# Invariance and relativity

Is it a fact of invariance that a person moving in an enclosed object cannot tell if he/she is moving at constant velocity or standing still (for case when he/she is not being accelerated nor in a gravitational field)? If so, would it be possible to perform an experiment within the closed object whereby a person adds a known amount of energy to an object with a known mass (older definition would have called this intrinsic mass) and then measure the acceleration of said object? The idea that an object that is in motion will require more energy to accelerate than an object rest. This would of course negate the idea that a person would not be able to tell if they were at rest or if they were moving at some velocity.

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Orodruin
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No, this is not possible. Energy is not a Lorentz scalar and depending on the frame you will be adding different amounts of energy. Relativity is perfectly self-consistent in this and the usual thing that people forget about is to use the relativistic versions of addition of velocities and acceleration relations.

OK, so energy is also dependant on relative motion? Thus is it expected that the person in the enclosed object would think they are adding x amount of energy when in fact they would be adding x amount of energy plus additional amount of energy?

Orodruin
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You cannot say that a person adds a specific amount of energy without specifying the frame. Therefore, there is no universal answer to "how much energy was added?". It all depends on the reference frame, just as velocity does. There will even be reference frames where energy is removed from the object.

Nugatory
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OK, so energy is also dependant on relative motion?
Yes. This is true even in classical physics. If I'm sitting in a train with a heavy object in my lap, I'll say that the speed and therefore the kinetic energy of the object is zero; someone not at rest relative to the train will say that the speed and therefore the kinetic energy of the object is non-zero.

Would both have to agree on the total energy (kinetic and potential)?

Orodruin
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Would both have to agree on the total energy (kinetic and potential)?
No. This is a common misconception. That energy is conserved (in every frame) does not mean that it is the same in every frame.

That's interesting.I never understood that before.Thanks.
Just to make sure I completely get it, conservation of energy (or mass, momentum, etc..), only occurs within each frame of reference?

DrGreg
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Just to make sure I completely get it, conservation of energy (or mass, momentum, etc..), only occurs within each frame of reference?
Yes.

Awesome I love learning new ideas. One last question about this. What happens when 2 inertial frames coincide (a collision). Would both parties describe the same event with the same amount of energy colliding of would they disagree on the amount of energy in the collision (assuming the collision didn't kill them off course).

No. This is a common misconception. That energy is conserved (in every frame) does not mean that it is the same in every frame.
This is interestingly how einstein proved e=mc^2.

PeterDonis
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This is interestingly how einstein proved e=mc^2
Can you give a reference?

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What happens when 2 inertial frames coincide (a collision). Would both parties describe the same event with the same amount of energy colliding of would they disagree on the amount of energy in the collision (assuming the collision didn't kill them off course).
Frames cannot collide - the idea makes no sense because a frame is just a rule for describing movement and where and when things happen. Suppose that I'm watching two objects, one coming from the left at 10 km/hr and one coming from right at 10 km/hr, and they collide. That's the description using a frame in which I am at rest. If you are moving at a speed of 10 km/hr relative to me, then using a frame in which you are at rest, one of the object is moving at 20 km/hr and the other is at not moving Or we could use some other frame in which one of the objects is moving at 50 km/hr and other one is chasing it from behind at 70 km/hr - an observer at rest in that frame would be moving at 60 km/hr relative to you.

Each of these three observers calculates a different amount of kinetic energy, both before and after the collision. However, all three will agree about the energy released by the collision (and presumably spent crushing and crumpling the colliding objects); and all three will agree that energy is conserved: the kinetic energy before the collision is equal to the sum of the kinetic energy after the collision and the energy released by the collision.

I assume that after the collision both objects are at rest with respect to a stationary observer (and buildings, trees, etc). If after the collision they have the same frame of reference, how can you say that frames cannot collide and that it makes no sense to claim that? If frames colliding makes no sense, maybe it is just a semantic issue. What about the frames collapse to become the same frame off reference? The idea still holds, if both objects can have a different evaluation of the total energy (in order to keep conservation of energy, momentum, mass) within their local frame, and then the end up at the same frame off reference, then something has to allow their new frame to agree with the total energy in their new frame that they share.

