# Can't Tell If you are shrinking?

1. Aug 14, 2014

### TheScienceOrca

They say there is no measurement if travelling in a ship at the speed of light you can do to tell whether you are travelling at the speed of light, because as everything shortens even your ruler shortens.

Well what if I threw a ruler in the direction opposite of the ships travel and with precise tools measured the increase in size compared to a ruler going to the speed of light in the ship.

Then you would be able to tell if you are moving anyway where in the universe even by yourself.

Sorry about all the theory of relativity questions, it has just really got my mind going.

2. Aug 14, 2014

### ghwellsjr

It's not clear exactly what you would do after throwing a ruler but if you could measure its length, it would be shorter, not longer.

But let's take it one step further: If two identical observers in two identical ships pass each other at some high speed which they can measure using the precepts of Special Relativity, they can each determine the length of the other ship by timing how long it takes for the other ship to pass and doing a simple calculation. They will both determine that the other ship is shorter than their own and by the same amount.

If you understand that, then you could do a similar thing with a ruler that someone threw towards you inside your ship. You could measure its speed and then see how long it took to pass you and calculate its length. It would be shorter.

3. Aug 14, 2014

### Orodruin

Staff Emeritus
You are massive and cannot travel at the speed of light. You could travel close to the speed of light relative to another object. However, you will never see any length contraction effect on objects that are traveling along with you.

4. Aug 14, 2014

### TheScienceOrca

If I threw the ruler in the opposite direction of travel then the ruler would have slower relative motion and thus be longer correct?

I was thinking of a machine inside the rocket ship travelling at the speed of light.

In this machine on one wall is a measuring tape that would be travelling at the speed of light.

A blast of air or some force would shoot the ruler through the chamber where high speed cameras would measure the change in size of the ruler.

Whether it be longer or shorter (longer if in opposite direction of travel I believe).

Anyway this would allow you to tell if you are travelling even with NO other rockets around you.

Looking back at it to counter my statement, the change in size would still happen at zero velocity. So the ruler must be thrown towards the front of the ship and if it doesn't shrink then you can only tell if you are travelling at the speed of light.

This same concept would still apply at the speed of light though.

5. Aug 14, 2014

### TheScienceOrca

There also isn't only 2 masses in the universe.

It's called theoretical physics for a reason.

6. Aug 14, 2014

### ghwellsjr

Just like speed is defined according to a frame of reference, so is length. If an object is traveling according to a frame of reference, it will be shorter along its direction of motion. If you transform to another frame of reference moving with respect to the original one, then different objects can have different speeds and therefore different length contraction. It doesn't matter if the object is moving along one direction or in the opposite direction.

7. Aug 14, 2014

### TheScienceOrca

Lets say I am bob I am standing in the ship going in some direction at the speed of light.

From my perspective I could be standing still, here is how I can tell I am moving at the speed of light.

If I throw a ruler towards the direction of travel no object can go faster then the speed of light so the ruler would not shrink in size, from bobs perspective.

Although if the ship is was not moving and I threw the ruler under precise measurement I could see the decrease in size of the ruler under VERY precise measurement.

8. Aug 14, 2014

### ghwellsjr

You've already been admonished by Orodruin that no massive object can travel at the speed of light so you can't claim that you are doing theoretical physics and continue to draw conclusions about what happens when a massive object is traveling at the speed of light.

If you change slightly to just under the speed of light then you will always have room for any object to be thrown at any speed less than that of light and calculate the new speed and from that the Length Contraction. I have already explained how this could be done. Please don't dismiss the answers you have already been given.

9. Aug 14, 2014

### TheScienceOrca

I understand what you are saying, Oroduin stated that when masses are travelling with you, in my scenario the ruler was not travelling with the rocket as it was being shot in the opposite direction at high rate of speed.

This length contraction you are explaining is what my question is about sorry if I am not communicating well.

If we were travelling at the speed of light in this rocket and I threw a ruler in the same direction of travel what would happen?

