# B Special Relativity vs Inertia

#### MarSuper

I have a question about Special Relativity. If a person is in a rocket ship traveling at 99.999999 percent the speed of light and they are standing at the back of the ship. Will they be able to walk to the front of the ship or will inertial resistance prevent them from doing so?

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#### jbriggs444

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I have a question about Special Relativity. If a person is in a rocket ship traveling at 99.999999 percent the speed of light and they are standing at the back of the ship. Will they be able to walk to the front of the ship or will inertial resistance prevent them from doing so?
As you read this, you are already moving at 99.999999 percent of the speed of light in the rest frame of a particle that is moving at 99.999999 percent of the speed of light relative to you. Do you experience any problems walking around?

One of the motivating postulates from which the theory of special relativity is derived is that the laws of physics work the same way regardless of what frame of reference you choose. The resulting theory is built to preserve that property. And it does.

#### Orodruin

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Your question is ill posed. For the person, the ship is not traveling at close to light speed. There is no such thing as objectively travelling at a particular speed (apart from light speed), not even in classical mechanics. You always need to state relative to what the thing is travelling at that speed.

#### Nugatory

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I have a question about Special Relativity. If a person is in a rocket ship traveling at 99.999999 percent the speed of light and they are standing at the back of the ship. Will they be able to walk to the front of the ship or will inertial resistance prevent them from doing so?
It's an easy experiment. Right now the room that you are sitting in is moving at 99.999999% of the speed of the light relative to something somewhere in the universe. (It's also moving at maybe thirty kilometers per second relative to the sun, and because of the earth's rotation and depending on how far north of south of the equator you are, about 3000 kilometers per hour relative to someone on the opposite side of the earth from you, and at speed zero relative to the earth under your feet, and 500 km/hr relative to the airplane overhead, and ....).

So get up and walk across the room.... Do you experience any difficulty doing so, and does it make any difference whether you consider your speed to be 99.99999c, or 30 km/sec, or 3000 km/hr, or zero, or 500 km/hr?

The key point is that it makes no sense to talk of the speed of anything unless you also say what that speed is relative to. All the interesting relativistic effects (time dilation, mass increase, length contraction) that you read about in non-serious introductions are not things that happen to you when you are moving, they are things that happen to other people's observations of you when you are moving relative to them. (And vice versa, because if you are moving relative to them, they are moving relative to you).

#### MarSuper

The ship is moving relative to the earth at 99.9999 percent the speed of light. I assumed everyone would assume that, sorry for the confusion.
@Nugatory Yes but all of the speeds you mention are relatively small relative to the speed of light. I would not expect to feel any resistance in the case mentioned. Here is what is confusing me, according to the Lorentz transformations. If I attempt to accelerate more when my ship is already moving forward at 99% the speed of light (Relative to Earth) it would take a massive amount of energy to accelerate just that little bit more. That extra energy for the increase in velocity would have to come from me or my ship in my frame of reference. If it is true that it would take an immense amount of energy just to go a little bit faster relative to Earth's frame of reference, How would I not notice the immense amount of energy and effort necessary to go just that little bit faster in my frame of reference. If I cannot accelerate to a rate above the speed of light relative to Earth I cannot go faster than that relative to every other object that is floating in space. In order to adhere to the maximum speed limit relative to the rest of the Universe it seems that once I get up to this rate of motion it becomes an absolute motion and things like the motion of a clock and my ability to move forward in the ship would be noticeably slower and more difficult. As relatively speaking everything else is only moving at very slow rates of speed. Everything else macroscopically speaking in the Universe is practically at a standstill relative to the speed of light. So how would I not feel or notice in my special frame of reference the immense amount of energy required to move faster? Hopefully you see what I am saying. There seems to be a contradiction. This is vexing me.

#### Orodruin

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The ship is moving relative to the earth at 99.9999 percent the speed of light. I assumed everyone would assume that, sorry for the confusion.
What you do not seem to understand is that this piece of information is irrelevant for the reply, as discussed above.

If I attempt to accelerate more when my ship is already moving forward at 99% the speed of light (Relative to Earth) it would take a massive amount of energy to accelerate just that little bit more. That extra energy for the increase in velocity would have to come from me or my ship in my frame of reference.
You have a fundamental misunderstanding here. Your "a little bit more" is frame dependent. The first thing you need to learn to understand this is relativistic velocity addition.

