/sci/ - Science & Math

[Anonymous No.4999194]

I have a nice conceptual puzzle to test your understanding of relativity:

Suppose (as is the case) that you lived in a universe where all dynamical laws were invariant with respect to Lorentz transformations. Would it be possible for the principle of relativity not to hold? Justify your answer.

Think carefully. I'm curious how many people will get it.

[Anonymous No.4999212]

Formulate the principle of relativity and what distinguishes it from all laws being Lorentz invariant.

Also, douchbag answer:
Sure, if there are no laws or if "spacetime" is zero dimensional.

[Anonymous No.4999225]

>>4999212
Principle of relativity: the laws of physics assume the same for in all frames of reference moving at constant velocity relative to one another.

You're given the equations of all dynamical laws as they appear in one particular reference frame, and you're told that they are all invariant with respect to the Lorentz transformaiton. Does the principle of relativity necessarily hold or not?

[Anonymous No.4999234]

>>4999225
What is "all dynamical laws"?
Give a list.

[Anonymous No.4999240]

>>4999234
QED, for example.

[Anonymous No.4999241]

>>4999240
What the fuck? You didn't prove anything.

[Anonymous No.4999242]

>>4999194
>the laws of physics assume the same for in all frames of reference moving at constant velocity relative to one another.
>all dynamical laws were invariant with respect to Lorentz transformations
This is literally the exact same statement.

[Anonymous No.4999244]

>>4999241
notsureiftrolling.jpg

[Anonymous No.4999248]

>>4999242
Is it? What if the coordinate transformation between reference frames was given by the Galilean transformation? Then the principle of relativity wouldn't hold.

[Anonymous No.4999246]

>>4999240
>asked to give a list
>gives only one example

Obviously logic isn't your strong suit.

[earl hickey No.4999250]

I have learned of vast new depths to my ignorance upon wikipedia-ing "lorentz transformation" but seeing as the theoretical universe is invariant I'd say yes, relativity may not hold. Relativity is but a theory...

[Anonymous No.4999251]

>>4999246
I'm not giving a list because a list is irrelevant to the question. You're not told what the laws are, only that they're all Lorentz invariant. Any other detail doesn't matter. I gave QED as an example in case you weren't sure what I meant by 'dynamical laws'.

[Anonymous No.4999254]

>>4999248
Wait, no.
If they laws are Galilean invariant (which they must be, if they are Lorentz invariant) relativity still holds.
Relativity still holds under Galilean transformation, i don't understand where you get the idea it wouldn't.

[Anonymous No.4999255]

>Suppose (as is the case) that you lived in a universe where all dynamical laws were invariant with respect to Lorentz transformations

I thought that was the principle of relativity.

[Anonymous No.4999261]

>>4999194

i haven't developed the formalism of 4-vectors and 4-tensors yet, so bugger off.


there was no reason to rub my nose in it

[Anonymous No.4999263]

>>4999254
Is it impossible that coordinate transformation between reference frames is given by the Galilean transformation, but that dynamical laws are invariant with respect to Lorentz transformation, not the Galilean transformation?

[Anonymous No.4999266]

>>4999254
>If they laws are Galilean invariant (which they must be, if they are Lorentz invariant)
Wat. No, this isn't true. Maxwell's equations are Lorentz invariant, but not Galileo invariant.

[Anonymous No.4999269]

Give a mathematical formulation of the problem. It is phrased way too vaguely.

[Anonymous No.4999287]

im not going to write out a proof, but invariant with respect to Lorentz transformations does imply that the principle of relativity holds. its the same thing. that's how QFTs are made to abide by relativity, you just make sure the Lagrangian is invariant under Lorentz transformations.

actually there is no proof, since the definition of relativity is that laws are invariant in frames connected by a Lorentz transformations.

the only way it cant be is if you are meaning this to be some trick question where "relativity" does not mean special relativity.

[Anonymous No.4999291]

>>4999248
see
>>4999287

[Anonymous No.4999299]

So basically what OP asked is trivially true by definition?

shitty troll is shitty

Well actually it doesn't surprise me. This guy with his Chomsky pictures has annoyed me more than once with inane shitposting.

[Anonymous No.4999300]

>>4999194
Well, yes. If the correct coordination transform between the frames of reference isn't the Lorentzian one.