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I assume that after the collision both objects are at rest with respect to a stationary observer (and buildings, trees, etc).
We can set things up so that after the collision the two objects are at rest with respect to the buildings and trees and other nearby stuff. This will happen if the objects have equal masses and approach each other from opposite directions with the same speed as measured in a frame in which the buildings and trees are at rest, and if the two objects stick together (or are crushed into one lump of twisted metal) in the collision.

However, that does not mean that after the collision they're at rest relative to a stationary observer. They aren't.

They're at rest relative to the buildings and trees - but those buildings and trees are attached to the earth, the earth is going around the sun, the sun is moving through interstellar space. An observer sitting leisurely at rest in his astronomical observatory on Mars, feet comfortably propped up on a table as he watches the collision on earth through his telescope, would consider the proposition that he's somehow less "stationary" than the buildings and trees on earth to be utterly absurd. Nonetheless, he can analyze the collision using the frame in which he is at rest (which of course is completely unaffected by the collision) and he will find that both energy and momentum are conserved. He will also agree with the all other observers anywhere in the universe and moving with any speed relative to him (including the very special case of an observer who happens to be at rest relative to buildings and trees on the surface of the earth near the collision site) about how much energy is released by the collision.

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If frames colliding makes no sense, maybe it is just a semantic issue. What about the frames collapse to become the same frame off reference? The
It's not a semantic issue, it goes to the heart of the definition of what a frame is.

You may be being misled by the very common but sloppy English language idiom in which we say that something is "in a frame". When someone says that something is "in a frame" or talks about "the frame of something", that's a convenient verbal shortcut for the more precise "Until I say otherwise, I will be doing all my calculations of speeds and positions and energies and momenta using a frame in which that something is at rest right now, no matter what it does later".

I guess my thought this is that once 2 objects are at rest with redirect to reach other they would be considered at the same frame of reference. And once they are at same reference they should be able to agree on the amount of energy of said collision. That seems like a paradox if they can have a different idea as to how much energy was involved in the collision.

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I guess my thought this is that once 2 objects are at rest with redirect to reach other they would be considered at the same frame of reference.
That's just not correct. Everything is always in all reference frames all the time - there's no such thing as being in one frame but not another.

The two objects are in the reference frame in which the Martian astronomer is at rest, and using that reference frame their speed after the collision is the same as the earth's speed relative to Mars. The two objects are also in the reference frame in which the buildings and trees near the site of the collision are at rest, and using that frame their speed after the collision is zero. In both frames the speed changes in the collision, but this speed change doesn't mean that either object is changing reference frames, or that before the collision when their speeds were different they were somehow in different frames.

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The way I envision it is that 2 object each have their own reference frame that is unique to their circumstance.
Thus 2 objects that are in motion relative to each other would each have their perspective on energy conservation.
While there can be an infinite amount of frames of reference (your Martian example being one), only one frame of reference would apply to a person at any given time (as measured by them). Thus, I expect that 2 people/objects in motion relative to each other would each have a unique frame of reference that the other does not share. Further, I expect that 2 objects that are not in relative motion with each other, should be able to agree on and share the same frame of reference (again, only looking at the frame of reference as measured by either of the 2 objects and not the potentially infinite other frames of reference). If either one of these 2 ideas is inaccurate, please help me to understand. If both of those 2 ideas are accurate, then there can be a case when 2 objects that started off with motion relative to each other and then came to rest with respect each other (after a collision), would have started off with unique frames of reference (as measured by each object), and then ended with a shared / agreed upon frame of reference after the collision. Thus I see a case where they wouldn't see the same conservation of energy prior to collision but then after the collision, they would have the same views of conservation of energy. How can they start of not agreeing on their perspective of conservation of energy but finally ending up agreeing on it.