#### PeroK

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The ship is moving relative to the earth at 99.9999 percent the speed of light. I assumed everyone would assume that, sorry for the confusion.
@Nugatory Yes but all of the speeds you mention are relatively small relative to the speed of light. I would not expect to feel any resistance in the case mentioned. Here is what is confusing me, according to the Lorentz transformations. If I attempt to accelerate more when my ship is already moving forward at 99% the speed of light (Relative to Earth) it would take a massive amount of energy to accelerate just that little bit more. That extra energy for the increase in velocity would have to come from me or my ship in my frame of reference. If it is true that it would take an immense amount of energy just to go a little bit faster relative to Earth's frame of reference, How would I not notice the immense amount of energy and effort necessary to go just that little bit faster in my frame of reference. If I cannot accelerate to a rate above the speed of light relative to Earth I cannot go faster than that relative to every other object that is floating in space. In order to adhere to the maximum speed limit relative to the rest of the Universe it seems that once I get up to this rate of motion it becomes an absolute motion and things like the motion of a clock and my ability to move forward in the ship would be noticeably slower and more difficult. As relatively speaking everything else is only moving at very slow rates of speed. Everything else macroscopically speaking in the Universe is practically at a standstill relative to the speed of light. So how would I not feel or notice in my special frame of reference the immense amount of energy required to move faster? Hopefully you see what I am saying. There seems to be a contradiction. This is vexing me.
If you are travelling near the speed of light relative to the Earth, then (among other things) your measurement of acceleration is different from someone on Earth. In principle, you could still be firing rockets that accelerate you locally at some (to you) constant acceleration, but those on Earth would measure your acceleration to be much smaller.

In your frame of reference, you are accelerating at a constant rate; whereas, those on Earth would measure your acceleration as diminishing over time.

So, you wouldn't actually experience any difficulty accelerating further (not in terms of force, energy or power).

There is nothing special about the Earth's frame of reference, so you could imagine the Earth receding from you at near the speed of light. This would be equivalent to the scenario where you are receding from the Earth. In that case, you would experience no special energy requirements to accelerate relative to something local.

#### PeroK

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@MarSuper One of the problems you have is trying to understand SR without understanding basic classical physics. Much of your confusion would apply in a classical scenario. For example:

Imagine a $1000 kg$ car travelling at $10m/s$ along a road; it then accelerates to $20m/s$. You are at rest relative to the road. Your measurements of change in kinetic energy of the car are:

$\frac12 m(v_1^2 - v_0^2) = 500 (400 - 100) = 150,000J$

However, someone in another car, travelling at $10m/s$ alongside the first car will see the car accelerate from $0$ to $10m/s$ relative to them and hence measure the change in kinetic energy to be:

$\frac12 m(v_1^2 - v_0^2) = 500 (100 - 0) = 50,000J$

You can see that energy and change in energy are actually dependent on your reference frame. And this is good, old classical physics. You may be vexed by that as well!

#### Nugatory

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You can see that energy and change in energy are actually dependent on your reference frame. And this is good, old classical physics!
This is a very important point. You have to understand the classical resolution of the apparent paradox that results from kinetic energy being a function of the square of the velocity (so that the energy required to accelerate an object from 0 to 1 km/sec is less than the energy needed to accelerate it from 10 to 11 km/sec, even though the difference between the two situations is just the difference between an observer initially at rest relative to the object and one initially moving at 10 km/sec backwards relative to the object) before you are ready to take on the relativistic version.

Exactly how you resolve the apparent paradox depends on the exact mechanism we're imagining to accelerate the object. The key is that there is always some reaction mass somewhere (by Newton's third law, you can't accelerate something in one direction without accelerating something else in the opposite direction). When you find this reaction mass and include it in the calculation you will find that the amount of energy that needs to be generated (fuel burned, effort expended by your muscles, ....) is the same no matter which frame you choose to do the calculation and even though the change in the kinetic energy of the accelerated object is different in different frames.

This was the subject of a very long thread a while back - I'll see if I can find it.

#### Ibix

Another way to put it - if I say that i am stationary and you are travelling at 99.9999%c then you would say that you are stationary and I am travelling at 99.9999%c. This is the principle of relativity. It's why Orodruin describes your question as ill-posed.

