Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Dimensional on 24/06/2022 23:28:58
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of space and time of a moving observer and a observer at rest? So if object A observes object B coming towards it very fast, A is at rest and should only have the time component and no spacelike component. But B can say the same thing. How does SR explain the componentry of this kind of scenario?
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How does SR explain the componentry of this kind of scenario?
Not sure what you mean by componentry. Observer A would say B time is dilated and it's length is contracted. Observer B would say A is time dilated and length contracted. Is that what you are asking about?
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How does SR explain the componentry of this kind of scenario?
Not sure what you mean by componentry. Observer A would say B time is dilated and it's length is contracted. Observer B would say A is time dilated and length contracted. Is that what you are asking about?
Sort of.
In the light cone, do the timelike trajectories of objects have a time component and a space component?
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Hi.
I'm still not certain what your question was about.
How does SR explain the componentry of this kind of scenario?
An objects motion is described by a 4-velocity. That is frame dependant. To determine the 4-velocity in one frame from the 4-velocity in another frame, you apply a Transformation (e.g. a Lorentz transformation).
Best Wishes.
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Hi.
I'm still not certain what your question was about.
How does SR explain the componentry of this kind of scenario?
An objects motion is described by a 4-velocity. That is frame dependant. To determine the 4-velocity in one frame from the 4-velocity in another frame, you apply a Transformation (e.g. a Lorentz transformation).
Best Wishes.
So just like we would break down a vector in a "normal" 2d space. For example, an object moves in a certain direction at 4 units in the x direction and 3 units in the y direction.
Does time and space have separate components like that?
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Hi.
Does time and space have separate components like that?
Yes and No.
The yes bit:
4-vectors are what are important in spacetime. These have 4 components, 3 of them are called spatial components and the other component is called the time component. You can write the spatial components first and the time component last but it's more common to write the time component first. It's also fairly common to start numbering the components from 0 and not from 1. The final slightly confusing thing you might see is that if you had a 4-vector X then you may see the components written as X0, X1, X2 and X3. Superscripts instead of subscripts like X0, X1 can be used.
For example r = ( ct, x, y, z) is the usual way of writing the position 4-vector of an object. It has a time component ct = c (the speed of light) multiplied by the position of the object on the time axis, t. It has spatial components x, y, z which are the position of the object along the x, y and z axis respectively. Now you could use t as the time component instead of ct but the algebra turns out to be much easier if you use c (the speed of light) multiplied by t as the time component.
The "no" bit
1. There's an unusual way of determining the magnitude of a 4-vector. You might see it called the "norm" or "Minkowski norm" of a 4-vector. For simple vectors used in Euclidean space or Newtonian mechanics, whenever you increase the size of one component the overall magnitude of the vector would increase. For 4-vectors that's not always the situation, you can increase the size of one component and end up reducing the overall magnitude of the 4-vector. The Minkowski metric is described in various places [For example, https://phys.libretexts.org/Bookshelves/Modern_Physics/Book%3A_Spiral_Modern_Physics_(D%27Alessandris)/3%3A_Spacetime_and_General_Relativity/3.1%3A_Minkowski_Metric ].
2. You are mainly discussing velocities and motion in your posts, rather than just positions. In ordinary Newtonian mechanics, velocities are just a rate of change of position with respect to the time co-ordinate. For 4-velocities we can't determine rates of change with respect to a fixed time co-ordinate, instead we must determine rates of change with respect to what is called the proper time for that object undergoing the motion.
What this boils down to is that spatial components of the 4-velocity are NOT exactly the spatial components of the ordinary Newtonian or 3-velocity that the object might have. Instead the spatial components are a multiple of the spatial velocity you would have assigned the object in Newtonian mechanics. Also it's not a fixed multiple, the multiple changes according to the Newtonian 3-velocity of the object. Specifically, the spatial components of the 4-velocity are given by γ (the gamma factor) multiplied by the spatial components of the 3-velocity.
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That might be more detail than you were after. Overall there is a lot of similarity between 4-velocities used in Special relativity and more conventional velocity vectors you might have seen in Newtonian mechanics. I've mentioned the differences because, in my limited experience, if we don't then it's human nature to run away with the idea that it's all exactly like Newtonian mechanics and ordinary 3-velocity vectors. You'll soon hit problems if you do that.
