# Going from Acceleration to Constant Velocity

1. Nov 3, 2008

### liamgibbs

New guy here with a question about Special Relativity and stopping acceleration. Forgive me if I have any of this wrong. I'm generally unable to follow physics for a long time before getting lost (I'm very right-brained--which means I'm artsy, not mathematical--and I've been told my brain can't organize details in a normal fashion), so I may not have my facts straight.

I've been reading Brian Greene's The Elegant Universe and, in it, he describes Einstein's special theory of relativity. Einstein claimed that any observer going at a constant velocity can claim everyone else is moving and he's standing still. Take the tried-and-true driving example. A guy driving in a constant westward direction at a constant 50 km/h can, accoring to special relativity, say that everyone else is traveling eastward at 50 km/h and he and his car are standing still. But once he accelerates, decelerates, or changes direction, he loses his right to claim that he's standing still. I hope I'm right so far, but tell me if I've got something confused.

Anyway, take someone who is traveling at just under the speed of light. While his mass may be a certain "number" while he's at rest, mass dilation says that his mass will grow exponentially so that he can attain a speed just under light's. Time dilation says that time will slow down for him. The Lorentz contraction states that he'll shrink along the direction of travel. Do I still have this right?

This is where I get confused. When he stops accelerating (i.e. he goes at a constant speed now, but doesn't stop moving), do his mass, size, and passage through time return to normal? If special relativity states now that he's on equal footing with anyone who is traveling at a constant velocity (including those who are standing still, if you can call anyone that), then he shouldn't be experiencing any of these dilations, right? Does his mass dilation et al reset to 0? If he decelerates, does that mean that these dilations start increasing again, since he's accelerating in the opposite direction?

2. Nov 3, 2008

### Fredrik

Staff Emeritus
Welcome.

All of this is true, but it doesn't really have anything to do with relativity. It's true in pre-relativistic mechanics too.

Yes.

No. All of those things depend on velocity only.

That's right. He wouldn't describe himself as being thinner than normal due to Lorenz contraction. He would describe you as being thinner than normal due to Lorentz contraction.

3. Nov 3, 2008

### Saw

Well, I am not the one who knows more here, but others may correct me if I am wrong and I may give you an approach suitable for your right-biased brain.

Relativity is a "model" that only considers inertial frames, that is to say, vehicles, if you wish, that are not subject to any interaction (i.e., any force) and so nothing happens with them = no acceleration = neither change of direction nor speed. They may have been accelerated in the past, but now they are not. They live peaceful lives, without any disturbance.

You may ask yourself, "how is it that they move without any force pushing them"? That is what Galileo and others discovered and Newton reaffirmed: an object, once it has been accelerated, will continue moving with regard to others at constant speed. If a force intervenes, it will disturb it (i.e., accelerate it), but it is not needed for the continuation of motion.

And you may also ask yourself, "where are these fortunate frames that live so peaceful lives, how is it that they are free from interaction?" Yes, that is true, on the Earth you will easily run into contact forces (friction with the ground, with the air...) and even in outer space there will always exist gravity: if you are very far away from any other mass, the attraction may be very small but it will exist... However, even if that assumption looks unreal, it is very practical. That is what a scientific model is: in order to simplify the reasoning, you imagine an ideal situation where complications are removed, find a solution and then, later on, when faced with real life, you just have to add one by one the complications and see how they change the picture.

And what do we find in this enchanted world of the model?

Classical, Galilean relativity declared that a passenger in such kind of vehicle (an inertial frame) will not observe anything abnormal: on a ship travelling steadily, without fluctuations, everything happens as on the ground, to the point that you should not be able to detect the motion through any experiment. For example, if you shoot bullets westwards and eastwards, they will travel in both directions at the same speed. The traditional explanation for this was that the objects that travel with you share the state of motion of the ship, because one by one and little by little they have been accelerated with the vehicle.

Special relativity added to that another postulate: the same applies to light. No experiment with light or other electromagnetic waves can enable you to detect the motion of your vehicle. This is easier said than understood, because at the same time, the theory admits what experiments have proved, that is to say, that the speed of light does not acquire the motion of the source. How can it be then? SR solves the paradox by explaining that the passengers of different ships will forcefully measure time and lengths in a manner that will lead each of them to hold that the speed of light is constant and, at the same time, they will not think that there is anything odd with their way of recording time or lengths… Others may find that your time is not the same as theirs, you will find that their time is not yours, but you will never detect anything abnormal within the walls of your enchanted world, precisely because all the time instruments of your kingdom suffer the same effect (this is like Sleeping Beauty, but just slowing down, without freezing) and all length instruments suffer the same effect as well (Lilliputians do not think they are short…).

So, getting to the point of your question, all the effects you mention (time dilation, length contraction, mass increase…) are predicated of inertial frames, i.e., non-accelerating vechiles. They are not “kept alive” by acceleration. Of course, if the vehicle you see racing by had not accelerated with regard to you or you with regard to it, you would not find that his time is different from yours. But once he is moving relative to you, the differences appear and should continue existing without the need of stepping on the gas. And what happens when you do decelerate? Well, if you accommodate your state of motion to mine, then we become passengers of the same vehicle and we will not find any difference between our respective approaches to time, length and so on. However, others, any other frame in the universe with a different state of motion will think (and measure!) that our time slows down and our sticks are too short.

How is it that we all see the straw (time dilation and all the queer things) on somebody else’s eye and not the beam in our own eye (the so called reciprocity effect)? That is a another story I am trying to understand myself, because it requires subtle mathematics…

4. Nov 4, 2008

### Naty1

Liam: Many of the people who post here can't follow physics either!!! ...don't worry about it...If I understood it all I wouldn't be here either
just a brief comment to supplement what's been said, not contradict anything.

