# B Is special relativity incomplete?

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1. Mar 3, 2016

### flexible_time

I feel a difficulty in understanding SP at fundamental level which is somewhat related with twin paradox.

Let me take a thought scenario: in empty space or vacuum two boxes(A and B) with their own light sources attached are separated from each other at a far distance r initially. If they are approaching to each other in different inertial reference of frame (they know this by receiving light signal sent from other), they would say ( assuming they can think and talk) that I am at rest and you are moving so what A think is $v_A=0, v_B=-v$ and what B think is $v_A=-v, v_B=0$. My understanding is that under SR two views are equally valid because SR only talks about the relative motion by comparing states between two inertial reference of frames.

In such cases, if my logic is right, then it generates a fundamental problem. Just single global event( two approaching to each other) can yield two different views which are valid under SR view. The first postulate of SR says that "1. The Principle of Relativity The laws of physics are the same in all inertial frames of reference" and it conflicts with the result of two boxes approaching. Can a single event create two different result? Where am I wrong?

2. Mar 3, 2016

### Staff: Mentor

The wording here is incorrect. You can't say that they are in "different inertial reference frames." You can have an inertial reference frame in which $v_A=0$, one in which $v_B=0$, one in which the center of mass of A and B is not moving, etc. But one an inertial frame is selected, all objects are in that frame.

How are the laws of physics different in the different reference frames?

By the way, you problem has nothing special to do with SR. You would get the same thing considering Galilean relativity. You should make sure that you understand the latter before embarking on SR.

3. Mar 3, 2016

### flexible_time

Let me ask differently. if A is selected as the one inertial reference frame, then what is correct interpretation about who is moving? A or B? Whose time flow slower? I guess SR cannot determine which view is correct.

4. Mar 3, 2016

### Staff: Mentor

There is no "correct" view. They are both right. They will not agree on the simultaneity of events, but the laws of physics are going to be the same for both.

5. Mar 3, 2016

### flexible_time

My concern is that how a single event can create two different physical result. Taking one side view of moving A means that A will age slowly and the other view will show different physical result. If both are right then we need to accept two paradoxical views at the same time. A's time flow slowly than B and B's time flow slowly than A.

6. Mar 3, 2016

### Ibix

This isn't paradoxical. Imagine two cars travelling at 30mph along straight roads that diverge at 10°. Each car will observe that the other car is falling behind because its forward velocity is only 30 cos 10. The point here is that the two cars disagree on what "forward" means. They are using different frames of reference.

Much the same thing is happening in the relativistic case. Time is a dimension - a direction. The twins disagree on which direction is "time" so they disagree about whose clocks are ticking slowly.

7. Mar 3, 2016

### flexible_time

I cannot get what you say "they disagree about whose clocks are ticking slowly".

Lets replace two boxes with twin babies and the initial distance is long enough to make a big difference in their growth when they join. As they are approaching, my belief is that they will see only one physical result either baby A growing faster than B or B growing faster than A but not both of them regardless they disagree or not.

8. Mar 3, 2016

### PeroK

And how is that any different from classical physics? Where velocity, momentum and kinetic energy are all frame dependent?

9. Mar 3, 2016

### Ibix

How are you going to get twin babies a long distance apart?

You have two possible answers. One is that they aren't actually twins, just born on the same day. The problem with that is that they are in motion relative to each other, and the relativity of simultaneity means that they won't agree on what "the same day" means. Only one of the two (A for the sake of argument) will say that the other was born on the same day. A will be older when they meet up. B will say that A was born much earlier than him so, although A's clock ticks slowly, he is unsurprised that A is older when they finally meet up.

The other answer is a proper twin paradox where the twins move apart and return. In that case the resolution is that the twin who travels changes his definition of "now back on Earth" when he turns around. The result is the same as one of the cars in my analogy above turning back towards the other - the car that was falling behind suddenly jumps ahead.

I strongly recommend looking up Minkowski diagrams. They are far and away the easiest way to understand what's happening in the twin paradox.