Since you can describe your rocket as stationary, of course you can walk to the front of it at any speed you like (you can have a CERN style accelerator swinging protons around at 99.9999%c relative to the rocket if you can front up the cash). Since I describe you as moving at 99.9999%c and you can't exceed c then obviously my description is slightly odd by every day standards. In fact, time dilation, length contraction, and the relativity of simultaneity conspire to produce a consistent answer. If I say your ship is moving at v and your ship says you are moving at speed u relative to it then I say that you are moving at $$u'=\frac {u+v}{1+uv/c^2}$$That is true at every day speeds as well - calculate $uv/c^2$ for highway speeds to see why we didn't notice the denominator for a few centuries.

#### jbriggs444

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@MarSuper
You can see that energy and change in energy are actually dependent on your reference frame. And this is good, old classical physics. You may be vexed by that as well!
Note that things are not as vexing as the posting by @PeroK might suggest. Some things stay the same regardless of the reference frame you choose. These things are called "invariant".

In classical physics, one invariant the amount of kinetic energy gain or loss in the complete system. Different inertial reference frames may disagree about which objects gain kinetic energy and which lose it. But all will agree on the total amount that is gained or lost. If the car gains 150,000J in one frame and only 50,000J in another, one can look closely and find the discrepancy buried in the change in the kinetic energy of the road.

Edit: as @Nugatory already pointed out in #9 above

#### Mister T

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The ship is moving relative to the earth at 99.9999 percent the speed of light. I assumed everyone would assume that, sorry for the confusion.
That's equivalent to the ship being at rest and Earth moving at that speed. So as others have pointed out, that assumption is not relevant.

By the way, engineers who work with things moving at speeds that high (called relativistic speeds) aren't really concerned with the speed so much as they are with $\gamma$. $$\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}.$$
To see why, let's do the arithmetic. For this case we have $\frac{v}{c}=0.999\ 999$ so $\gamma \approx 700$.

(Meaning each would observe the other contracted to a length 700 times shorter along the direction of relative motion. Likewise each would observe the other's clock to be running 700 times slower than their own. And each would observe the other's total energy to be 700 times greater than its rest energy.)

Now, if we increase the speed by just 90 parts per million, to 99.99999 percent of the speed of light, $\gamma$ becomes about 2200.

Measuring instruments may not be able to detect that small of a difference in speed. But everyone is certainly aware of the huge difference in the values of $\gamma$. Mainly because of the huge amount of additional energy required to go from 700 times the rest energy to 2200 times the rest energy.

#### MarSuper

Thanks for the replies Perok, Nugatory, IBix, Jbriggs444, and Mister T as for Orodruin your response was of absolutely no value it was presumptuous and curt in other words just saying I don't understand or a question is ill posed is not helpful. Explain in detail like the others have done here. Don't try to appear smart, be smart and explain. I understand Special Relativity. I have read dozens of books and articles on the subject. I get it. There is something about it that is unsettling to my mind. That is what I am trying to say and that is why I asked the question to hopefully get someone to put answer out there that resonates better with my thinking. To make it clear. To make it make sense.

What I still have trouble with is the invariance of Special Relativity at high velocity. I found the explanation of all the others very helpful and courteous and it was more what I was looking for, Thanks guys.

A statement like this is very helpful.
(Meaning each would observe the other contracted to a length 700 times shorter along the direction of relative motion. Likewise each would observe the other's clock to be running 700 times slower than their own. And each would observe the other's total energy to be 700 times greater than its rest energy.)
I really liked it spelled out like this. Even in this statement I have problems. It is true as long as the conditions remain static. What happens when the rocket ship turns around and returns to the frame of reference of the earth. Then the clocks will not be the same the one on the rocket will be slower. Why? Because it is the object that actually moved, it accelerated not the earth. This to me is an indication of absolute motion. If things are invariant in the relative reference frames then why aren't the clocks at the same time when the rocket returns? Something changed in one of the reference frames.

Some things stay the same regardless of the reference frame you choose. These things are called "invariant".

I am not really arguing about Special Relativity and concepts and postulates within it. There is something in the interpretation of Special Relativity that just does not seem correct.

The part that bothers me is that there should be away to detect absolute motion. Let me try another example if I have a planet like earth that is moving at some speed relative to space and I get in a rocket ship and accelerate away from earth in that rocket then it is the rocket that moved not the earth. It accelerated the earth did not. The Rocket is the one that really moved and when it gets back to earth its the rocket's clock that will have run slower not the earth's clock. Perhaps might I say that absolute motion can be detected only when something accelerates. Is that a fair statement?