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The way I envision it is that 2 object each have their own reference frame that is unique to their circumstance.
Thus 2 objects that are in motion relative to each other would each have their perspective on energy conservation.
While there can be an infinite amount of frames of reference (your Martian example being one), only one frame of reference would apply to a person at any given time (as measured by them). Thus, I expect that 2 people/objects in motion relative to each other would each have a unique frame of reference that the other does not share. Further, I expect that 2 objects that are not in relative motion with each other, should be able to agree on and share the same frame of reference (again, only looking at the frame of reference as measured by either of the 2 objects and not the potentially infinite other frames of reference).
Everything that I have bolded above is wrong and makes me wonder if you're even bothering to read the earlier posts in this thread.

The objects do not have a perspective on energy conservation, although observers watching them collide might. The objects do not have reference frames and they do not share reference frames. Observers do not have reference frames or share reference frames.

Instead, observers use reference frames (not necessarily the one in which the observer might be at rest) to assign values at a particular moment to the velocities of the objects they are observing. They use these values to make calculations about energy and momentum conservation.

Now, go back and try writing your description of the collision and energy and momentum conservation, as seen by two different observers who are moving relative to one another, without saying things like "in a reference frame" or "having a reference frame" or "sharing a reference frame" or "the reference frame of..." or "this object's reference frame" or "this observer's reference frame". Instead, allow the words "reference frame" to appear only in the phrase "calculated using a reference frame in which...."

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I envision an example of enclosed object (with observer and another object) traveling at 99% speed of light (with respect to anything you want to imagine). I then think the observer could add a fixed amount of energy to the object that he/she possess and measuring the increase in speed of the object (with respect to observer). I expect this would be vastly different than a situation where the enclosed object was at rest (again with respect to anything that can wish to imagine). I say this because reaching the speed of light becomes harder and harder the closer get to traveling at the speed of light.
OK, that's a more reasonable question. The bolded statement seems to suggest that you can detect how close to the speed of light you are by measuring how difficult it is to further increase the speed of an object by adding energy to it. So why doesn't that work?

The answer starts with rule number one of relativity problems: Whenever you talk about something travelling at some speed, you have to say what that speed is relative to, which is another way of saying that you have to specify which frame you're using to define speeds. You can use any frame you want, you don't have to use a frame in which you are at rest. When an astronomer on earth says that the earth is moving at 100,000 km/hr, chances are he's using a frame in which the sun is at rest and both Jupiter and the Earth are moving in circles around it. When he says an airplane overhead is moving at 500 km/hr, chances are he's using a frame in which the surface of the earth at his feet is at rest - if he used the frame in which the sun is at rest the speed of the airplane would have to include the rotational and the orbital velocity of the earth.

The bolded statement violates this rule when it says "the closer we get to travelling at the speed of light" without saying who that speed is relative to. So let's put that part back in - now we have "The closer we get to the speed of light relative to some observer, the harder it becomes to further increase our speed relative to that observer". (Note that our speed relative to ourself is always zero).

The experiment we're going to perform is to take some massive object that is at rest relative to us, add some energy to it; see how its speed changes as a result; compare the results using a frame in which we are at rest and a frame in which we are moving at close the speed of light; and see if we can use these results to determine whether we're really at rest or close to the speed of light. To be definite, we'll start with a four kilogram object that is at rest relative to us. We will add ##10^{17}## Joules of energy to it (that's a lot of energy - several hundred very large nuclear weapons going off together); this will increase its kinetic energy by ##10^{17}## Joules and that's enough to increase its speed relative to us from zero to .6c. (I get this result from the relativistic formula for the relationship between velocity and kinetic energy).