10. Mar 3, 2016

### flexible_time

What I understand is that SR is better than classical view in understanding time and space at the fundamental level. I just want to know whether SR is complete and more specifically there is a way to know there a inertial reference frame of single system is standing still or moving.

11. Mar 3, 2016

### Ibix

SR does not cover situations where gravity is important. For that you need General Relativity. Otherwise it is complete, self-consistent and well tested.

There is no answer to the question "is something moving or not" unless it is accelerating. While it is accelerating it is undeniably moving. However there is no detectable difference between unaccelerated motion and no motion, so there you are always free to pick any object not under acceleration and declare it to be at rest.

12. Mar 3, 2016

### PeroK

You seem to think that "object A has a velocity of v" is a law of physics. And, that if another observer concludes that, in his/her reference frame, object A has velocity 0, then a law of physics has been broken.

But, the specific velocity of a specific object is not a law of physics and there is no confict if two observers disagree about that. Although, as an aside, they do not really disagree about anything. Since both observers know the relationship between their reference frames, they would agree on the velocity of object A in both reference frames: it's simply that they choose to use different reference frames to measure things.

One of the reasons you don't understand SR is that you don't understand reference frames - even in the simpler case of classical physics, where time and space are absolute. Although, even in classical physics there is no such thing as absolute motion: every inertial reference frame has equal status and the laws of phyics must hold in them all. Until you grasp that, then understanding SR is going to be problematic for you.

13. Mar 3, 2016

### Staff: Mentor

The way you talk about the paradox you think you see implies you want to know if SR is correct. Yes, it is.
There is not. As said above, just as in Galilean relativity, you can arbitrarily declare one or the other to be "moving" and the other "stationary".

14. Mar 3, 2016

### flexible_time

When I created this thread, I tried to pull the gravity what GR cares about by mentioning that "in empty space or vacuum" to minimize the effect of gravity and my main focus was the relation between the velocity and the time tick rate of a single system.

I think I understand pretty well what you say. My question begins based on your statements. As russ mentioned, I understand that I can arbitrarily declare one or the other be "moving" and the other "stationary" and the law of physics is always same in both reference frame. But what I don't understand in this thought experiment is that what SR can predict about whose time tick rate is slower than the other. Having in mind that the time dilation described within SR is the function of velocity of a system(http://scienceworld.wolfram.com/physics/TimeDilation.html), arbitrarily declaring the velocity of A either $v_a=0$ or $v_a=v$ seems to lead to the different world in future. In A reference view with the declaration $v_a=0$, the time flow of B will flow slower than A and in A reference view with the declaration $v_a=v$, the time flow of B will flow faster than A. It is hard to accept that the arbitrary choice on the declaration of the velocity lead to different future. Is the time dilation a illusion?

Let's make it simple. Let me know what SR can say about whose time tick rate flow slower than the other, A or B.

15. Mar 3, 2016

### Ibix

Whichever one you have declared to be moving ticks slower. Since the two clocks are moving, you cannot unambiguously compare them at two times without accelerating one of them so that they meet again. This means that there are no physical consequences to the arbitrary choice of frame - you just get different descriptions of the same scenario.

I think you are confusing different descriptions of one thing with descriptions of two different things.

16. Mar 3, 2016

### Staff: Mentor

By the way, this apparent paradox is resolved when the two objects are brought together to become stationary together. The simplest case would have one fire a rocket to join up with the other, and you would typically (though you don't have to) declare that one was moving and now it isn't.

17. Mar 3, 2016

### PeroK

The simple answer to that is:

1) Each clock ticks at the same rate in a frame of reference where it is at rest. Compared to a third clock, say.

2) Each clock ticks slower than the third clock if it is moving in a frame of reference at rest with respect to the third clock.

3) Each clock tick slower than the other in the other's frame of reference.

Neither clock has absolute velocity; neither clock has absolute time dilation; neither clock ticks faster or slower absolutely.