For example, it can be useful to consider the magnitude of a 4-velocity vector. An ordinary object with some positive rest mass always has a 4-velocity vector of magnitude c (the speed of light). That magnitude can be shared out between the time component and the spatial component of the objects 4-velocity. An object at rest (in a given frame which we will use to assign the velocity vector) has all of its velocity in the time component while the spatial components would have the value 0. Meanwhile, an object in motion (in the given frame) has a non-zero value in the spatial components of the 4-velocity and a correspondingly lower value* in the time component.
Best Wishes.
* LATE EDITING: I don't like this on a second reading. It's precisely one of those examples where you could have a larger numerical value for the time component but that is actually reducing the overall magnitude of the 4-velocity and not increasing it (because the Minkowski metric subtracts the time component instead of adding it). It's fair to say the object has less velocity through time and many Pop Sci articles will do this - but it's not correct to imply that the numerical value you find written in the time component of the 4-velocity has to be smaller.
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Hi.
Does time and space have separate components like that?
Yes and No.
The yes bit:
4-vectors are what are important in spacetime. These have 4 components, 3 of them are called spatial components and the other component is called the time component. You can write the spatial components first and the time component last but it's more common to write the time component first. It's also fairly common to start numbering the components from 0 and not from 1. The final slightly confusing thing you might see is that if you had a 4-vector X then you may see the components written as X0, X1, X2 and X3. Superscripts instead of subscripts like X0, X1 can be used.
For example r = ( ct, x, y, z) is the usual way of writing the position 4-vector of an object. It has a time component ct = c (the speed of light) multiplied by the position of the object on the time axis, t. It has spatial components x, y, z which are the position of the object along the x, y and z axis respectively. Now you could use t as the time component instead of ct but the algebra turns out to be much easier if you use c (the speed of light) multiplied by t as the time component.
The "no" bit
1. There's an unusual way of determining the magnitude of a 4-vector. You might see it called the "norm" or "Minkowski norm" of a 4-vector. For simple vectors used in Euclidean space or Newtonian mechanics, whenever you increase the size of one component the overall magnitude of the vector would increase. For 4-vectors that's not always the situation, you can increase the size of one component and end up reducing the overall magnitude of the 4-vector. The Minkowski metric is described in various places [For example, https://phys.libretexts.org/Bookshelves/Modern_Physics/Book%3A_Spiral_Modern_Physics_(D%27Alessandris)/3%3A_Spacetime_and_General_Relativity/3.1%3A_Minkowski_Metric ].
2. You are mainly discussing velocities and motion in your posts, rather than just positions. In ordinary Newtonian mechanics, velocities are just a rate of change of position with respect to the time co-ordinate. For 4-velocities we can't determine rates of change with respect to a fixed time co-ordinate, instead we must determine rates of change with respect to what is called the proper time for that object undergoing the motion.
What this boils down to is that spatial components of the 4-velocity are NOT exactly the spatial components of the ordinary Newtonian or 3-velocity that the object might have. Instead the spatial components are a multiple of the spatial velocity you would have assigned the object in Newtonian mechanics. Also it's not a fixed multiple, the multiple changes according to the Newtonian 3-velocity of the object. Specifically, the spatial components of the 4-velocity are given by γ (the gamma factor) multiplied by the spatial components of the 3-velocity.
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That might be more detail than you were after. Overall there is a lot of similarity between 4-velocities used in Special relativity and more conventional velocity vectors you might have seen in Newtonian mechanics. I've mentioned the differences because, in my limited experience, if we don't then it's human nature to run away with the idea that it's all exactly like Newtonian mechanics and ordinary 3-velocity vectors. You'll soon hit problems if you do that.
For example, it can be useful to consider the magnitude of a 4-velocity vector. An ordinary object with some positive rest mass always has a 4-velocity vector of magnitude c (the speed of light). That magnitude can be shared out between the time component and the spatial component of the objects 4-velocity. An object at rest (in a given frame which we will use to assign the velocity vector) has all of its velocity in the time component while the spatial components would have the value 0. Meanwhile, an object in motion (in the given frame) has a non-zero value in the spatial components of the 4-velocity and a correspondingly lower value in the time component.
Best Wishes.
Thanks, this is very helpful. But I was afraid of that answer because it leads to my issue in the OP.
For example, imagine just 2 dimensions of spacetime for simplicity sake. There is an x axis and a time axis. Object A thinks it is at rest on the x axis, and object B observes itself as being at rest on the x axis too. However, they are on a collision course.
I understand that relativity says that both A and B are correct in thinking that they are at rest. But in reality, because they are on a collision course, only one of them can actually be at rest where r = ( ct, 0, n/a, n/a), right? Or am I missing something here?
