If we stick to situations where special relativity is applicable, then we have no way to directly measure difference between time passed on earth and on spaceship, as their clocks can be synchronized only once (when they are in the same place). Thus it has no meaning to question where time goes slower.
What they will see is different question. When spaceship goes away from earth astronauts will see that processes on earth take longer than usual (simply from Doppler’s effect with relativistic corrections), and so do earthlings. When spaceship goes toward earth, astronauts see that processes on earth go faster than usual.
The person in the space ship will experience time twice as slow as people on earth. So the person in the spaceship would expect people on earth to age twice as quickly.
I targeted this part of your reasoning. Time on spaceship is moving slower (in a sense) than time on earth in reference frame where earth is stationary, yes, but it doesn’t follow that time on earth therefore moves faster than time on spaceship in reference frame of spaceship, quite opposite.
t'=\gamma(t-vx/c^2)
It is both valid when t is measured in reference frame of spaceship and in reference frame of earth.
Thus time in reference frame of muon is moving slower relative to our reference frame and time in our reference frame is moving slower relative to muon’s reference frame.
They decay in different places then where they’re created. If you look at it from different points of reference, it would change.
If you take the spacetime interval, which is invariant under Lorentz transformation, you’d find that the “time” they take isn’t affected by speed.
If SR hadn’t been discovered, I’d have just skipped that step. SR as it’s believed to work is impossible if subjective experience is all-or-nothing, so the belief that it exists that way is evidence that subjective experience is a sliding scale. That said, I don’t consider it a particularly convincing part of the argument.
This isn’t stuff I just memorized. I know why it’s true. I know how to derive it from first principles. In fact, I have.
I’ve seen multiple sources talking about it. I’ve read about the experiments proving it from multiple sources.
Physics is the same in all reference frames. Light travels at a constant speed relative to any reference frame. Everyone knows this. I’ve never seen it disputed in any good source.
My confidence level is well over 99.9%, at least. Being wrong about this means either I have false memories, or consistent fiction is being spread on a massive scale.
Ok if you are interested I will walk through your calculation to prove:
“If you’re moving away from Earth at 87% of the speed of light, time dilation would make it look like time on Earth is passing half as fast. From your point of reference, everyone will live twice as long.”
Hopefully by the end one of us sees a flaw in our reasoning and/or wording.
Imagine you’re moving directly away from the Earth at sqrt(3)/2 c. From your point of reference, it’s moving away from you. Someone on Earth has a set of mirrors with a photon bouncing between them. The mirrors are perpendicular to your path, so there’s no length contraction. (That part can be proven separately, if you wish.) For simplicity, let’s assume the mirrors are a meter apart.
From your point of reference, the x component of the velocity of the photon is sqrt(3)/2c. The total speed is c.
v_total^2 = v_x^2 + v_y^2
c^2 = [sqrt(3)/2 c]^2 + v_y^2
v_y^2 = c^2 − 3⁄4 c^2
v_y^2 = 1⁄4 c^2
v_y = 1⁄2 c
Since the y component of the velocity is half the speed of light, the clock will only run at half speed from your point of reference. It will run at full speed from the point of reference of someone standing right next to it, so from your point of reference, they’re moving at half speed.
Separate thread. Wikipedia often does not do a great job on this type of topic for some reason. Example:
The standard textbook approach treats the twin paradox as a straightforward application of special relativity. Here the Earth and the ship are not in a symmetrical relationship: the ship has a turnaround in which it undergoes non-inertial motion, while the Earth has no such turnaround. Since there is no symmetry, it is not paradoxical if one twin is younger than the other. Nevertheless it is still useful to show that special relativity is self-consistent, and how the calculation is done from the standpoint of the traveling twin.
The argument completely neglect the initial acceleration of the ship and only considers the U-turn acceleration. The symmetry is broken with initial acceleration.
It doesn’t really start until after the initial acceleration.
Imagine that the ship just passed the Earth, rather than taking off from it. Everything would work out the same, but turning around is clearly the only break in symmetry.