Everything is relative to a frame of reference: velocity, momentum, energy (as classical physics), length of an object, tick rate of a clock, rate at which physical processes take place (additionally in SR).

18. Mar 3, 2016

### flexible_time

I hope to find where I confused at.

I think one possible way to determine who is moving or rest in the journey would be storing some same amount of radioactive decaying materials and informing the remaining quantity to each other. If the time rate of a moving object flow 2x slower that the one at rest, radioactive decaying rate of the material in moving box will be halved so whenever they compare the remaining quantity, they will know who is moving unambiguously. It seems to me that the existence of the decaying material does not change the time flow rate of boxes. It is confusing me.

19. Mar 3, 2016

### ZapperZ

Staff Emeritus
This is wrong.

The radioactive decay rate remains THE SAME in its rest frame. If you have Ba137, you'll measure its half life as 2.55 minutes. Another person in another moving frame, having the same identical Ba137 will ALSO measure its half life as 2.55 minutes. So how can you tell that that person is moving and you're not?

It is when you measure the time of decay of THAT person's Ba137 is when you measure something different. But that person also measures the same difference when he/she looks at your Ba137! By simply comparing both of your observations, there is a perfect symmetry. You cannot tell who is actually "moving".

Zz.

20. Mar 3, 2016

### stevendaryl

Staff Emeritus
The problem is that if you have two hunks of uranium, in order to compare them to see which one has decayed more, you have to bring them back together. The details of how you do that determine which one has "aged more".

Here's an analogy: Suppose you have two roads, Highway A and Highway B, that meet at an angle of, say, 30 degrees. On each road, there are distance markers, one every 100 meters. Now suppose that Highway A runs East-West, and Highway B runs Southwest-Northeast. As you move along Highway A, when you pass a distance marker, you can look to your left (straight north) to see the corresponding distance marker on Highway B. What you will find is that the distance along Highway B will show a longer total distance than for Highway A. The ratio will be: $\frac{\delta D'}{\delta D} = \frac{1}{cos(30)} \approx 1.155$ where $\delta D'$ is the change in the distance along Highway B, and $\delta D$ is the change in the distance along Highway A. You can reason as follows: "If this ratio keeps up, then when the two roads get back together, the total distance along Highway B will be longer than the total distance along Highway A." But surely the reasoning should work just as well for someone traveling on Highway B! That seems to be a paradox. But the paradox is resolved by the fact that, in order for the two highways to meet to compare distance markers, either one or the other highway must bend (or both). Which distance is longer when they get back together depends on how each bends.

21. Mar 3, 2016

### Ibix

We don't keep talking about cars on roads just for the fun of it, by the way. Paths through space have a lot (although not everything) in common with paths through spacetime. In particular, bodies in motion in space have their notions of forward in time rotated through a (hyperbolic) angle with respect to each other. That's why the analogy with cars moving along roads at an angle to one another is relevant.

22. Mar 6, 2016

### bahamagreen

Motion can be confusing... in fact I might be confused, myself. :)

Imagine two objects in relative motion.

If you are thinking from the standpoint that there is such a thing as absolute motion (and absolute rest), then you may believe:

1] Perhaps both objects are in absolute motion

2] At least one of the objects must be in absolute motion

3] Both objects cannot be in absolute rest

4] Although you don't know how it is allocated between the two objects, you know for certain that there is some motion.

The tricky thing is that last one, number four. The certainty of motion seems to be the certainty of absolute motion in spite of absolute rest being undetectable... this certain motion when the allocation of it between the objects is unknown comprises relative motion which may be allocated freely and variously between the two objects pending the choice of inertial frame from which to observe and measure.

Ibix wrote in post #5, "There is no answer to the question "is something moving or not" unless it is accelerating."

That may seem to be strictly true when a single object is in question; and still but not quite as strongly true when multiple objects with relative motions are in question... in the sense that the allocation of an absolute motion is not possible for an individual object, but it certainly is possible to say that there is actual true absolute motion without regard to an absolute rest when multiple objects have relative motion.