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I understand that relativity says that both A and B are correct in thinking that they are at rest. But in reality, because they are on a collision course, only one of them can actually be at rest where r = ( ct, 0, 0, 0), right? Or am I missing something here?
When you say only one of them is actually at rest, that sets off alarm bells. I don't see the difference if A thinks they are at rest or if B thinks they are at rest, even though they collide. From A's point of view he is stationary on the X axis and moving vertically parallel to the Y (time axis). A sees B moving at an angle to the X and y axis until he intersects A at some point on the Y axis. Replace the B with A in the above scenario and that is B's viewpoint as stationary on the X axis.
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I understand that relativity says that both A and B are correct in thinking that they are at rest. But in reality, because they are on a collision course, only one of them can actually be at rest where r = ( ct, 0, 0, 0), right? Or am I missing something here?
When you say only one of them is actually at rest, that sets off alarm bells. I don't see the difference if A thinks they are at rest or if B thinks they are at rest, even though they collide. From A's point of view he is stationary on the X axis and moving vertically parallel to the Y (time axis). A sees B moving at an angle to the X and y axis until he intersects A at some point on the Y axis. Replace the B with A in the above scenario and that is B's viewpoint as stationary on the X axis.
So then which one is the vector r = ( ct, 0, n/a, n/a)? Is it A, B, neither?
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Hi.
You're suggesting that A and B can't both be stationary - but they can. The only restriction is that they can't both be stationary in the same frame of reference.
Without worrying too much about special relativity, just in ordinary Newtonian mechanics, you can see that if A is stationary but B is moving towards it then there will be a collision. Also if B was stationary but A was moving toward it then there will be a collision. Either one can be declared to be stationary, you just can't declare both of them to be stationary.
If you examine that restriction carefully, it is just saying that there isn't a frame of reference (a simple co-ordinate system) where the velocity of A would be 0 AND ALSO the velocity of B would be 0 at the same time.
Exactly the same can happen in special relativity - A or B can be stationary - it's completely your choice. However, having made that choice you've effectively decided what frame of reference you will be using. If the two objects were on a collision course then the other object won't be stationary in that frame.
I don't know if it will help but I'll try and phrase this another way: The object A does not have a velocity that is absolute and everyone agrees on. The moment you decide or declare that it is stationary you have made a choice. You have picked out a frame of reference that you will use from among many that could have been used. That assigns a velocity of 0 to the object A. However, that velocity does not become permanently imprinted on the object like some mark that everyone can see. It is NOT an intrinsic property of that object, it is a frame-dependant property. If you now declare that object B was actually stationary then you have (unavoidably) abandoned the old reference frame and decided to use a different one. The velocity of object A in the old frame was 0 but that is not important, it wasn't an absolute or intrinsic property that object A had - and it does not remain as the velocity of object A now you're using a different frame of reference.
Best Wishes.
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Hi.
You're suggesting that A and B can't both be stationary - but they can. The only restriction is that they can't both be stationary in the same frame of reference.
Without worrying too much about special relativity, just in ordinary Newtonian mechanics, you can see that if A is stationary but B is moving towards it then there will be a collision. Also if B was stationary but A was moving toward it then there will be a collision. Either one can be declared to be stationary, you just can't declare both of them to be stationary.
If you examine that restriction carefully, it is just saying that there isn't a frame of reference (a simple co-ordinate system) where the velocity of A would be 0 AND ALSO the velocity of B would be 0 at the same time.
Exactly the same can happen in special relativity - A or B can be stationary - it's completely your choice. However, having made that choice you've effectively decided what frame of reference you will be using. If the two objects were on a collision course then the other object won't be stationary in that frame.
I don't know if it will help but I'll try and phrase this another way: The object A does not have a velocity that is absolute and everyone agrees on. The moment you decide or declare that it is stationary you have made a choice. You have picked out a frame of reference that you will use from among many that could have been used. That assigns a velocity of 0 to the object A. However, that velocity does not become permanently imprinted on the object like some mark that everyone can see. It is NOT an intrinsic property of that object, it is a frame-dependant property. If you now declare that object B was actually stationary then you have (unavoidably) abandoned the old reference frame and decided to use a different one. The velocity of object A in the old frame was 0 but that is not important, it wasn't an absolute or intrinsic property that object A had - and it does not remain as the velocity of object A now you're using a different frame of reference.