But it would signify some conserved quantity.

[Anonymous No.4999311]

>>4999300
>coordination
coordinate

[Anonymous No.4999319]

>>4999287
No, you are wrong. By that reasoning, principle of relativity doesn't hold in GTR, as frames aren't connected by Lorentz transform there.

Principle of relativity states only that all physical laws are independent of frames of reference. Nothing more. Lorentzian transformation is separate postulate in STR.

[Anonymous No.4999330]

>>4999300
> If the correct coordination transform between the frames of reference isn't the Lorentzian one.
Surprisingly, this isn't possible. If all dynamical laws are Lorentz invariant, then it necessarily follows that the coordinate transformations are the Lorentz transformations. Coordinate transformations are not independent of dynamical laws. Kinda cool, no?

I was hoping someone would answer like you did, so I can show off something I learned today, but unfortunately everyone else got sidetracked...

[Anonymous No.4999338]

>>4999330
>kinda cool

No, kinda trivial. You're an edgy undergrad retard.

[Anonymous No.4999342]

>>4999338
>trivial
So prove it.

[Anonymous No.4999345]

>>4999330
Yeah, thinking about it, it's quite obvious. The only reasonable way to define frames of reference are so that the physical laws are independent of them.

So, even if some funny maths is going on behind it (which I doubt) this must be the final result.

[Anonymous No.4999351]

>>4999342
Why should I? I did it once and I won't bother doing it again. That shit is freshman undergrad physics.

[Anonymous No.4999457]

>>4999319
yes, you can have some forms of relativity that don't use Lorentz transformations, but Lorentz transformations imply SR, because SR is built on it. in GR becasue then you are adding another condition that must be satisfied (which is why its called equivalence, not relativity), so until OP defines relativity this is all meaningless. supersymetry can be seen as a form of relativity too in that case.

[Anonymous No.4999590]

>>4999457
Brush up on relativity bro. Postulates of Lorentz transform and principle of relativity are completely separate in SR.

[Anonymous No.4999611]

>>4999590
OK, the relativity principle and postulate of speed of light, from which the Lorentz transform follows are separate.

[Anonymous No.4999628]

>>4999590
>>4999590
if its completely separate, how does Lorentz invariance grantee the principle of relativity?

[Anonymous No.4999677]

>>4999628
You don't understand what principle of relativity means. Lorentz invariance guarantees that laws are equivalent in all reference frames *that are connected with lorentz transform*.

You have to have principle of relativity AND some other postulate to get that correct coordinate transform is the Lorentz one.

Principle of relativity has broader meaning and its statement is unchanged between SR and GR.

[complainer !!bieENIgma64 No.4999716]

>>4999194
>Would it be possible for the principle of relativity not to hold?
If particles could travel backwards in time... Then the principle would not hold.

[Anonymous No.4999751]

>>4999677
in that case, no. Lorentz invariance does not guarantee relativity, you can always add another type of reference frame that is arbitrary in which relativity does not hold. relativity then doesn't even hold in our universe.

[Anonymous No.5000114]

ITT: physicsfags think they know math

[Anonymous No.5000157]

Suppose poop is stinky (the stinky poop principle). Would it be possible for the poop principle not to hold? What if the poop principle were the tasty poop principle?

[Anonymous No.5000262]

All classical and relativistically invariant physical laws known to humanity are generated from a Lorentz scalar produced from the action functional.

In quantum the same is true but now you have an integral over a time sliced action functional <span class="math">\mathrm{exp}(iS)[/spoiler], the path integral.

Special relativity only deals with a Minkowski spacetime. GR deals with any spacetime that is a solution of the field equations (Minkowski is a vacuum solution thereof). This is equivalent, still, to encoding the metric of whatever solution you have in terms of a Poincare group connection.

The Poincare group is the group of all isometries of spacetime which hold the laws of physics the same in every frame. The principle of relativity is defined such that all physical laws are required to be invariant with respect to the action of the Poincare group on spacetime. There is no difference.

If you can create a list of laws which are Lorentz invariant, the principle of relativity will always hold. The action functional still produces a Lorentz scalar regardless of if you are using general or special relativity.

[Anonymous No.5002433]

OP you have delicious chomsky pics

[Anonymous No.5002500]

>>5000157
the well known "Durian World" hypothesis