Question

What am I doing wrong while proving time dilation using Minkowski space-time diagram?

Answer 1

Hello mate here is your answer.

So, just to clarify your approach:

You take events A and C occurring at the same location x′a=x′cxa′=xc′ but different times t′ata′ and t′ctc′ in the primed frame. You also take event B occurring at the same time as A in the primed frame, t′b=t′atb′=ta′, but at the same location as C in the unprimed frame, xb=xcxb=xc. For events B and C you then apply the invariance of the space-time interval

c2(tb−tc)2−(xb−xc)2=c2(t′b−t′c)2−(x′b−x′c)2c2(tb−tc)2−(xb−xc)2=c2(tb′−tc′)2−(xb′−xc′)2

and in view of xb=xcxb=xc, t′c=t′atc′=ta′, obtain

c2(tb−tc)2=c2(t′a−t′c)2−(x′b−x′c)2c2(Δt)2=c2(Δτ)2−(Δx′)2c2(tb−tc)2=c2(ta′−tc′)2−(xb′−xc′)2c2(Δt)2=c2(Δτ)2−(Δx′)2

Lastly, the Lorentz transform of Δx′=x′b−x′cΔx′=xb′−xc′ gives Δx′=γ(xb−vtb)−γ(xc−vtc)≡γvΔtΔx′=γ(xb−vtb)−γ(xc−vtc)≡γvΔt, and you conclude, correctly, that cΔt=cΔτ/γcΔt=cΔτ/γ.

Your "problem" is that regardless of the substitution t′c=t′atc′=ta′ your final relation still gives (tb−tc)=γ(t′b−t′c)(tb−tc)=γ(tb′−tc′). Let's tally up what we have:
If we use events B and C in the unprimed frame, but A and C in the primed frame, we find that. The time interval between events B and C occurring at the same location in the unprimed frame appears time dilated wrt the time interval between event C and an event A occurring in the primed frame at the same location as C but at the same time as B.The last piece of information, "occurring in the primed frame at the same time as B", is the crucial one: we can replace event A with any other event, at any location, as long as it "occurs in the primed frame at the same time as B".Otherwise, if we dispense with event A and simply refer to events B and C only, we just find that.The time interval (tb−tc)(tb−tc)between two events B and C occurring at the same location in the unprimed frame appears time dilated in the primed frame.

Hope it helps you.

Answer 2

Explanation:

Explanation:

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TIME DILATION

according to theory of relativity there is a postulate used that nothing can travel higher than the speed of light

means

more than

299792458m/s

and our universe is limited at this speed so if any object will travel at the speed of light then the physical forces stop that.

means any object can travel 99.99% of speed of light but not 100%.

so

if any object goes near the speed of light then the time dilation occurs in order to maintain the physical laws and a limited speed of universe.

here

in pic

the formula of time dilation is given.

Travelling into the future is a real thing.

lets take an example

1 second for us is not the same as 1 second for a person is in space

Essentially time flows slower from someone with respect to someone else.

The technical term for this is *Time Dilation*

In simple words, it means Slowing Down of Time

So there are two ways in which time can slow down.

• Relativistic Time Dilation (Special Relativity)

• Gravitational Time Dilation (General Relativity)

Relativistic Time Dilation

This concept came out when Albert Einstein published his Special Theory of Relativity in 1905.

What it says is that time flows slower for anything is moving faster or closer with speed of light

Let's scale this up to what we call Relativistic Speeds

Gravitational Time Dilation

This concept came around when Albert Einstein published the General Theory of Relativity in 1915.

The concept is that presence of a Gravitational Field slows down Time.

The stronger the gravity, the more is the time dilation.