Best Wishes.
I understand what you are saying. However, there does seem to be an absolute difference between *only* the ct vector (the direction of time) and having a component of ct *with* a component in the x direction. From an objective point of view, it should be noticeable which object has more of which component.
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From an objective point of view, it should be noticeable which object has more of which component.
That is implying a preferred frame. In other words it seems you are saying 'objectively' one of them is 'really' moving in the x direction. The fact of the matter is the movement can only be relative to another object so there can be no absolute velocity.
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From an objective point of view, it should be noticeable which object has more of which component.
That is implying a preferred frame. In other words it seems you are saying 'objectively' one of them is 'really' moving in the x direction. The fact of the matter is the movement can only be relative to another object so there can be no absolute velocity.
But since they are moving towards each other, (keeping this in special relativity) doesn't that mean that at least one of them must be moving in the x direction?
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But since they are moving towards each other, (keeping this in special relativity) doesn't that mean that at least one of them must be moving in the x direction?
Yes, there's clearly movement on the x-axis. A could say only B is moving and B could say that only A is moving and a 3rd observer may say both A and B are moving and they would all be correct. No one however can say which is moving in an absolute way.
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But since they are moving towards each other, (keeping this in special relativity) doesn't that mean that at least one of them must be moving in the x direction?
Yes, there's clearly movement on the x-axis. A could say only B is moving and B could say that only A is moving and a 3rd observer may say both A and B are moving and they would all be correct. No one however can say which is moving in an absolute way.
Since we know for certain that at least one of A or B is moving (or both), then how can either claim to not be moving?
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Since we know for certain that at least one of A or B is moving (or both), then how can either claim to not be moving?
Because velocity is relative. Let me say it again, velocity is relative. There is no way to tell If A is moving towards B or B is moving towards A. I can say A is moving and B is stationary relative to some arbitrary reference point or I could say the opposite based on difference arbitrary reference point. So either can claim to be stationary because it is all relative.
How can either claim to be not moving?
I can give a sleeping pill and after you are asleep, I could load you on a spaceship with no windows and send you into space at 1,000,000 kph. When you awake traveling at 1,000,000 kph it would not feel like you were moving. As a matter of fact there is no test that you can perform that would tell you if you were traveling at 1,000,000 kph or 0 kph.
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Since we know for certain that at least one of A or B is moving (or both), then how can either claim to not be moving?
Because velocity is relative. Let me say it again, velocity is relative. There is no way to tell If A is moving towards B or B is moving towards A. I can say A is moving and B is stationary relative to some arbitrary reference point or I could say the opposite based on difference arbitrary reference point. So either can claim to be stationary because it is all relative.
How can either claim to be not moving?
I can give a sleeping pill and after you are asleep, I could load you on a spaceship with no windows and send you into space at 1,000,000 kph. When you awake traveling at 1,000,000 kph it would not feel like you were moving. As a matter of fact there is no test that you can perform that would tell you if you were traveling at 1,000,000 kph or 0 kph.
I don't think my point has come across properly.
Imagine the spatial (x), temporal (y) plane. Only one of A and B can have 0 velocity in the x direction, and this is true before you choose the reference point.
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Hi.
I don't think my point has come across properly.
I think your point has been understood. It's just not agreed and the difficulty now is only trying to explain why.
Imagine the spatial (x), temporal (y) plane. Only one of A and B can have 0 velocity in the x direction, and this is true before you choose the reference point.
Let's just start by saying no: It's not so much that only one of them can 0 velocity which is important, instead it's that either one of them could have 0 velocity. Before you choose a reference frame there's nothing at all that restricts or informs you about the velocity of A or B. You have completely free choice to assign any velocity you want to A or B, restrictions for the velocity of the other object don't appear until after you have decided what the velocity of the first object will be.
Can someone explain me why we talk about "light cone" ?
The original Poster (OP) has requested that you put this question in a new thread. That may help to avoid confusing the OP.
Mod edit: New topic here https://www.thenakedscientists.com/forum/index.php?topic=85049.0
Best Wishes.
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Let's just start by saying no: It's not so much that only one of them can 0 velocity which is important, instead it's that either one of them could have 0 velocity. Before you choose a reference frame there's nothing at all that restricts or informs you about the velocity of A or B. You have completely free choice to assign any velocity you want to A or B, restrictions for the velocity of the other object don't appear until after you have decided what the velocity of the first object will be.
I definitely think that we both understand each other's argument.