But suppose we consider this same experiment using a frame in which we're already moving at .9c when we start the experiment? There's probably someone somewhere in the universe who is moving at .9c relative to us, and he'll be at rest in this frame, but we don't need him to use this frame - we can always calculate using whatever frame we want. If we use this frame to describe the speeds, we and the object are both moving at .9c before the experiment. We add ##10^{17}## Joules to the object, its kinetic energy increase by ##10^{17}## Joules, and its speed increases from .9c to .974c (I got this from the same kinetic energy formula as well as the formula for relativistic addition of velocities - google for that if you're not already familiar with it).

That's what we mean when we say that it gets harder to increase your speed as you get closer to c. But you can see that this is completely unhelpful for deciding whether we're at rest or moving at .9c. If we do the experiment, we'll see the object accelerate from zero to .6c; the fact that someone else in some far distant galaxy who might not even exist would be just as happy saying that it accelerated from .9c to to .974c tells us nothing.

[..] If an observer does not have a reference frame that could limit their ability to measure accurately cause and affect from adding energy to an object in their possession then I envision an example of enclosed object (with observer and another object) traveling at 99% speed of light (with respect to anything you want to imagine). I then think the observer could add a fixed amount of energy to the object that he/she possess and measuring the increase in speed of the object (with respect to observer). I expect this would be vastly different than a situation where the enclosed object was at rest (again with respect to anything that can wish to imagine). I say this because reaching the speed of light becomes harder and harder the closer get to traveling at the speed of light.
I'm not totally sure what you have in mind, but perhaps it's similar to what was demonstrated by Bertozzi, as discussed here: https://en.wikipedia.org/wiki/Tests_of_relativistic_energy_and_momentum#Bertozzi_experiment

Of course, the lab itself can also be regarded as being in motion as it's on the surface of the Earth. Is that what you mean?

OK, that's a more reasonable question. The bolded statement seems to suggest that you can detect how close to the speed of light you are by measuring how difficult it is to further increase the speed of an object by adding energy to it. So why doesn't that work?

The answer starts with rule number one of relativity problems: Whenever you talk about something travelling at some speed, you have to say what that speed is relative to, which is another way of saying that you have to specify which frame you're using to define speeds. You can use any frame you want, you don't have to use a frame in which you are at rest. When an astronomer on earth says that the earth is moving at 100,000 km/hr, chances are he's using a frame in which the sun is at rest and both Jupiter and the Earth are moving in circles around it. When he says an airplane overhead is moving at 500 km/hr, chances are he's using a frame in which the surface of the earth at his feet is at rest - if he used the frame in which the sun is at rest the speed of the airplane would have to include the rotational and the orbital velocity of the earth.

The bolded statement violates this rule when it says "the closer we get to travelling at the speed of light" without saying who that speed is relative to. So let's put that part back in - now we have "The closer we get to the speed of light relative to some observer, the harder it becomes to further increase our speed relative to that observer". (Note that our speed relative to ourself is always zero).

The experiment we're going to perform is to take some massive object that is at rest relative to us, add some energy to it; see how its speed changes as a result; compare the results using a frame in which we are at rest and a frame in which we are moving at close the speed of light; and see if we can use these results to determine whether we're really at rest or close to the speed of light. To be definite, we'll start with a four kilogram object that is at rest relative to us. We will add ##10^{17}## Joules of energy to it (that's a lot of energy - several hundred very large nuclear weapons going off together); this will increase its kinetic energy by ##10^{17}## Joules and that's enough to increase its speed relative to us from zero to .6c. (I get this result from the relativistic formula for the relationship between velocity and kinetic energy).

But suppose we consider this same experiment using a frame in which we're already moving at .9c when we start the experiment? There's probably someone somewhere in the universe who is moving at .9c relative to us, and he'll be at rest in this frame, but we don't need him to use this frame - we can always calculate using whatever frame we want. If we use this frame to describe the speeds, we and the object are both moving at .9c before the experiment. We add ##10^{17}## Joules to the object, its kinetic energy increase by ##10^{17}## Joules, and its speed increases from .9c to .974c (I got this from the same kinetic energy formula as well as the formula for relativistic addition of velocities - google for that if you're not already familiar with it).