No the symmetry breaking event would just be further back in time. Also you could not call it the twin paradox, because you would not be able to explain how one of the twins got into the moving reference frame with out accelerating.
It doesn’t matter how they accelerated before the experiment began, so long as their clocks are synchronized. If they’re in the same place, they can synchronize their clocks.
You seem to missing some key information like why the photon has an x and y velocity rather then just an x or a y.
I suggest that you start with the space time interval, since it is conserved over Lorentz transformation and solve for t1 where t1 is the time rest frame. (t1>t0) where t0 is the start of the experiment and t1 marks the end of the experiment.
It has to have an x and y velocity. It’s just that one of them can be zero. I calculated what they were, and neither was zero.
What do you mean by the start and end of the experiment? The moment the photon leaves one mirror, and the moment it gets to the other?
I’ll let t = t1 - t0, x = x1 - x0, and y = y1 - y0, where (x0, y0, t0) marks the start of the experiment and (x1, y1, t1) marks then end. You can’t give just the time due to the relativity of simultaneity.
The spacetime interval is zero (it always is with light). So that’s sqrt(x^2 + y^2 - t^2) = 0. Setting y to one and solving for x, you get x = sqrt(t^2 − 1). Solving for t = 2, you get x = sqrt(3). This means that, from the point of reference where the light is moving up one meter and horizontally sqrt(3), it takes two meters per c, as opposed to one in the planet’s frame. The photon is moving horizontally at the same rate as the planet. Thus, if the planet moves sqrt(3) meters horizontally between the light moving from one mirror to the other, everything takes twice as long as if it doesn’t move at all.
I have downvoted this, and all comments by both parties in the remainder of this conversation between
Davorak and DanielLC. I would prefer to see fewer comments like these. Furthermore, you both seem to be incapable of resolving the disagreement, which requires actually understanding what the other guy is trying to say. And failing that, you seem incapable of ending the dispute which requires actually understanding that what you are doing is not working.
Even if one part has a good idea what the problem in communication is does not mean that that party automatically knows how to solve the problem or know weather or not they can solve it. The only way to find out sometimes is to try and see.
Reading your comment I get the impression you think the conversation was a hostile one. I did not have any hostile feels or thoughts taking part in that conversation. I did not get the impression that any were direct at me either.
Also it was in a discussion that was already hidden from the main discussion page so I had the impression that it would not bother the general population. Am I incorrect? Were these comments thrust on the general population in the recent posts section? I did not think of that possibility if that was the case.
Resolving technical issues can take a long time on a message board. So can getting to the point where you understand that you will not be able to find common ground. Discouraging these types of conversations in my opinion will also discourage technical conversations in the long run. I will have less incentive to try and explain complex issues that I am well versed or learn complex issues from another if long conversations where both parties are making an effort(apparently at least) to communicate.
Here is my attempt to end or drastically change the nature of the conversation. This was the point where I could not see the conversation being productive any longer without a drastic change. I guess you think that where I drew the line was different enough from where I should have that it ended up being damaging?
Even if one party has a good idea what the problem in communication is does not mean that that party automatically knows how to solve the problem or know whether or not they can solve it. The only way to find out sometimes is to try and see.
Too true.
Reading your comment I get the impression you think the conversation was a hostile one.
No, I didn’t think you two were hostile. (If anyone showed hostility here it was me. :( Sorry about that.)
I had the impression that it would not bother the general population. Am I incorrect? Were these comments thrust on the general population in the recent posts section?
No, only in the Recent Comments list. Nevertheless, we do try to maintain standards here using the karma system. In my opinion (and please note—this is only one opinion) your debate went on too long. I probably over-reacted—in part because the topic was special relativity and I have witnessed far too many fruitless online debates on the subject.
I hope my assholery doesn’t drive you away. And your response to my bad manners earned my upvote.
in part because the topic was special relativity and I have witnessed far too many fruitless online debates on the subject.
Too true. I am still getting grips on what the community is like.