Here may be a clearer way to see my issue. Imagine a very simple universe where there only exists object A and an object B. They are on a collision course. Scientist A, (from another dimension) uses object A as a point of reference. But scientist B (from yet a different dimension than scientist A) uses object B as a reference. Each scientist is going to end up with a different description of this universe from using special relativity.
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Here may be a clearer way to see my issue. Imagine a very simple universe where there only exists object A and an object B. They are on a collision course. Scientist A, (from another dimension) uses object A as a point of reference. But scientist B (from yet a different dimension than scientist A) uses object B as a reference. Each scientist is going to end up with a different description of this universe from using special relativity.
So what's your issue?
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Here may be a clearer way to see my issue. Imagine a very simple universe where there only exists object A and an object B. They are on a collision course. Scientist A, (from another dimension) uses object A as a point of reference. But scientist B (from yet a different dimension than scientist A) uses object B as a reference. Each scientist is going to end up with a different description of this universe from using special relativity.
So what's your issue?
That each scientist is going to end up with a different description of this universe from using special relativity.
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Hi.
That each scientist is going to end up with a different description of this universe from using special relativity.
Yes, exactly this sort of thing does happen.
There are some questions you can ask which are going to be frame dependant - they have answers but the answers will depend on the frame of reference you have chosen.
For example, the question "is object A moving?" is something that the two scientists will not agree on. Hopefully they will know the answer is frame dependant so they will answer more cautiously: "Well, no, not in this frame of reference anyway".
Fortunately, there are some questions that can be asked and answered more objectively: "Will the two objects collide" is something that both scientists will agree on.
Best Wishes.
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Hi.
That each scientist is going to end up with a different description of this universe from using special relativity.
Yes, exactly this sort of thing does happen.
There are some questions you can ask which are going to be frame dependant - they have answers but the answers will depend on the frame of reference you have chosen.
For example, the question "is object A moving?" is something that the two scientists will not agree on. Hopefully they will know the answer is frame dependant so they will answer more cautiously: "Well, no, not in this frame of reference anyway".
Fortunately, there are some questions that can be asked and answered more objectively: "Will the two objects collide" is something that both scientists will agree on.
Best Wishes.
But when looking at my scenario, SR seems to give two different answers. Since either object can be considered the object at rest, then each scientist is going to get a different answer.
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But when looking at my scenario, SR seems to give two different answers. Since either object can be considered the object at rest, then each scientist is going to get a different answer.
I don't really know how many different ways it can be explained to you that there ARE 2 different answers and both of the answers are correct for the frames they are measured in. I understand that this goes against our intuition, but sometimes our intuition is not correct. Our intuition tells us that if we are moving towards a light then the speed of that light should be c + our speed, but that is wrong. We can measure the speed and it is a fact that our intuition is wrong.
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Here may be a clearer way to see my issue. Imagine a very simple universe where there only exists object A and an object B. They are on a collision course. Scientist A, (from another dimension) uses object A as a point of reference. But scientist B (from yet a different dimension than scientist A) uses object B as a reference. Each scientist is going to end up with a different description of this universe from using special relativity.
So what's your issue?
That each scientist is going to end up with a different description of this universe from using special relativity.
This really doesn’t need scientists from a different universe and it isn’t down to special relativity.
It was Galileo who first pointed out that if you were in a cabin on a ship you would not be able to tell if the ship was moving, or in which direction unless you had information from outside the room. He concluded that it was reasonable to consider two moving ships as one stationary and the other moving or vise versa and the laws of physics remain the same. For example, if a ship is moving and firing a cannon at a stationary ship, the trajectory of the cannon ball relative to the first ship is exactly the same if the first ship is stationary and the second moving. When we consider this scenario in space where there are no fixed references, it becomes more obvious. It is called Galilean Relativity. Einstein added the effects of the constancy of the speed of light and extended Galileo’s principle to Special Relativity.
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But when looking at my scenario, SR seems to give two different answers. Since either object can be considered the object at rest, then each scientist is going to get a different answer.
I don't really know how many different ways it can be explained to you that there ARE 2 different answers and both of the answers are correct for the frames they are measured in. I understand that this goes against our intuition, but sometimes our intuition is not correct. Our intuition tells us that if we are moving towards a light then the speed of that light should be c + our speed, but that is wrong. We can measure the speed and it is a fact that our intuition is wrong.
If both answers are correct, then doesn't that mean that 2 different universes can exist depending on which object you choose to be at rest?