Perhaps I don't understand that, and that is what caused my mistake. I thought that the ruler would not change in size as it couldn't go over the speed of light.

10. Aug 14, 2014

### zbe

You can't travel at the speed of light. You can get arbitrary close to it though.

You are missing the point that speed is relative. With respect to Bob, the ruler will travel with whatever speed he throws it. It doesn't matter if Bob is in a train, in a hotel or in a spaceship - as far as he is concerned he and ruler are stationary wrt to each other (until he throws it).

11. Aug 14, 2014

### Flatland

But your ruler is stationary from your perspective so you will observe the ruler to shrink no matter which direction you throw it.

12. Aug 14, 2014

### TheScienceOrca

Well the ruler would shrink if thrown even at stationary because the ruler isn't stationary when thrown

13. Aug 14, 2014

### TheScienceOrca

Ok lets keep in mind this is just theoretical, if we are close to speed of light, nothing can go faster than speed of light, so imagine a ruler bolted onto the floor of the space ship if you throw the rule and it doesn't shrink relative to the ruler that is going close to c then you must be travelling within the speed of light - the speed of the ruler thrown.

If my logic make sense

14. Aug 14, 2014

### ghwellsjr

I explained this in post #4.

You have to define the speed of each object according to an Inertial Reference Frame (IRF). Stationary objects are not Length Contracted. Moving objects are along the direction of motion. The faster they move, the more the Length Contraction. You can then transform to another IRF moving with respect to the first one. This can change the speed of each object and therefore its Length Contraction. If you transform from a frame in which one object was moving and had Length Contraction to a frame in which it is stationary, it will no longer have Length Contraction but some other object may.

So if you have a spaceship traveling at close to c, then a ruler bolted to the floor will be Length Contracted to a great extent. Then if you had another ruler thrown at an even higher rate of speed, it will be Length Contracted to a greater extent. But if you transform to the rest frame of the space ship, the ruler bolted to the floor will no longer be Length Contracted and the thrown ruler will be Length Contracted to a lesser extent than before. Then you can transform to the rest frame of the thrown ruler and it will not be Length Contracted but the ruler bolted to the floor will be.

Just remember, no matter how fast the space ship is traveling, when you transform to its rest frame, a ruler can be thrown at any speed short of c.

15. Aug 14, 2014

### zbe

Relative to what?

Close to c relative to what? You specified it is bolted to the floor. So it is stationary wrt to the 2nd ruler (before 2nd ruler is thrown).
Also "shrink" isn't really appropriate word IMHO. Its length contracts in the direction of motion.

It doesn't because you are still missing the point of relative velocity.

16. Aug 14, 2014

### TheScienceOrca

Ok Bob is flying in an airship which has a long chamber in the back for experiments.

This airship is flying close to c through space.

A measuring tape is displayed across the floor of the chamber. If a ruler is shot at a very high speed (theoretical) lets say we shot the ruler at .5c the shrinkage in length in the direction of motion would be measurable.

So if we knew how much the "shrinkage" was at rest, we would be able to find out if we were above .5c as the shrinkage would then be different then expected.

We are able to do these measurements as the measuring tape and ruler are different masses.

I have used measuring tape for the chamber which shrinks with the space ship and ruler for the object being shot to avoid confusion.

You could even imagine a 1cm block being shot and it shrinks to lets say .5cm for example at .5c

So if you were going .6c and it only shrinked to lets say .6cm you would know that it is off by 1cm which means the velocity the ship is going must be .6c

As the block can't go faster than the speed of light.

This should be a more clear explanation

17. Aug 14, 2014

### TheScienceOrca

In regards to your post ghwells my IRF and only frame of reference for the above post is BOB

18. Aug 14, 2014

### Orodruin

Staff Emeritus
The ruler will never shrink when observed within a frame in which it is at rest. It never has a universal length that will be independent of the frame it is observed in. Even if you are moving at 0.999999999999c relative to me along with the ruler, the ruler will be at rest in your frame and therefore you will measure its length to be the rest length. As an observer in a frame which is moving at a velocity 0.999999999999c relative to you, I *will* however measure the length to be shorter than the rest length.

