2013
11. Jun 29, 2013

### ghwellsjr

If that's the sort of thing you had in mind, you should have said so in your first post. We can't read your mind.

Practically, there never will be a time "when humans begin to be capable of interstellar travel". The situation will never actually occur. Sorry.

12. Jun 29, 2013

### ghwellsjr

You can't travel at the speed of light so let's shelve this issue until later and then maybe you'll understand why.

Your best way to understand situations like this is to draw the frame with its objects on a spacetime diagram and then use the Lorentz Transformation process to see what the same situation looks like for a different frame moving with respect to the original one.

Here's a diagram for your situation where earth is shown in blue, you are shown in red traveling away from earth at 0.5c and you fly past another object in black coming towards the earth at -0.5c. Note that no speeds exceed c (or even one-half c). The dots represent one-year intervals of time for you and each object:

Now we want to see how fast you (in red) are going with respect to the black object so we transform to its speed of -0.5c:

As you can see, your speed in the rest frame of the black object is 0.8c, not 1c like you thought.

We could repeat this process as many times as you want and you'll never get to c. Hopefully, this answers the issue that I shelved earlier.

No, photons are defined to travel at c in any inertial reference frame you want to pick or transform to, not 2c, not 0.5c, not any other speed. Nothing that travels at less than c in any inertial frame will travel at c or greater in any other inertial frame.

Every inertial frame limits everything to less than c except for light which travels at c in all inertial frames.

Here is a diagram for your red ship in which it is at rest:

Now you can see that the black object is traveling at -0.8c.

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13. Jun 29, 2013

### pearmtn

Thank you for pointing out that by a Lorentz transformation the total relative velocity is still less than 1c. I guess what's still confusing me is that if there is at least one point in the universe that is completely still, such as the center of the universe, then c is not just relative to two bodies, but an actual intrinsic limit on velocity.

I know that it is said that there is no privileged frame of reference in physics, but it seems that the center of the universe could be used to measure the absolute velocity of all objects. As this relates to the initial question, if you could somehow measure your mass with respect to the center of the universe then you could theoretically determine your Lorentz factor and optimize your acceleration until the Lorentz factor goes to zero (I imagine rotation somewhat complicates things...).

14. Jun 29, 2013

### WannabeNewton

There is no absolute center of the universe in the sense that every point in the universe is just as valid a center as any other, if the universe is homogenous and isotropic (this is a philosophical prejudice coming from the Copernican principle which has been verified to a rather great degree by observation).

15. Jun 29, 2013

### ghwellsjr

I don't think it's useful to think of c being relative to two bodies and it's completely unnecessary. In Special Relativity, you should think of c (and all other speeds) as being relative to an Inertial Reference Frame (IRF). Time and space is specified throughout the reference frame and all speeds, locations of objects, etc. are uniquely defined or specified anywhere. If you think of speeds as relative between two objects, then you have the problem of taking up the gap between the two objects when they are changing their speeds. Sometimes, we use terminology that makes it sound like we are talking about the speed between two objects but we really are using that as a shortcut for saying the speed of one object in the rest frame of the other object.

There is no unique center to the universe. Just like any IRF is just as good as any other IRF, any location is just as good a candidate for the center of the universe as any other. And the origin of any IRF is just as good a candidate for the "best" rest point as any other.

Even if we were to consider the mass of an object to vary with its speed (an out-dated notion), we still would have no way to measure that variation, just like we cannot measure or detect absolute motion and just like we cannot detect our own Time Dilation or Length Contraction. Everything appears to be completely the same in any IRF.

16. Jun 29, 2013

### Simon Bridge

Wow, that's a lot of activity while I was asleep.
I see someone has introduced you to space-time diagrams ... Jason Hinson does an accessible introduction to special relativity in his Relativity and FTL Travel FAQ - only the last section deals with the special problems of FTL travel, the rest should help with how you think about relativity.

Your first question could be answered without using SR at all so I left it off.
Did you get a chance to review the Galilean relativity concepts?

The others have pretty much covered it - I'll add my 2c below, and try to give you pointers for further reading.