More specifically, if A is chosen to follow the direction of the time dimension, or, "be only in time" (I can't remember the proper wording; it's been a long time since I took linear algebra), then B will have a spatial component and temporal component, and vice versa.
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Here may be a clearer way to see my issue. Imagine a very simple universe where there only exists object A and an object B. They are on a collision course. Scientist A, (from another dimension) uses object A as a point of reference. But scientist B (from yet a different dimension than scientist A) uses object B as a reference. Each scientist is going to end up with a different description of this universe from using special relativity.
So what's your issue?
That each scientist is going to end up with a different description of this universe from using special relativity.
This really doesn’t need scientists from a different universe and it isn’t down to special relativity.
It was Galileo who first pointed out that if you were in a cabin on a ship you would not be able to tell if the ship was moving, or in which direction unless you had information from outside the room. He concluded that it was reasonable to consider two moving ships as one stationary and the other moving or vise versa and the laws of physics remain the same. For example, if a ship is moving and firing a cannon at a stationary ship, the trajectory of the cannon ball relative to the first ship is exactly the same if the first ship is stationary and the second moving. When we consider this scenario in space where there are no fixed references, it becomes more obvious. It is called Galilean Relativity. Einstein added the effects of the constancy of the speed of light and extended Galileo’s principle to Special Relativity.
I would like to know how the components of time vs space work in SR. It seems, from where I am at in my knowledge, that the temporal component and the spatial component can swap, aka fabric of spacetime. Sure that's fine if it gives us correct results for what we need to know now, but if it doesn't make sense objectively, then it is only a matter of time before SR/GR gives false answers and paradoxes, which it already has.
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Hi.
If both answers are correct, then doesn't that mean that 2 different universes can exist depending on which object you choose to be at rest?
Does there need to be two universes just because there's two different ways of describing it?
You can go outside and measure your bicycle and find it's 1 metre long.
I can go outside and measure your bicycle and find it's 39 inches long.
Presumably, you wouldn't have thought that there must be two different universes, one where the bicycle is 1 metre and the other where it is 39 inches. You'd probably be quite happy to accept that I was using inches and you were using metres, we were just using different measurements to describe the same physical thing.
However, if what you meant was that (for at least some things) there's no objective reality, then I'd agree with you.
None-the-less, at the moment (as described by Colin2B) you haven't really described a situation that required much more than simple Gallilean relativity and it might be best to just push complications from special relativity to one side for a moment. It's not important here.
More specifically, if A is chosen to follow the direction of the time dimension, or, "be only in time" (I can't remember the proper wording; it's been a long time since I took linear algebra)
I think this could be a problem or misunderstanding. You could choose to make object A stationary and that would make the spatial component of its 4-velocity 0. However 0 is something, it is a numerical value. The object still has an ordinary spatial velocity, it's just that the magnitude of that velocity is 0. I probably need to rephrase this - the object is always found somewhere in space it doesn't vanish and exist "only in time" or anything weird like that. The object is found at the same place in space at all times, it has 0 velocity which just means it's location doesn't change with time.
The spatial 3-velocity is (0, 0, 0) it is not ( n/a, n/a, n/a )
Best Wishes.
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Hi again.
I would like to know how the components of time vs space work in SR. It seems, from where I am at in my knowledge, that the temporal component and the spatial component can swap, aka fabric of spacetime.
It is a fascinating topic and I'm glad you're interested. I'm sure people can recommend references and texts. We might need a little more guidance as to what your current level of experience is. It doesn't matter, by the way, none of us were born knowing anything about SR. More-over, you're going to need to be the one giving me some good references in a few years, please.
Here's an example:
Pre-requisite: Someone who studied some Maths and Physics at school to about age 17. For example a United Kingdom AS level.
The resource: Freely available YT videos of lectures presented by Prof. Leonard Susskind of Stanford University.
Time required: There are many (I think 10) lectures although much more than just SR is covered. Each lecture is about 1.5 hours. You could sensibly skip some introductions (you won't care about essay deadlines etc.), however, realistically you should expect to watch several hours of lectures and give yourself some extra time to think through and try some problems yourself.
Alternatives include some good textbooks. Much faster alternatives include assorted "Pop Sci" videos which will race over the topics in under 20 minutes - but that's never going to offer the full understanding.
Anyway.... the main point is that I couldn't present SR any better than the existing texts and resources for the topic and I'm also fairly sure a forum is not ideal for the task. However, if there were some specific issues you wanted to discuss then I'm sure people on this forum will try and help.