That's what we mean when we say that it gets harder to increase your speed as you get closer to c. But you can see that this is completely unhelpful for deciding whether we're at rest or moving at .9c. If we do the experiment, we'll see the object accelerate from zero to .6c; the fact that someone else in some far distant galaxy who might not even exist would be just as happy saying that it accelerated from .9c to to .974c tells us nothing.
Well that's even more interesting to me now. Thanks for your patience with me. If I am seeing this accurately, then two things standout. First, the fact that you can use any frame of reference you want to seems a little flawed. This is because if I take measurements (specifically the measurement of the massive object that I add energy to), this will then force me to evaluate the response of the added energy within my frame. This is exactly what I was inferring when I mentioned that every one (object) has a reference frame unique to them. While I am free to use any frame (per your point), there would only be one frame that actually matched my results that I would be able to witness. The second thing, even more interesting (at least to me), is that while I already was able to grasp that relativity necessarily meant that there could be multiple frames of reference that would not agree on the velocity of an object (very easy to visualize and understand), there would be multiple frames of references that would not agree on simultaneity (again fairly easy to grasp), and lastly that there would be multiple frames of reference that would not agree on the time of events (or time in general). All three of these are somewhat fairly obvious phenomenon (although relativity of time takes some effort and level of getting used to). What is interesting to me now is that multiple reference frames would not even agree if events happened (or not). Here is a thought experiment that brings this to life for me. Assume that a person has ability to bounce an object off of a forward facing wall by adding energy an object to accelerate it. Assume further that this object, once it bounces off of said wall and returns back to where it originated, has the ability to kill the person that sent it hurling. Thus, the person that was on the aforementioned suicide mission would (I assume), be successful within his/her frame of reference (again bringing to light that every one has their own frame of reference that affects their world). Also, to other observers that saw the enclosed spacecraft travelling at 99% speed of light (or some high value of travel), I expect there could be a case where the object never was able to reach the wall and hence not able to bounce back. Of course, without bouncing back, the object would not kill said person. Thus now relativity seems to bring us to the Schrodinger's cat concept of a life form being both dead and alive at the same time (depending on frame of reference). Is any of this an accurate depiction of relativity? If it is, are there any test cases that prove the idea of multiple frames of reference having different states simply due to relative motion?

Janus
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What is interesting to me now is that multiple reference frames would not even agree if events happened (or not). Here is a thought experiment that brings this to life for me. Assume that a person has ability to bounce an object off of a forward facing wall by adding energy an object to accelerate it. Assume further that this object, once it bounces off of said wall and returns back to where it originated, has the ability to kill the person that sent it hurling. Thus, the person that was on the aforementioned suicide mission would (I assume), be successful within his/her frame of reference (again bringing to light that every one has their own frame of reference that affects their world). Also, to other observers that saw the enclosed spacecraft travelling at 99% speed of light (or some high value of travel), I expect there could be a case where the object never was able to reach the wall and hence not able to bounce back. Of course, without bouncing back, the object would not kill said person. Thus now relativity seems to bring us to the Schrodinger's cat concept of a life form being both dead and alive at the same time (depending on frame of reference). Is any of this an accurate depiction of relativity? If it is, are there any test cases that prove the idea of multiple frames of reference having different states simply due to relative motion?
This is incorrect. Any event that occurs according to one frame occurs in all frames.

Let's say our spacecraft observer propels the object forward at 1% of c, as measured relative to him by him. Thus in his frame the object travels at 1% of c away from him, hits the wall and returns at 1% of c, hitting and killing him.

The frame in which the ship is traveling at 99% of c sees this: The object travels forward at 99.0197049% of c or 0.0197049% of c relative to to the ship. It hits the wall and rebounds, so that after hitting the wall it is now moving at 98.8979901% of c or .02009898% of c relative to the ship in the opposite direction, hitting and killing the ship observer.

There is no frame where the object does not return to and strike the ship observer.