My hope for the conversation was that the technical part of the problem would get solved and then we could have a juicy conversation on why one person or the other had map that mismatched the territory.
You may have over reacted, everyone does and then you did a good job recovering which is usually the most important part.
If we stick to situations where special relativity is applicable, then we have no way to directly measure difference between time passed on earth and on spaceship, as their clocks can be synchronized only once (when they are in the same place). Thus it has no meaning to question where time goes slower.
What they will see is different question. When spaceship goes away from earth astronauts will see that processes on earth take longer than usual (simply from Doppler’s effect with relativistic corrections), and so do earthlings. When spaceship goes toward earth, astronauts see that processes on earth go faster than usual.
Edit: Sorry for very tangential post.
Are you saying your argument is true with the strict application of only SR or that in is true in reality?
I would say it can not be true in reality because muons and other particles take a measurably longer amount of time to decay as their speed increases.
I targeted this part of your reasoning. Time on spaceship is moving slower (in a sense) than time on earth in reference frame where earth is stationary, yes, but it doesn’t follow that time on earth therefore moves faster than time on spaceship in reference frame of spaceship, quite opposite.
It is both valid when t is measured in reference frame of spaceship and in reference frame of earth.
Thus time in reference frame of muon is moving slower relative to our reference frame and time in our reference frame is moving slower relative to muon’s reference frame.
They decay in different places then where they’re created. If you look at it from different points of reference, it would change.
If you take the spacetime interval, which is invariant under Lorentz transformation, you’d find that the “time” they take isn’t affected by speed.
If SR hadn’t been discovered, I’d have just skipped that step. SR as it’s believed to work is impossible if subjective experience is all-or-nothing, so the belief that it exists that way is evidence that subjective experience is a sliding scale. That said, I don’t consider it a particularly convincing part of the argument.
This comment and your other comment do not demonstrate your knowledge of SR to me.
What is your confidence level that you are correct in your previous statements?
This isn’t stuff I just memorized. I know why it’s true. I know how to derive it from first principles. In fact, I have.
I’ve seen multiple sources talking about it. I’ve read about the experiments proving it from multiple sources.
Physics is the same in all reference frames. Light travels at a constant speed relative to any reference frame. Everyone knows this. I’ve never seen it disputed in any good source.
My confidence level is well over 99.9%, at least. Being wrong about this means either I have false memories, or consistent fiction is being spread on a massive scale.
Ok if you are interested I will walk through your calculation to prove:
“If you’re moving away from Earth at 87% of the speed of light, time dilation would make it look like time on Earth is passing half as fast. From your point of reference, everyone will live twice as long.”
Hopefully by the end one of us sees a flaw in our reasoning and/or wording.
You may be interested in the twin paradox.
Imagine you’re moving directly away from the Earth at sqrt(3)/2 c. From your point of reference, it’s moving away from you. Someone on Earth has a set of mirrors with a photon bouncing between them. The mirrors are perpendicular to your path, so there’s no length contraction. (That part can be proven separately, if you wish.) For simplicity, let’s assume the mirrors are a meter apart.
From your point of reference, the x component of the velocity of the photon is sqrt(3)/2c. The total speed is c.
v_total^2 = v_x^2 + v_y^2
c^2 = [sqrt(3)/2 c]^2 + v_y^2
v_y^2 = c^2 − 3⁄4 c^2
v_y^2 = 1⁄4 c^2
v_y = 1⁄2 c
Since the y component of the velocity is half the speed of light, the clock will only run at half speed from your point of reference. It will run at full speed from the point of reference of someone standing right next to it, so from your point of reference, they’re moving at half speed.
Separate thread. Wikipedia often does not do a great job on this type of topic for some reason. Example:
The argument completely neglect the initial acceleration of the ship and only considers the U-turn acceleration. The symmetry is broken with initial acceleration.
It doesn’t really start until after the initial acceleration.
Imagine that the ship just passed the Earth, rather than taking off from it. Everything would work out the same, but turning around is clearly the only break in symmetry.