Best Wishes.
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Hi.
If both answers are correct, then doesn't that mean that 2 different universes can exist depending on which object you choose to be at rest?
Does there need to be two universes just because there's two different ways of describing it?
You can go outside and measure your bicycle and find it's 1 metre long.
I can go outside and measure your bicycle and find it's 39 inches long.
Presumably, you wouldn't have thought that there must be two different universes, one where the bicycle is 1 metre and the other where it is 39 inches. You'd probably be quite happy to accept that I was using inches and you were using metres, we were just using different measurements to describe the same physical thing.
However, if what you meant was that (for at least some things) there's no objective reality, then I'd agree with you.
None-the-less, at the moment (as described by Colin2B) you haven't really described a situation that required much more than simple Gallilean relativity and it might be best to just push complications from special relativity to one side for a moment. It's not important here.
I think this is outside of the scope of Galilean relativity because nothing is actually moving in GR. GR implies a block universe.
So the idea of an object to be moving relative to another object doesn't really make any sense in a block universe.
I think this could be a problem or misunderstanding. You could choose to make object A stationary and that would make the spatial component of its 4-velocity 0. However 0 is something, it is a numerical value. The object still has an ordinary spatial velocity, it's just that the magnitude of that velocity is 0. I probably need to rephrase this - the object is always found somewhere in space it doesn't vanish and exist "only in time" or anything weird like that. The object is found at the same place in space at all times, it has 0 velocity which just means it's location doesn't change with time.
The spatial 3-velocity is (0, 0, 0) it is not ( n/a, n/a, n/a )
Best Wishes.
Yes, I certainly agree. I tried to explain that I forgot the proper term of a vector that is only in a specific R. Sorry for the confusion.
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Hi again,
I think this is outside of the scope of Galilean relativity because nothing is actually moving in GR. GR implies a block universe.
I'm easily confused. GR is usually an abbreviation of "General Relativity" but I'm going to assume you are using it as an abbreviation of Galilean Relativity.
I'm not really sure that Galilean Relativity does fully demand the idea of a block universe. I think we usually forumlate the notion of a block universe after we accept Special Relativity. However, the fine details about what a "block universe" means may not be all that important. Just simple Newtonian mechanics already suggests something we would call a "deterministic universe". This just means that, if Newtonian mechanics is correct, then you should be able to calculate where everything will be and how it is moving at any time in the future from knowledge about where it is and how it is moving now. Similarly, you should also be able to calculate where it was and how it was moving at any point in the past from knowledge about the present. Overall then, if you had knowledge about the present than it's just a matter of doing some calculations - there's nothing uncertain about the future or past, you would have full knowledge of that.
A deterministic universe doesn't necessarily mean that the future has already happened, just that that there's nothing especially uncertain or undetermined about it.
Special Relativity (SR) probably pushes the notion of a deterministic universe a bit further. One of the things a good text or lecture course about SR might discuss is the example of what is called the "Andromeda paradox" or Rietdijk–Putnam–Penrose argument ( https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument ). These sorts of topics are one of the ways in which you could build up to a more complete notion of a block universe. Specifically, where you could start to argue that all instants of time and space seem to need to exist. It's worth mentioning that although these things often have names like "paradox" it's just because Physicist's and Philosopher's have good publicity and media agents and they select the titles. They aren't usually impossible or logical paradoxes, it's just that it sounds more interesting to call it a "paradox" instead of "an intersting thing".
Additionally, it's not entirely fair to say that the idea of a "Block Universe" is an idea in Physics. It's an idea in Philosophy that is based on some ideas in Physics, although they often call it "Eternalism". Physics doesn't really care if you favour a Block universe or Presentism, it just offers some models and allows some predictions to be made. It's not offering any fundamental truth about how the universe really is, only a few models that seem to be useful. More to the point, you can easily reconcile Special Relativity with Presentism if you try. One option is to accept that when an object experiences an acceleration than the universe around them is changed.
(Please don't get too worried about ideas like a deterministic universe - there's loads of things in physics that can offset or alleviate any concerns, like Chaos theory and quantum uncertainty but that falls outside the scope of this thread).
So the idea of an object to be moving relative to another object doesn't really make any sense in a block universe.
