Understanding Relativity and the Potential for Faster-than-Light Travel"

[jbar18]

I was having a discussion with my physics teacher the other week (I'm an A-level student) about the speed of light. We were doing some questions about black holes sucking in light. Long story short, we both got confused about relativity. I put forward the idea that massive objects can move at the speed of light, they just can't be observed going at the speed of light.

What I'd always thought was that the consequences of a massive object traveling at the speed of light were only what a relatively stationary observer would see, and if we were to pretend that you could somehow get to the speed of light you wouldn't suddenly become infinitely massive and infinitely thin etc., that's just what a stationary observer would see. But then, relative to you, the stationary observer would be traveling at the speed of light, so you would observe the same of them, but to yourself you would appear normal. Where am I wrong? Am I wrong?

That lead me to wonder about whether it is at all possible that we are moving at light speed, or maybe faster. Since the only way that we know our speed is by looking at other things, if for example our galaxy were moving faster than the speed of light somehow, we would not know. The speed of light would still be observed, and relative to everything else that we can see we would not be moving anywhere near the speed of light. Could this be possible?

So this is kind of two questions in one. Firstly, are the consequences of traveling at high speeds only what is observed, but don't 'really' happen (I hope I'm getting the question across right)? And secondly, if that is correct, what implications does that have on the attainability of light speed? These questions are purely theoretical, please humor any silly things I've said.

The best thing I've come up with is that velocity is essentially irrelevant without two objects. So even if it were only that the speed of light is not observable in massive objects, it is in essence the same as not being able to travel at that speed at all, since nothing would observe the object traveling at the speed of light and the object would not observe anything else doing so either. In this way the 'actual' speed of the object is completely irrelevant because speed is always relative.

Sorry if I've answered my own question with that last part, but I'd still like to hear from you clever folk on this matter :)

And sorry about the massively long post, it's my first time :)

Thanks for any answers or comments.

 

[Dale]

Firstly, are the consequences of traveling at high speeds only what is observed, but don't 'really' happen (I hope I'm getting the question across right)?

No. All of the relativistic effects (length contraction, time dilation, relativity of simultaneity) are not optical effects, but are what remains after you correctly account for the finite speed of light.

 

[jbar18]

No. All of the relativistic effects (length contraction, time dilation, relativity of simultaneity) are not optical effects, but are what remains after you correctly account for the finite speed of light.

If you mean what I think you mean, I don't just mean optical effects. I mean any form of measurement to measure your mass or length. So what I'm getting at is that, relative to yourself, you always appear to be normal regardless of how fast you are going, or even if you are accelerating (in free space you would not know if you were accelerating or not without some sort of contact force). So if you were to move at any speed, you would still appear normal to yourself. Is this correct?

 

[DaveC426913]

So what I'm getting at is that, relative to yourself, you always appear to be normal regardless of how fast you are going, or even if you are accelerating (in free space you would not know if you were accelerating or not without some sort of contact force). So if you were to move at any speed, you would still appear normal to yourself. Is this correct?

That is correct.

 

[jbar18]

Brilliant, thanks.

So what exactly would this imply? Forgive me if I'm missing something simple, I haven't really thought about this enough.

If your mass only increases from a stationary observer's perspective, does this not imply that the energy requirements to accelerate to the speed of light are also only from an observer's perspective? Doesn't the energy required to accelerate also become relative? Or am I getting mixed up?

 

[Dale]

So what I'm getting at is that, relative to yourself, you always appear to be normal regardless of how fast you are going, ... So if you were to move at any speed, you would still appear normal to yourself. Is this correct?

Yes. Not only that, but all of the laws of physics would also appear normal. This is what is implied by the 1st postulate.

even if you are accelerating (in free space you would not know if you were accelerating or not without some sort of contact force)

You have to be careful here to distinguish between proper acceleration and coordinate acceleration. You would not know about coordinate acceleration, but you would know about proper acceleration. I think that is probably what you were implying by the term "contact force" although I would not generally include e.g. a classical EM force in the term "contact force" and they can cause proper acceleration.

 

[Dale]

If your mass only increases from a stationary observer's perspective, does this not imply that the energy requirements to accelerate to the speed of light are also only from an observer's perspective? Doesn't the energy required to accelerate also become relative? Or am I getting mixed up?

Yes, energy is a relative, or frame-variant, quantity. However, remember that your velocity relative to yourself is always 0 by definition, so the energy in the observer's frame is the one that matters. Your frame is non-inertial.

 

[jbar18]

You have to be careful here to distinguish between proper acceleration and coordinate acceleration. You would not know about coordinate acceleration, but you would know about proper acceleration. I think that is probably what you were implying by the term "contact force" although I would not generally include e.g. a classical EM force in the term "contact force" and they can cause proper acceleration.

What exactly do you mean by coordinate acceleration and 'proper' acceleration? Does coordinate acceleration just mean accelerating in principle without being pushed etc.? If that's what it means then yes that is what I meant by contact force. But then what about something like gravity? I was under the impression that the only reason we feel force when we are falling to the Earth is because there is also a resisting force, in the case of falling this would be the E.M. interaction between the atoms of our body and the atoms in the air (I'm treating air resistance as a contact force). But in open space there would be no resistive forces, so how would you be able to tell that you were accelerating?

 

[Dale]

What exactly do you mean by coordinate acceleration and 'proper' acceleration?

Coordinate acceleration is the second derivative of position wrt time. Proper acceleration is the acceleration measured by an ideal accelerometer.