Special relativity is assumed to apply to situations with no gravity, no acceleration, where space is straight and flat.

Acceleration is a feature of general relativity which Einstein in his genius realized was equivalent to gravity...each exerts a force on mass.

A major difference between special and general relativity is that in special relativity space is flat (Eucledean, like straight line x,y,z axis) and light travels in straight lines; in general relativity, gravity curves space and so that curved space bends/curves light. ( Remember this paragraph to help make interpretations.)

You should read other threads here under relativity as the discussion will be of great assistance in looking at different situations. It's really hard to understand relativity without some time to pass to gain perspective. Even Einstein struggled before formulating special relativity as he studied frames of reference and how Newton's formulations might be suspect.

I have ELEGANT UNIVERSE here at home so if you get stuck reference a chapter and page # and I'll try to assist....I have read it twice and will probably go a third round next summer.

5. Nov 19, 2008

### liamgibbs

Sorry I'm back after so long. A move, a loss of Internet connection, and my own low Internet availability... but here I am.

I might be off then. Velocity is a direction and speed of travel, right? If the velocity of Something is the same, then wouldn't that Something be able to say it's standing still? If so, how can it say that it's gained mass? Or... then would it be everything else that is moving that can say that the Something gained mass?

This is because, to him, I'm moving in the opposite direction, right? If I were moving parallel to him at the same speed, we'd both perceive each other as having our normal masses?

This would be if I'm initially going faster, then decelerate to let you catch up, then accelerate to match your speed? We'd both perceive our mass/time/length differently until we're moving at the same velocity. Am I right?

That's good to hear. I've kind of gotten the feeling over time that I shouldn't trust my own understanding of a subject, that I'm always missing something. Maybe I'm not. If everyone needs to go through a book several times to get it, mabe I'm okay.

I've been going through them, but sometimes my brain is "full" and I have to step away for a short while to "digest."

Actually, I've given Elegant Universe a break (well... my library said I had to return it) and have moved onto Greene's The Fabric of the Cosmos, but I'd really like to return to Elegant Universe once I get a better understanding of where I got stuck (thus this thread).

6. Nov 19, 2008

### JesseM

In relativity all notion of "speed" is only relative to some frame of reference or another--if two ships are moving relative to one another at constant velocity, there's no objective truth about which is "really" moving faster, in the first ship's rest frame the second ship is moving faster while in the second ship's rest frame the first ship is moving faster. Similarly, time dilation and length contraction depend on your choice of frame--in the first ship's frame, the second ship's clock is running slower than the first ship's clock, but in the second ship's frame this is reversed, with the first ship's clock running slower than the second ship's clock in this frame. There's no objective truth about whose clock is "really" running slower in this situation.

7. Nov 19, 2008

### Fredrik

Staff Emeritus
Yes, but only in "something's" own rest frame. To "stand still" means to have the same spatial coordinates at any time, so if something is standing still or not clearly depends on the coordinate system.

If objects A and B have the same velocity in frame F, then the velocity of B in the inertial frame that we would normally associate with A's motion is zero (and vice versa).

It can't. The relativistic mass of an object with rest mass m is $\gamma m$, where

$$\gamma=\frac{1}{\sqrt{1-v^2/c^2}}$$

and v is the speed of the object in the frame we're using. The frame we're associating with an object moving at constant velocity "by default" is an inertial frame where the object is stationary. So if A and B have the same velocity in frame F, B would say that the relativistic mass of A is the same as its rest mass (since v=0).

Yes.

8. Nov 20, 2008

### MeJennifer

That is not correct, acceleration or change in direction does not imply absolute movement.

For instance when you stand on the Earth the surface of the earth is constantly accelerating upwards but that does not imply the surface of the earth undergoes an absolute movement.

All movement is relative under general relativity.

9. Nov 20, 2008

### liamgibbs

So, if Person A and Person B are moving away from each other they both perceive each other's passage through time as slower, but their own as normal. Got it. But... then neither one of them is actually moving slower through time? It's just how it's perceived? Now I'm more confused.

I think you just broke my brain. Mabye I'm not understanding what "absolute" and "relative" mean. Can anyone give quick definitions so I know if I'm confusing them or not? Sorry to be so elementary about this.

10. Nov 21, 2008

### JesseM

You're correct, at any given moment there is no objective physical truth about which is "actually moving slower through time", different inertial frames disagree about this and all inertial frames are equally valid. At the same time, all frames will end up predicting the same thing about local events like what two different clocks read at the moment they are right next to each other--so if A and B start out at the same position with their clocks reading the same time and then move apart, and after some time B accelerates to turn around and returns to A, all frames will agree on the times both their clocks read at the moment they reunite. In this case, if A moved inertially the whole time while B accelerated to turn around, that means that B's clock will have elapsed less time when they reunite. So all frames will agree that B's clock ran slower on average throughout the entire trip, although they can disagree on whose clock was ticking slower at specific moments--some frames might say that A's clock was moving slower than B's before B turned around but then B's slowed down to a rate even slower than A's after the turnaround, while other frames might say the opposite, with A's clock running slower than B's after the turnaround but B running slower than A before.
Basically, I think if the value of a quantity is "absolute", that means there's a physical procedure to measure it which will give the same answer regardless of what coordinate system (reference frame) you use; if the value is "relative", that just means it's relative to your choice of coordinate system, like velocity.

Last edited: Nov 21, 2008
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