19. Aug 14, 2014

### TheScienceOrca

That is if the ruler is moving with the ship, in my scenario it is not. It is projected in the motion of direction. Since the projectile can not exceed c we will be able to measure the change in length relative to the expected change in length that bob has measured at rest.

This will allow bob to know if he is travelling at the speed of light, and which direction he is travelling in.

Bob may have to shoot the projectile perpendicular to each other to know which way bob is travelling.

20. Aug 14, 2014

### zbe

"Through space" is invalid definition. You are always measuring velocity with respect to some other object. So how could you possibly know that you are moving if the spaceship was the only thing in space? You couldn't and that's the whole point.

The rest of the post is irrelevant - you can do your experiment wherever you want and you will always get the same result - the ruler with contract by factor gamma, which in your case of 0.5c is ~1.15.

21. Aug 14, 2014

### Orodruin

Staff Emeritus
If you are Bob, you are at rest in an inertial frame. Regardless of which direction you throw the rod, it will shrink as measured in your inertial frame. For Alice who is the observer you were moving at 0.9999999999c relative to, whether or not it shrinks or expand will depend on the direction you throw it in - but you simply cannot make a distinction.

22. Aug 14, 2014

### TheScienceOrca

How can I not lets say bob flies his ship to alices planet.

While on Alices planet in his large experiment room he performs a series of the following test:

He shoots a 1CM cube in 4 directions at a very fast speed .999999c

Using bobs advanced technology he can measure the change in size of the cube exactly.

Lets saying his cube shrinks to .1cm when fired normally at rest on alices planet.

There is measuring tape on the floor attached to the ship which gives the measurements so that scale of measurement changes when the ship approaches the speed of light.

Bob can also measure the speed of objects relative to him exactly, with his extremely advanced vision goggles.

Bob then tracks this data of the "shrinkage".

If flying from bobs perspective he can from now on prove that he is moving by doing the following test.

Fire the cube in 4 directions.

If the cube shrinks to .1cm and is measured at a speed less than when fired bob now knows he is travelling faster than he was on alices planet, even if they were moving on alices planet. If the cube doesn't shrink to .1cm then bob knows that the fired cube is in the opposite direction of travel.

23. Aug 14, 2014

### TheScienceOrca

I clearly state relative to c.

24. Aug 14, 2014

### zbe

What?

---

You still can't grasp that velocity is a relative quantity. Do you understand that you are traveling at this very moment at 0.9c relative to some star in our universe? And you are also traveling at 0.5c wrt to some other star. And you are also traveling at 0.8c wrt to some galaxy. Etc, etc. So what? This doesn't affect your experiments.

25. Aug 14, 2014

### Orodruin

Staff Emeritus
Ok, so let us imagine the following:
• Alice and Bob have a relative velocity of 0.99c toward each other.
• They both shoot out boxes of a given size toward each other as well as away from each other.
The prediction of special relativity will be the following for Alice:
• Alice will observe that both of the boxes she fired become shorter.
• Alice will observe that the box Bob fired toward her has a higher velocity than Bob and thus is going to be more contracted than it was before Bob fired it.
• Alice will observe that the box Bob fired away from her has a lower velocity than Bob and thus is going to be less contracted than it was before Bob fired it.
For Bob, the situation would be
• Bob will observe that both of the boxes he fired become shorter.
• Bob will observe that the box Alice fired toward her has a higher velocity than Alice and thus is going to be more contracted than it was before Alice fired it.
• Bob will observe that the box Alice fired away from her has a lower velocity than Alice and thus is going to be less contracted than it was before Alice fired it.
As you can see, the situation is completely symmetric. There is therefore no way to claim that either Alice or Bob is at some sort of absolute rest. This is not even particular to special relativity, already in classical mechanics velocities are all defined relative to something and there is no notion of absolute rest.