If an accelerometer measures 0 for all axes of acceleration and rotation then we can build an inertial reference frame around it. In such an inertial reference frame the coordinates of the accelerometer could be expressed in three-vector notation as:
(x(t),y(t),z(t))=(0,0,0)
The coordinate acceleration would also be 0, the same as the proper acceleration.

However we could do the following coordinate transform:
X=1/2 g t² + x
Y=y
Z=z

In such a reference frame the coordinates of the accelerometer would be:
(X(t),Y(t),Z(t))=(1/2 g t², 0, 0)
Where the magnitude of the coordinate acceleration would be g even though the proper acceleration would remain 0.

 

[Upisoft]

If I'm getting that right you suggest that it is not impossible for massive object to travel at speed of light, it is only impossible to observe it doing so.

So, the object disappears for any observer. But the object itself will have the same relation to any observer. Thus the best way to make a massive object to travel at the speed of light is to make it disappear out of existence.

 

[JesseM]

Coordinate acceleration is the second derivative of position wrt time. Proper acceleration is the acceleration measured by an ideal accelerometer.

Also, at any given moment your proper acceleration is just your coordinate acceleration in the inertial frame where your instantaneous velocity is zero at that point. And the proper acceleration measured on an accelerometer also corresponds to the G-force you'd feel on board the accelerating ship.

You can travel with constant proper acceleration forever and an observer in some fixed inertial frame will see your coordinate acceleration continually decreasing as you approach c, so you can never quite reach it. For more on this, see http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html .

 

[jbar18]

If I'm getting that right you suggest that it is not impossible for massive object to travel at speed of light, it is only impossible to observe it doing so.

This is near enough what I was getting at.

On another related point though, if the speed of light is unattainable by any massive object, what about massless objects? For example, do photons accelerate to the speed of light, or do they 'start' at that velocity? Moreover, why is the speed of light also the speed limit for massless particles? If the thing that hinders a massive object's ability to attain light speed is a lack of energy, why don't photons of higher energy travel faster? At a guess I'd say that the increase of frequency with higher energy photons is analogous to the increase of mass in massive particles. Would this be correct? I'm just trying to think of reasons why a photon itself is limited by this speed, since the only thing stopping mass is the fact it would require infinite energy.

Can anyone enlighten me?

 

[DaveC426913]

This is near enough what I was getting at.

On another related point though, if the speed of light is unattainable by any massive object, what about massless objects? For example, do photons accelerate to the speed of light, or do they 'start' at that velocity?

They start at that velocity.

Moreover, why is the speed of light also the speed limit for massless particles?

c is the speed limit of the universe.

Actually, don't look at it as a speed limit at all. Look at it as geometry. It is no more possible to go faster than c than it is to go north of the north pole, or have the rise on a graphed function be more vertical than straight up (trying to go "more vertical" does not get you going backwards).

If the thing that hinders a massive object's ability to attain light speed is a lack of energy,

It isn't. Disabuse yourself of this notion.

 

[jbar18]

c is the speed limit of the universe.

Actually, don't look at it as a speed limit at all. Look at it as geometry. It is no more possible to go faster than c than it is to go north of the north pole, or have the rise on a graphed function be more vertical than straight up (trying to go "more vertical" does not get you going backwards).

Haha, physics is brilliant.

I still don't get what is so special about the particular speed c. Why does the speed of an electromagnetic wave link space and time so intricately? I guess its probably the backbone of relativity, but I haven't come across anything enlightening yet as to how and why all these different things are linked by c. Sure there are equations, but is there any intuitive explanation which could help to visualise it all? I'd be really grateful if anyone could explain in as simple way as possible.

 

[JesseM]

Haha, physics is brilliant.

I still don't get what is so special about the particular speed c. Why does the speed of an electromagnetic wave link space and time so intricately? I guess its probably the backbone of relativity, but I haven't come across anything enlightening yet as to how and why all these different things are linked by c. Sure there are equations, but is there any intuitive explanation which could help to visualise it all? I'd be really grateful if anyone could explain in as simple way as possible.

I think it's more confusing if you define c as the "speed of an electromagnetic wave"--rather c is a basic constant in the equations of relativity which has nothing specifically to do with light (for example, it appears in the equations for time dilation and length contraction), and presumably there's some way of deriving the conclusion in quantum physics that all massless particles (including photons but also other massless particles like gluons) must move at c.

 

[Dale]

I still don't get what is so special about the particular speed c.

The thing that is special about the particular speed c is that it is the same in all inertial reference frames, it is frame invariant. This is the geometry that Dave mentions. Everything else stems from that.

 

[Naty1]

... why all these different things are linked by c. Sure there are equations, but is there any intuitive explanation which could help to visualise it all? I'd be really grateful if anyone could explain in as simple way as possible.

nobody knows why, but to get an intuitive visualization Lee Smolin has an interesting diagram in Chapter 3 of THE FABRIC OF THE COSMOS#...he plots three paths thru spacetime where x,y axis are space and a third axis is t...at constant velocity the path is straight, rotational acceleration results in a corkscrew path and linear acceleration results a curved trajectory...so geometrical shapes provide of trajectories in spacetime provide the absolute standard that determines whether something is acelerating...


#Note...excellent insights without much formal mathematics...lots of intutive stuff derived from the formal mathematics...

The othr side of the coin is that muchof relativityis NOT intuitive...except maybe to Einstein...and the NON intuitive nature of relativity is discussed many places, one beingf Brian Greene's THE ELEGANT UNIVERSE, page 25+...for example the fact that observers moving relative to each other will NOT agree on their observations of either space or time...

The fact the the speed of light is constant while space and time are NOT constants seems to defy our everyday observations...