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2h
comment Can we physically “time travel” to the future?
@Jim: This will be my last comment. I suggest you review your own word usage of "silly". I merely suggested you were being unimaginative, with no superlative descriptions in the sentence you described. I had been treating you with respect, and I do not see how terms like "unimaginative simpletons", "true genius" etc coming from. To be honest I suspect if any "professional physicist" would use such a language. To point out your error more precisely, imagine an infinite string of events $A_{n}$ at time $T=\frac{1}{n}$. If you start with $T=0$, which event will you consider as the 'first' event?
8h
comment Can we physically “time travel” to the future?
@Jim: Of course I did. I hope you realize that $\sum \frac{1}{n^2}<\infty$. From the $A_{-10^{10}}$th to $A_{0}$, there is a total time gap of $T<\frac{\pi^{2}}{6}$ available. No "first traveler" is needed, and your whole argument of "first traveler" is absurd. I will continue my challenge to ask you find a real logical inconsistency not considered by me so far. But maybe it is time for me to stop arguing with you for your clear lack of imagination.
1d
comment Can we physically “time travel” to the future?
@Jim: So so far, all your arguments has been focused on this or that way my argument is wrong, even though it got rejected every time. Can you come up with something more original yourself to show time travel is impossible? There must be something else being wrong as well, if this is physically inviable.
1d
comment Can we physically “time travel” to the future?
@Jim: No, I do not think it would violate it, as I suggested, $A$ could take place for $C$ which time travel forward as well.
1d
comment Can we physically “time travel” to the future?
@Jim: I do not think you need to have a first traveller to exist at all. Let the time interval to be $\frac{1}{n^{2}}$ apart from each other, then you can extend infinitely back without reaching the origin of the universe, if arbitrarily small time interval is realistic. I hope you realize that "silly" and "logically inconsistent" are two different terms.
1d
comment Can we physically “time travel” to the future?
@JerrySchirmer: $B$'s physical properties are the same as $A$ in $T_2$. But at $T=T_2+S$ its property would have changed, say due to some external force. Then when $A$ appears and its physical property is exactly what we recorded at $T_2$, we can tell the difference between $A, B$. It is not clear to me if $A, B$'s coexistence would violate conservation of energy, since $A$'s appearance would be fill in $C$'s disappearance at time $T_2+S$. But to avoid this inconvenience maybe it is better to assume they did not coexist throughout the experiment.
1d
comment Can we physically “time travel” to the future?
@Jim: So, here is one way to detect if object $A$ has underwent a time travel forward process. At time $T=T_{2}$, suppose we have recorded $A$'s attributes by certain data. At time $T=T_{2}+S$, $A$ is going to reappear somewhere with identical physical properties. Then we have an object $B$, which has replaced $A$ since $T_{2}$, hence underwent time $S$ by the observer. Assuming $B$ did not disappear at $T_{2}+S$, then we can experimentally determine the difference between $A,B$ since $B$ has underwent $S$.
1d
comment Can we physically “time travel” to the future?
@Jim: Also, discard an idea not by its logical correctness but by "silly" is strange to me. My idea may be absurd, but I do not see how it related to such strange term. You suggested that I am effectively arguing for special relativity -did you want me to suggest this is "silly" to me as well because you did not read my question carefully? I do not think this helps in the discussion at all.
1d
comment Can we physically “time travel” to the future?
@Jim: I think you mistunderstood what I wrote again. The difference is in different pattern at a micro-level such that all its attributes like momentum, energy, etc in any local frame is preserved. But the difference is detectable via experiment on a large scale. I do not think this violates anything. Also, I think you did not think far enough -if $A$ can be replaced by $B$, $B$ can be replaced by $C$, etc, then the whole string of objects may form an physical indistinguishable continuum to the observer. Then the fact that we did not notice it would be it has been going on all the time.
1d
comment Can we physically “time travel” to the future?
@Jim: There is no "real case" here. I am proposing a theoretical question and concerned about its theoretical via ability. There must be some reason what I am concerning is not true, because it sounds ridiculous to me as well. So I am willing to be persuaded.
1d
comment Can we physically “time travel” to the future?
@Jim: No, I do not believe so. The self-similarity in randomization could exist at a micro-level which showed all statistical physical properties are the same, but experiments will be able to tell them apart due to the difference in inner structure. I do not think conservation law is powerful enough to rule out this case.
1d
comment Can we physically “time travel” to the future?
@JerrySchirmer: I did come here to hear arguments on physical principles, I am looking for an argument to show time travel forward is impossible. But you cannot show me why this is not true. First you miscomprehend the question and tried to force me to use special relativity, then you argue on conservation laws which can be preserved by an infinite sequence. Neither is persuasive to me.
1d
comment Can we physically “time travel” to the future?
@Jim: This is not true. The object's last observation by $A$ is at $T_{2}$, not at $T_{1}$. The object might underwent whatever physical process during the $[T_{1},T_{2}]$ interval, but it cannot travel by special relativity because during $T_{2}$ and $T_{2}+S$ all its physical properties are the same.
1d
comment Can we physically “time travel” to the future?
@JerrySchirmer: Why? You gave me an argument I already considered when I proposed the question, and you threatened to vote to close it. I do not understand.
1d
comment Lebesgue integration
@user5462: I would encourage you to learn it any way, it is abstract but is useful for many purposes. Once you know real analysis and functional analysis well, you are prepared to study more advanced mathematical physics, which often involve a fair amount of PDE.
1d
comment Can we physically “time travel” to the future?
@Kyle: So, I am looking for some principle more powerful than symmetry which forbids time travel forward. It is mathematically simple - we shift the time for $A_{1},A_{2}\cdots $, etc such that each one takes in place of the previous one. But I want to know why this is impossible.
1d
comment Can we physically “time travel” to the future?
@Kyle: But I think the point is, self similarity could exert in every local volume, and the two objects still may not be identical. If the self similarity is under Plank scale, then all symmetry will be preserved, but a carefully designed experiment might still tell $A,B$ apart.
1d
comment Lebesgue integration
I think this is a good question, but might be more suitable for math.stackexchange.
1d
comment Can we physically “time travel” to the future?
@Kyle: This could be accounted for if $A$ and $B$ are different objects with random homogeneous composition. Then at any microsopic level they are self-similar and as a result the basic physic properties (energy, momentum, charge, etc) are the same. But because the pattern of randomization is different, $A,B$ are different objects. So we can distinguish them apart.
1d
comment Can we physically “time travel” to the future?
@JerrySchirmer: But this might be accounted for, if there are other object $B$ being transported in the same fashion and "filled in" the gap left by the disappearance of object $A$. Then overall energy, momentum, charge, etc will still be conserved.