No the symmetry breaking event would just be further back in time. Also you could not call it the twin paradox, because you would not be able to explain how one of the twins got into the moving reference frame with out accelerating.
It doesn’t matter how they accelerated before the experiment began, so long as their clocks are synchronized. If they’re in the same place, they can synchronize their clocks.
You seem to missing some key information like why the photon has an x and y velocity rather then just an x or a y.
I suggest that you start with the space time interval, since it is conserved over Lorentz transformation and solve for t1 where t1 is the time rest frame. (t1>t0) where t0 is the start of the experiment and t1 marks the end of the experiment.
It has to have an x and y velocity. It’s just that one of them can be zero. I calculated what they were, and neither was zero.
What do you mean by the start and end of the experiment? The moment the photon leaves one mirror, and the moment it gets to the other?
I’ll let t = t1 - t0, x = x1 - x0, and y = y1 - y0, where (x0, y0, t0) marks the start of the experiment and (x1, y1, t1) marks then end. You can’t give just the time due to the relativity of simultaneity.
The spacetime interval is zero (it always is with light). So that’s sqrt(x^2 + y^2 - t^2) = 0. Setting y to one and solving for x, you get x = sqrt(t^2 − 1). Solving for t = 2, you get x = sqrt(3). This means that, from the point of reference where the light is moving up one meter and horizontally sqrt(3), it takes two meters per c, as opposed to one in the planet’s frame. The photon is moving horizontally at the same rate as the planet. Thus, if the planet moves sqrt(3) meters horizontally between the light moving from one mirror to the other, everything takes twice as long as if it doesn’t move at all.
You are going to have to set up your problem more rigorously and clear if we are to continue this conversation.
edit: typo
The light is staying between the mirrors, which means it’s moving diagonally, which means it will take longer.
Where in that are you getting lost?
I have downvoted this, and all comments by both parties in the remainder of this conversation between Davorak and DanielLC. I would prefer to see fewer comments like these. Furthermore, you both seem to be incapable of resolving the disagreement, which requires actually understanding what the other guy is trying to say. And failing that, you seem incapable of ending the dispute which requires actually understanding that what you are doing is not working.
Even if one part has a good idea what the problem in communication is does not mean that that party automatically knows how to solve the problem or know weather or not they can solve it. The only way to find out sometimes is to try and see.
Reading your comment I get the impression you think the conversation was a hostile one. I did not have any hostile feels or thoughts taking part in that conversation. I did not get the impression that any were direct at me either.
Also it was in a discussion that was already hidden from the main discussion page so I had the impression that it would not bother the general population. Am I incorrect? Were these comments thrust on the general population in the recent posts section? I did not think of that possibility if that was the case.
Resolving technical issues can take a long time on a message board. So can getting to the point where you understand that you will not be able to find common ground. Discouraging these types of conversations in my opinion will also discourage technical conversations in the long run. I will have less incentive to try and explain complex issues that I am well versed or learn complex issues from another if long conversations where both parties are making an effort(apparently at least) to communicate.
Here is my attempt to end or drastically change the nature of the conversation. This was the point where I could not see the conversation being productive any longer without a drastic change. I guess you think that where I drew the line was different enough from where I should have that it ended up being damaging?
Too true.
No, I didn’t think you two were hostile. (If anyone showed hostility here it was me. :( Sorry about that.)
No, only in the Recent Comments list. Nevertheless, we do try to maintain standards here using the karma system. In my opinion (and please note—this is only one opinion) your debate went on too long. I probably over-reacted—in part because the topic was special relativity and I have witnessed far too many fruitless online debates on the subject.
I hope my assholery doesn’t drive you away. And your response to my bad manners earned my upvote.
Too true. I am still getting grips on what the community is like.
My hope for the conversation was that the technical part of the problem would get solved and then we could have a juicy conversation on why one person or the other had map that mismatched the territory.
You may have over reacted, everyone does and then you did a good job recovering which is usually the most important part.