This does not seem any more peculiar than absolute acceleration without the need for an absolute rest from which to base it.

However, the present standpoint is that there is no detectable or theoretically useful absolute rest. It is from that standpoint that motion must be considered... carefully.

Using accelerations as suggested above can also be a bit confusing because co-moving objects within the universal expansion do not experience accelerations, yet their mutual distance magnitudes accelerate, so now the four ideas listed above are all messed up and not even the "certain" forth one is held to be true.

23. Mar 6, 2016

### Mister T

Each must see the other's clock running at a slower rate. Symmetry requires it because otherwise you'd have a way to distinguish between a state of rest and a state of uniform motion.

There is a way to resolve what is, in your mind, an apparent paradox. That is, it's possible for each to see the other's clock as running slow in a logically consistent way. You first have to open your mind to the possibility. I suggest you look at this Insight article:

24. Mar 7, 2016

### flexible_time

It is the prediction based on SR, but seems to be inconsistent with the result. I can see it as an analogy with the famous so called "Unstoppable Force paradox". Bear with me to explain more for those who are not familiar with it.

"This term originates from a story (see the Kanbun example) in the 3rd century BC philosophical book Han Feizi.[2] In the story, a man was trying to sell a spear and a shield. When asked how good his spear was, he said that his spear could pierce any shield. Then, when asked how good his shield was, he said that it could defend from all spear attacks. Then one person asked him what would happen if he were to take his spear to strike his shield; the seller could not answer. This led to the idiom of "zìxīang máodùn" (自相矛盾), or "self-contradictory". "

SR says, borrowing your view point, that in view of A, A must see B's clock running at a slower rate and in view of B, B must see A's clock running at a slower rate. Here I think what SR says about A and B is similar to what the Chinese sales man who is trying to sell spear and shield. I am really curious about the answer when we ask "what would happen if A meet B?". Will each other see younger than himself/herself if they are twin? Or will see same aged twin? It is our common belief that unstoppable forces and immovable objects cannot both be true at the same time. Similarly, it seems to me that younger than B and younger than A cannot both be true at the same time.

From now, it is just my opinion which may be wrong. Where the paradox comes from? What is common in both paradoxical cases? I think it comes from the fact that there is only relativistic difference. Lets assume that the unstoppable force means a force with infinite amplitude and the immovable object means a mass with infinite mass. Then can we say the infinite force stronger than infinite mass so that unstoppable force win against immovable object or vice versa? Is there any such thing a number bigger than infinity? It is my view point that if we are allowed to use only the relative difference by comparing two with no absolutely measurable/comparable property, then we are not able to escape from seeing a sort of paradox like this case. If we accept it is true that "There is no answer to the question "is something moving or not" unless it is accelerating.", then the paradox is unavoidable. I could not find a way to resolve this paradox yet and am still searching for. Would be appreciable if you correct me.

I just wanted to know my observation on this issue will make sense to others. What I have in mind is just a crazy private idea which is close to science fiction, not matured yet and quit long to write down so hesitant to write such a crazy personal view here. Anyhow I would like to keep learning and sharing more about the most fundamental level of understanding about time, space, mass and the universe.

25. Mar 7, 2016

### stevendaryl

Staff Emeritus
Of course not "at the same time". A and B have different notions of what "at the same time" means.

Let's name some events:
$e_1$: Alice and Bob depart at some relative speed of $v$ (let's pick $v=0.866 c$, which means a time dilation factor of two). Assume that they are both 20 years old.
$e_2$: Alice turns 25.
$e_3$: Bob turns 25.
$e_4$: Alice turns 30.
$e_5$: Bob turns 30.

In Bob's frame, $e_2$ and $e_5$ are simultaneous. So Bob concludes that he is 5 years older than Alice.
In Alice's frame, $e_3$ and $e_4$ are simultaneous. So Alice concludes that she is 5 years older than Bob.

There is no contradiction between these views. The two just have a different notion of which events are simultaneous with which other events.