Is Planck temperature really the highest temperature?Actually I was learning about Wien's displacement law. It states that λ T = 2.898 × 10 − 3 m KThis is actually a part of Planck's law where the Planck's constant originated.Now Planck's temperature is given as T p = h c 5 2 π G k b 2 = 1.416 × 10 32 KNow Planck's length is 1.616 × 10 − 35 mNow since the smallest possible wavelength is Planck's length, we can say wavelength of the electromagnetic radiation is Planck's length (Assume the energy doesn't create a black hole).Now according to Wien's displacement law, l p T = 2.898 × 10 − 3 m KNow solving this we get 1.79 × 10 32 K, which is higher than the actual Planck's temperature.Since this displacement law is completely derived from Planck's law, it bit frustrated me. I'm a bit confused. Is it the limit of the displacement law or my flaw?Please rectify this.(Sorry if I made any mistake. I'm new to this one. Please explain my mistake. I'm glad to hear that.)

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Is Planck temperature really the highest temperature?Actually I was learning about Wien&#039;s displacement law. It states that  λ  T  =  2.898  ×      10          −      3        m  KThis is actually a part of Planck&#039;s law where the Planck&#039;s constant originated.Now Planck&#039;s temperature is given as      T          p        =                    h                  c          5                            2        π        G                  k          b          2                      =  1.416  ×      10          32        KNow Planck&#039;s length is   1.616  ×      10          −      35        mNow since the smallest possible wavelength is Planck&#039;s length, we can say wavelength of the electromagnetic radiation is Planck&#039;s length (Assume the energy doesn&#039;t create a black hole).Now according to Wien&#039;s displacement law,      l    p    T  =  2.898  ×      10          −      3        m  KNow solving this we get   1.79  ×      10          32        K, which is higher than the actual Planck&#039;s temperature.Since this displacement law is completely derived from Planck&#039;s law, it bit frustrated me. I&#039;m a bit confused. Is it the limit of the displacement law or my flaw?Please rectify this.(Sorry if I made any mistake. I&#039;m new to this one. Please explain my mistake. I&#039;m glad to hear that.)

candydulce168nlid · Accepted Answer

When you derive a formula for some quantity, the result you get is often a product of powers of the parameters of the problem and fundamental constants of the theory and some real number that tends to be close to   1. For example, the Newtonian escape velocity is       2    G    m          /        r  ; the real factor there is       2    ≈  1There&#039;s a general expectation that quantities of interest in quantum gravity are likely to be products of powers of the fundamental constants   ℏ  ,  c  ,  G and some real factor close to   1. The actual factor, and the actual meaning of the quantities, depends on the theory.So maybe in the correct theory of quantum gravity, lengths/temperatures in the vicinity of the Planck length/temperature have some significance, but it probably won&#039;t be precisely the Planck length/temperature, and the significance probably won&#039;t be that it is the minimum length / maximum temperature.You got a value close to the Planck temperature from the Planck length and Wien&#039;s constant because they&#039;re all equal to products of fundamental constants times a unitless factor close to   1, but the value you got is a bit different because the unitless factors aren&#039;t quite the same. The Planck length isn&#039;t the smallest possible wavelength (probably).

Is Planck temperature really the highest temperature? Actually I was learning about Wien's displac

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