Once again I understand Special Relativity I have read books on it and run through the equations and studied the results. My problem with it is difficult to put in words but I just seem to have this funny feeling in my mind that somehow it is incomplete in someway. Some vitally import way. The constancy of the speed of light bothers me. Why is it the particular velocity that it is? Keep in mind I already know about Maxwell and permittivity and permeability no need to go there. There is a layer underneath those two constants we need to understand better. Why does light slow down when traveling in different mediums? What really bothers me is the speed limit, this speed limit must be exceedable somehow. Arghhhh!

#### jbriggs444

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Because it is the object that actually moved, it accelerated not the earth. This to me is an indication of absolute motion. If things are invariant in the relative reference frames then why aren't the clocks at the same time when the rocket returns? Something changed in one of the reference frames.
One invariant is whether an object accelerates. Objects that are subject to no net force do not accelerate relative to an inertial frame. All inertial frames agree on whether an acceleration did or did not occur. The space craft that goes out, accelerates and comes back is not at rest in any one inertial frame for the entire trip. All inertial frames agree on this. The frame of reference within which the space craft is at rest the entire time is not inertial. This can be seen because in this frame, the Earth accelerates dramatically partway into the trip despite being subject to no net force. [And the space craft remains at "rest" despite being subject to rather large forces].

Pick any one of the three inertial reference frames in the traditional twins paradox and you can explain the same observable events.

#### Orodruin

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I understand Special Relativity.
You might not like it, but you do not. Trying to immerse yourself into spelled out computations is fruitless unless you understand what they actually mean. I, as others, have tried to point you in the correct direction. I am sorry if it upsets you, but I am not going to use silk gloves just so that you can feel better about having misconceptions - I am going to spell them out. That you get the illusion of understanding if you see spelled out computations does not mean that you actually understand what is going on.

Why? Because it is the object that actually moved, it accelerated not the earth.
This is a misconception of the twin paradox. The twin paradox arises solely due to failure to take the relativity of simultaneity into account when one of the twins change inertial system and therefore simultaneity convention. Acceleration has nothing to do with it except for being a means for changing rest frame.

This to me is an indication of absolute motion.
Again, you would be wrong in this conclusion. As jtbriggs just said, you can pick any inertial frame and get the same result. Already in classical mechanics there is no absolute motion and the derivation of SR fundamentally rests upon this assumption as well so you simply cannot get a theory in which absolute motion exists.

If things are invariant in the relative reference frames then why aren't the clocks at the same time when the rocket returns?
Because doing things properly in any inertial frame you will not get this result. You can even do it using two frames for the travelling twin, but you must correct for the different simultaneity conventions in these frames or you will end up with the "paradox".

Once again I understand Special Relativity I have read books on it and run through the equations and studied the results.
Again, your statements indicate that you have not yet understood SR.

it was presumptuous and curt in other words just saying I don't understand or a question is ill posed is not helpful
What is presumptuous is to claim that you understand something that you clearly do not. Furthermore, I gave you the solution to your question already in the first post:
For the person, the ship is not traveling at close to light speed.
Had you started from here instead of focusing on me calling your question ill posed (when it was) we would have been in a different position and you might have learned something.

#### Ibix

Perhaps might I say that absolute motion can be detected only when something accelerates. Is that a fair statement?
No. Orodruin's Insight Article is one place to look for what is going on with the twin paradox, which is what you are getting at here. The easiest way to see it is to understand that elapsed time is the spacetime equivalent of distance travelled through space. Two different routes from point A to point B are not necessarily the same distance. Similarly, two different routes from event A to event B do not necessarily have the same duration. Acceleration only appears to be significant because of the way the twin paradox is usually constructed.

Once again I understand Special Relativity I have read books on it and run through the equations and studied the results. My problem with it is difficult to put in words but I just seem to have this funny feeling in my mind that somehow it is incomplete in someway. Some vitally import way. The constancy of the speed of light bothers me. Why is it the particular velocity that it is? Keep in mind I already know about Maxwell and permittivity and permeability no need to go there. There is a layer underneath those two constants we need to understand better.
There is an invariant speed; this is a consequence of the principle of relativity (plus some assumptions about isotropy and homogoneity). If that speed is finite you get Einsteinian relativity; if it is infinite you get Galilean relativity. The speed of light is a red herring here - light just happens to travel at the invariant speed (that's an overstatement - there are good reasons for massless particles being required to travel at the invariant speed) and nothing would be different about relativity if it travelled slower.