Are you sure? Movement is described just as a rate of change of one thing (position) with respect to something else (time). So this is just a ratio of a small change in one variable to the corresponding small change in another variable. Just because we, human beings, tend to experience and think of time a certain way, doesn't necessarily grant it any special nature. It's just something, some variable, we can use to calculate rates of change with respect to. We could have some other variable like S - let's give it a silly name like "entropy of the universe" - and just calculate rates of change of position with respect to S.
Sometimes the thing we've chosen to calculate rates of change with respect to won't be all that useful. Older scientists probably did think that determining rates of change with respect to the visible width of the moon could be useful - I mean it's a perfectly good rate of change to determine. However, it just doesn't seem to be as useful for building mathematical models as determining rates of change of position with respect to something else.
Best Wishes.
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I think this is outside of the scope of Galilean relativity because nothing is actually moving in GR. GR implies a block universe.
So the idea of an object to be moving relative to another object doesn't really make any sense in a block universe.
I think @Eternal Student has answered this, but some personal views.
I tend to think of General Relativity (GR) as a chart such as used by a ship navigator. S/he can plot the ship’s current, past and future positions in both space and time, but it doesn’t imply that the ship still exists at all those positions. Alternatively you can think of your sat nav which shows your current position and past and future - compatible with a moving spotlight view of time.
Galilean Relativity is most definitely about movement and different views of that movement, but in no way does it imply different universes. If I’m watching a road race from one side of a road I might describe the competitors as moving left to right, whereas someone on the other side of the road would say right to left. One universe two viewpoints.
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Hi again,
I think this is outside of the scope of Galilean relativity because nothing is actually moving in GR. GR implies a block universe.
I'm easily confused. GR is usually an abbreviation of "General Relativity" but I'm going to assume you are using it as an abbreviation of Galilean Relativity.
I'm not really sure that Galilean Relativity does fully demand the idea of a block universe. I think we usually forumlate the notion of a block universe after we accept Special Relativity. However, the fine details about what a "block universe" means may not be all that important. Just simple Newtonian mechanics already suggests something we would call a "deterministic universe". This just means that, if Newtonian mechanics is correct, then you should be able to calculate where everything will be and how it is moving at any time in the future from knowledge about where it is and how it is moving now. Similarly, you should also be able to calculate where it was and how it was moving at any point in the past from knowledge about the present. Overall then, if you had knowledge about the present than it's just a matter of doing some calculations - there's nothing uncertain about the future or past, you would have full knowledge of that.
A deterministic universe doesn't necessarily mean that the future has already happened, just that that there's nothing especially uncertain or undetermined about it.
Special Relativity (SR) probably pushes the notion of a deterministic universe a bit further. One of the things a good text or lecture course about SR might discuss is the example of what is called the "Andromeda paradox" or Rietdijk–Putnam–Penrose argument ( https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument ). These sorts of topics are one of the ways in which you could build up to a more complete notion of a block universe. Specifically, where you could start to argue that all instants of time and space seem to need to exist. It's worth mentioning that although these things often have names like "paradox" it's just because Physicist's and Philosopher's have good publicity and media agents and they select the titles. They aren't usually impossible or logical paradoxes, it's just that it sounds more interesting to call it a "paradox" instead of "an intersting thing".
Additionally, it's not entirely fair to say that the idea of a "Block Universe" is an idea in Physics. It's an idea in Philosophy that is based on some ideas in Physics, although they often call it "Eternalism". Physics doesn't really care if you favour a Block universe or Presentism, it just offers some models and allows some predictions to be made. It's not offering any fundamental truth about how the universe really is, only a few models that seem to be useful. More to the point, you can easily reconcile Special Relativity with Presentism if you try. One option is to accept that when an object experiences an acceleration than the universe around them is changed.
(Please don't get too worried about ideas like a deterministic universe - there's loads of things in physics that can offset or alleviate any concerns, like Chaos theory and quantum uncertainty but that falls outside the scope of this thread).
Sorry, I should not have brought any of this up. It does not add much to my initial issue.
So the idea of an object to be moving relative to another object doesn't really make any sense in a block universe.
Are you sure? Movement is described just as a rate of change of one thing (position) with respect to something else (time). So this is just a ratio of a small change in one variable to the corresponding small change in another variable. Just because we, human beings, tend to experience and think of time a certain way, doesn't necessarily grant it any special nature. It's just something, some variable, we can use to calculate rates of change with respect to. We could have some other variable like S - let's give it a silly name like "entropy of the universe" - and just calculate rates of change of position with respect to S.
I am currently watching the videos that you posted from Leonard Susskind. Maybe this will help me.