The FAQ will show you how measuring the speed of light (as distance between two objects divided by travel time) will always give you the same number. Since this is very important, you should also look up how the speed of light is actually measured in real life.

That all observers measure the same speed for light is what requires us to use Lorentz transformations to account for the difference in observations of different observers.

i.e. if you fired two missiles at 0.75c, but in opposite directions, then, in your rest-frame, the separation of the two rockets would increase at 1.5c. However, as you have seen, that is not what observers on each rocket would "see" is going on.

The "speed limit" isn't on how fast you can go, it is how fast you will ever see anything else go. You are always at rest in your own reference frame.

There is a habit of thought in which you think of speed as something that can happen to you against a generally stationary backdrop (trees, ground, road, etc.) and getting rid of this habit of thought can be quite hard.

That would be a reasonable analysis if there were some spot in the Universe which was completely still. However, there is no place in the Universe that is still. That would imply a privileged reference frame and, as you know...
A center to the Universe implies that there is a privileged reference frame - since there is no privileged reference frame, then there is no center.

You have touched on concepts of invariance and cosmology here. One of the cool things about physics is how fast quite a simple inquiry can get to fundamental concepts concerning the nature of reality.

The FAQ should give you a good start on special relativity without needing too much higher math - but you will need a grounding in math to continue properly. Good luck and have fun.

17. Jun 29, 2013

### WannabeNewton

The homogeneity and isotropy of the universe is actually with respect to a privileged reference frame.

18. Jun 29, 2013

### Simon Bridge

So reword what I said to account for that.
i.e. is there a reference frame in which an observer would see a center for the universe?

19. Jun 29, 2013

### acesuv

"Standing still" only makes sense when in reference to another object - you can "stand still" relative to another person, but there is no universal "still".

20. Jun 30, 2013

### ghwellsjr

Could you please point out exactly where in your FAQ this shown? I couldn't find it.

Do you mean look up in you FAQ or somewhere else? I couldn't find it in your FAQ

21. Jun 30, 2013

### Simon Bridge

Chapter 1 ... the bit with the light bouncing between mirrors I think.
It uses the concept the other way around, but I suspect you already know how this works.

No - look that up by googling for "how to measure the speed of light" or something.
Surely you already know how this is done - they tend to rely on timing over a fixed distance in some way, usually indirect - the one with the rotating disks springs to mind.

It's not my FAQ btw.

22. Jun 30, 2013

### Phy_Man

What you could do is fix a laser in the system in which you're leaving (home) towards the system you are going to (destiation). Measure the frequency of the photons in the home system before you leave. Then no matter where you are, so long as you're near the beam. you can measure the speed that you're moving with respect to the Earth system by measuring the Doppler shift of the photons in the laser beam.

23. Jun 30, 2013

### Staff: Mentor

I think that this is the system that the OP is looking for:

Assuming ideal accelerometers and ideal clocks then you can always calculate your speed and position relative to your starting speed and position without reference to any external object. Note, it is still a relative number, it is relative to your initial momentarily co-moving inertial frame.

24. Jun 30, 2013

### Simon Bridge

From post #2:
Though you also need to account for gravitational fields I guess.

Hasn't OP moved on though?
@pearmtn: ???

25. Jun 30, 2013

### ghwellsjr

Even if you turn the concept around, the FAQ is describing a two-way process for light. If you were to measure the speed of light bouncing between two mirrors, you would take twice the distance between the two object (mirrors) and divide by the round-trip travel time as measured by a single clock located at one of the mirrors. Your statement "distance between two objects divided by travel time" implied to me that you were talking about measuring the one-way speed of light which is not measurable but defined in any Inertial Reference Frame which is the point I emphasized in post #12. Of course, you can use the definition of the one-way speed of light to synchronize a second clock at the other mirror and them "measure" the one-way speed of light but all you would be doing is verifying your ability to synchronize that second clock.

And you will find that every one of those measurements is a round-trip measurement which doesn't address the OP's question "about how the speed of light is an invariant constant".