What really bothers me is the speed limit, this speed limit must be exceedable somehow.
Why? Because you want it to be?

#### PeroK

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this speed limit must be exceedable somehow. Arghhhh!
For that I believe you need some dilithium crystals and an unassuming engineer with a dodgy Scottish accent.

#### Ibix

For that I believe you need some dilithium crystals and an unassuming engineer with a dodgy Scottish accent.
Sadly, even Mr Scott cannae break the laws of physics...

#### MarSuper

@Ibix

You bring up a good point when you ask
Why? Because you want it to be.

It just seems to me it is a necessary thing. We must be able to travel faster than light or we will never be able to get off the earth and visit other worlds. Just a side thought.

Another corollary to what I said earlier was that it would require an unbounded amount of energy to accelerate an object to speeds approaching that of light, from rest in any reference frame other than that of a beam of light. And so unless you think you have access to a very-literally infinite source of energy (and in finite time at that), you cannot accelerate anything up to the speed of light. That statement comes from Einstein. My question is what is holding back the ship from accelerating to the speed of light? Why does it take an infinite amount of energy to accelerate to the speed of light? Still why can't the ship break the light speed barrier? What is holding it back relative to the rest of the Universe? Keeping in mind I already know what the equations say. I am looking for the physical interpretation.

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#### jbriggs444

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We must be able to travel faster than light or we will never be able to get off the earth and visit other worlds.
The laws of physics care not for what we want to do.

#### Mister T

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What happens when the rocket ship turns around and returns to the frame of reference of the earth. Then the clocks will not be the same the one on the rocket will be slower.
There's a difference between a clock being slower and a clock being behind. The clock that changed directions will be behind the one that didn't, but if both clocks are at rest in the same frame of reference they will run at the same rate.

Because they took different paths through spacetime AND they reunited.

These answers won't be meaningful to you until you work out the details for yourself. You need to understand what Einstein's relativity says about clock synchronization. You need to understand that proper time is the time that elapses between events that occur at the same place in a given frame of reference, so that for observers at rest in other frames of reference the time that elapses between those same two events will be larger.

The part that bothers me is that there should be away to detect absolute motion.
There isn't. Nature is different from your expectations of the way it should be.

Let me try another example if I have a planet like earth that is moving at some speed relative to space
There is no such thing as motion relative to space.

There is no experiment you can perform that will distinguish between a state of rest and a state of uniform motion. The two things are one in the same.

#### Nugatory

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What is holding it back relative to the rest of the Universe?
It's not being "held back", any more than the curve $y=1/x$ is being "held back" from reaching $y=0$.

It may be easiest to see how this works if you take the energy as a function of speed $E=\gamma{m_0}c^2$ and invert it to get the speed as a function of energy: $v=c\sqrt{1-m_0/E}$. For every possible value of $E$ there will be a corresponding speed and none of these speeds is $c$.

#### Nugatory

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Let me try another example if I have a planet like earth that is moving at some speed relative to space and I get in a rocket ship and accelerate away from earth in that rocket then it is the rocket that moved not the earth. It accelerated the earth did not. The Rocket is the one that really moved and when it gets back to earth its the rocket's clock that will have run slower not the earth's clock. Perhaps might I say that absolute motion can be detected only when something accelerates. Is that a fair statement?
As @Mister T has pointed out, the rocket's clock did not run slower. Confusing the twin paradox (in which the travelling twin's clock ends up behind stay-at-home's) with time dilation (in which a moving clock runs slow relative to a clock at rest) is a common mistake that has been extensively discussed in other threads here.

#### Stephanus

I have a question about Special Relativity. If a person is in a rocket ship traveling at 99.999999 percent the speed of light and they are standing at the back of the ship. Will they be able to walk to the front of the ship or will inertial resistance prevent them from doing so?
Why not. As far as the person concern he's at rest. Perhaps if I can rephrase your question.
If a person is in a rocket ship traveling at 99.999999 percent the speed of light relative to an object and they are standing at the back of the ship...
So the object wouldn't be able to walk away from you at a certain speed...

#### Stephanus

But, did I see that the OP name crossed?

"Special Relativity vs Inertia"

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